Subject Index

When the page number of an index entry refers to a definition, then the page number is in italics. When the index entry appears in a footnote, then the letter “n” is appended to the page number. A page range for a topic indicates that either the topic is discussed in the given page range or that each page in the range mentions the topic.

0 A admissible order, 200 0-balanced quadtree, 405, 407, 814 A-series paper, 783 AESA, 599, 601, 643–650, 650n, 691, 862 A-tree, 283n, 573 incremental nearest neighbor query, ∗ 1 A -algorithm, 347, 493, 535 645–646 1-2 brother tree, 280n AABB. See axis-aligned bounding box k nearest neighbor query, 645–646 1-balanced quadtree, 405, 407 (AABB) range query, 644–645 1-irregular quadtree, 405 ABOVE field search hierarchy, 645, 650 1DSEARCH, 16 edge record in layered dag, 252 aggregation 1nf. See first normal form (1nf) access structure, xv, 165, 195 explicit. See explicit representation active border, 469 implicit. See implicit representation 2 active rectangle 2-3 tree, 65, 442, 718, 722 aging, 46, 46 multidimensional measure problem, 449 2-3-4 tree, 442, 722, 722 AHC. See Adaptive Hierarchical Coding plane-sweep method, 429 2-d Fibonacci condition, 223, 223, 225, (AHC) AdaBoost machine learning technique, 687 782–783 ALGOL, xx, 743 Adaptive Hierarchical Coding (AHC), 71, 2-d range tree. See also two-dimensional ALGOL W, xx, 743 221, 222, 782 range tree alignment problem, 403, 403, 405–408 adaptive hierarchical triangulation (AHT), all closest pairs query, 485 2DSEARCH, 17 401–402, 401, 407 2nf. See second normal form (2nf) all nearest neighbor join (ANN join), 486n, adaptive k-d tree, 58–59, 61, 69–71, 73–74, 490 3 129–130, 186, 189–190, 460, 620, all nearest neighbors problem, 76, 485 (3,0)-AVD, 367, 582, 584–585, 584, 853 763, 775–776 α-balanced region, 64 3nf. See third normal form (3nf) regions, 224 amortization cost analysis, 143, 731 adaptive quadtree, 475 angle property, 348, 348–349 4 adaptive uniform grid, 10n animation, 423 4-adjacent adaptively sampled distance field (ADF), ANNBFTRAV, 558 blocks, 217n 362–365, 363, 373, 803 ANNBFTRAVFARTHEST, 565, 850 locations (pixels), 200n approximation error, 363–365 ANNFNDFTRAV, 564, 849 4-shape, 230 absolute, 364 ANNFNDFTRAVFARTHEST, 565, 851 adaptive, 364 ANNINCFARTHEST, 565, 851 7 relative, 364 ANNINCNEAREST, 559 7-shape, 231 skeleton of object, 364–365 ANNOPTBFTRAV, 560 address of a cell in space, 192, 195 8 ANNOPTBFTRAVFARTHEST, 565, 851 8-adjacent ADF. See adaptively sampled distance field ANNOPTDFTRAV, 564, 849 blocks, 217n (ADF) ANNOPTDFTRAVFARTHEST, 565, 851 locations (pixels), 200n ADJ, 218 approximate farthest neighbor query, 563 adjacency graph, 424 absolute error bound, 563 9 adjacency matrix, 317 relative error bound, 563 9-shape, 230 adjacency number of a tiling, 198 approximate k nearest neighbor finding ADJQUAD, 754 best-first algorithm

969 approximate k nearest neighbor axis-aligned bounding box (AABB), 195 outer box. See outer box in balanced finding (continued) axis-parallel polygon, 195, 409, 409n box-decomposition tree (BBD-tree) best-first algorithm (continued) partitioning box. See partitioning box in general, 557–559 B balanced box-decomposition tree MAXNEARESTDIST, 560 B-partition, 111 (BBD-tree) equivalence relation, 490, 557, 651–652 regular. See regular B-partition shrink operation. See shrink operation in fuzzy logic. See fuzzy logic B-rectangle, 111 balanced box-decomposition tree locality sensitive hashing (LSH). See B-region, 111 (BBD-tree) locality sensitive hashing (LSH) B-tree, xviii, 8, 62, 93, 97–98, 98n, 106, split operation. See split operation in SASH (Spatial Approximation Sample 114–116, 136–137, 140, 163, 183, balanced box-decomposition tree Hierarchy). See SASH (Spatial 187, 189, 255–256, 277, 279, 282– (BBD-tree) Approximation Sample Hierarchy) 283, 285–286, 289, 294, 298–299, trial midpoint split operation. See trial approximate k-center, 623 305–308, 310–311, 442, 479, 663, midpoint split operation in balanced approximate k-nearest neighbor finding 670, 717–727, 718, 769, 772, 791, box-decomposition tree (BBD-tree) equivalence relation, 656 815, 872–873 balanced four-dimensional k-d tree, 461, approximate nearest neighbor query, balanced. See balanced B-tree 482 61, 557–565, 848–852. See also biased. See biased B-tree four-dimensional representative point ε-nearest neighbor deletion, 720–722, 726–727, 873 rectangle representation, 460–462, incremental algorithm, 559–560 rotation, 720 826–827 k nearest. See approximate k nearest insertion, 719–720, 722, 726 point query, 462 neighbor finding bottom-up, 726 rectangle intersection problem, 460–462 minimum-ambiguity k-d tree. See rotation, 719, 726. See also deferred space requirements, 477–478 minimum-ambiguity k-d tree splitting window query, 462, 477–478 probably approximately correct (PAC). top-down, 727 balanced quadtree, 405 See probably approximately correct order, 718 balancing (PAC) nearest neighbor query search, 719, 722, 727, 873 weight balancing. See weight balancing vp-tree. See vp-tree space requirements, 722 ball partitioning, 598, 598, 604–613, 46 storage utilization, 724–725 approximate splitting, + 855–856 Approximate SVD transform matrix, 674, B -tree, 97–98, 98n, 100, 103, 166–167, balltree, 567, 622 674–675 171, 183, 216, 255, 279, 366, 411– band, 385, 385 approximate Voronoi diagram (AVD), xxii, 415, 510, 587–588, 725–726, 725, BANG file, 82, 107n, 114–118, 125, 129, 367, 486, 580–585, 580, 853 815 167, 171, 256, 479, 581 (3,0). See (3,0)-AVD deletion, 727, 873 exact match query, 114–115, 479 (t,ε) See (t,ε) order, 279 . -AVD + two-dimensional representative point Approximating and Eliminating Search prefix. See prefix B -tree rectangle representation, 464 Algorithm (AESA). See AESA search, 727, 873 BAR tree. See balanced aspect ratio tree arc tree, 383, 383, 386, 812 back-to-front algorithm (painter’s (BAR tree) area-area intersection, 386 algorithm), 236, 787 base prototypes, 623 curve-curve intersection, 386 balanced aspect ratio tree (BAR tree), batched dynamic data structures, 429 architecture, 425 64–65, 64, 70, 764 BBD-tree. See balanced box-decomposition area-based rectangle representations, α-balanced. See α-balanced region tree (BBD-tree) 466–483, 827–833 aspect ratio. See aspect ratio of region BD-tree, 74n, 79–83, 87, 107n, 115–116, arrangement, 824 canonical cut. See canonical cut 115n, 169, 171, 182, 190, 581, 767, array pyramid, 266–270, 267, 790 canonical region. See canonical region 776 irregular grid. See irregular grid array fat region. See fat region exact match query, 82, 87 pyramid k-cut. See k-cut partial range query, 82, 87 aspect ratio of region, 64, 70, 580 k-cuttable. See k-cuttable range query, 82 atomic tile, 197 one-cut. See one-cut BELOW field ATree, 220, 220, 222, 233, 782 reduction factor. See reduction factor edge record in layered dag, 252 attribute, 1n skinny region. See skinny region best-first incremental nearest neighbor augmented Gabriel graph (AGG), 642–643, balanced B-tree, 164 query. See incremental nearest 642, 860–862 balanced binary search tree, 14, 18–19, 430, neighbor finding nearest neighbor query, 643 433, 440–441, 445, 718, 821–822 best-first k nearest neighbor query. See k augmented gh-tree, 621 balanced box-decomposition tree (BBD- nearest neighbor finding Authalic coordinates, 232 tree), 64, 74n, 82–87, 83, 581, 584, Bezier´ methods, 620 AVL tree, 7, 65–66, 82, 164, 718 767 BFTRAV, 549 axes, 467 centroid shrink operation. See centroid BFTRAVFARTHEST, 553, 847 axial array, 11, 136 shrink operation in balanced biased B-tree, 8 axial directory, 11 box-decomposition tree (BBD-tree) bicubic Bernstein-Bezier´ surface, 402 axis, 1n inner box. See inner box in balanced bidistance function, 640 axis capacity, 476 box-decomposition tree (BBD-tree) big O, xx axis lines, 467 BIGMIN, 92

970 BIN field bitmap representation, 5–6, 9, 13 BSP tree. See Binary Space Partitioning cnode record in MX-CIF quadtree, 470 compressed. See compressed bitmap tree (BSP tree) bin method, 434, 443 representation BSPR. See Binary Searchable Polygonal rectangle intersection problem, 443 bk-tree, 610, 610–612 Representation (BSPR) binary heap, 20n BLACK value bucket, 3, 12 Binary Line Generalization Tree (BLG- NODETYPE field data. See data bucket tree), 384, 384, 386 node record in MX quadtree for points, overflow. See overflow bucket binary quadtree, 211 41 point. See point bucket binary search tree, 164, 187 node record in PR quadtree, 46 primary. See primary bucket analogy in deletion in point k-d tree. See BLG-tree. See Binary Line Generalization region. See region bucket point k-d tree Tree (BLG-tree) bucket adaptive k-d tree, 61, 62 analogy in deletion in point quadtree. See BLISS, 744 bucket address, 729n point quadtree block, 193 bucket capacity, 45, 75, 375 deletion, 31, 52 black, 206 bucket generalized k-d trie, 74, 97, 110–111 Binary Searchable Polygonal white, 206 bucket generalized pseudo k-d tree, 61, Representation (BSPR), 384, block-nested loop 61–64, 68, 98, 102–103, 116 384 skyline query. See skyline query bucket merging compound section. See compound bnode record EXCELL. See EXCELL section MX-CIF quadtree, 470 grid file. See grid file simple section. See simple section Boolean query, 3 bucket methods, 95–164, 95, 170–171, Binary Space Partitioning tree (BSP tree), BoostMap, 686–687, 686, 700 183–184, 768–775 xxiii, 66–68, 66, 70, 88, 224, 224, Borsuk-Ulam Theorem, 88n grid directory. See grid directory methods 233–237, 260, 269, 450, 464n, bottom-up region quadtree construction. storage utilization, 163–164 573–576, 620, 787 See region quadtree tree directory. See tree directory methods autopartitions, 234 boundary face, 336 bucket PM quadtree, xxiii, 374, 374 multi-object. See multi-object BSP tree boundary model, 313–346, 374, 794–799 bucket PM1 quadtree, 374, 375–376 visibility number, 236 Boolean set operations, 372 bucket PM2 quadtree, 374, 375–376, 809 visibility problem, 233–234 unambiguous. See unambiguous bucket PM3 quadtree, 374 binary tree boundary model bucket PMR k-d tree, 82 extended. See extended binary tree Boundary Representation (BRep). See bucket PMR quadtree, 97 BINCOMPARE, 470–471, 828 boundary model bucket polygon quadtree, 260, 261–262 binomial heap, 20n boundary-based object representation, 192, vertex. See vertex bucket polygon bintree, 49, 160, 162, 221–223, 221, 226– 312–408, 794–803, 805–814 quadtree 227, 233, 256, 260, 305–306, 372, image-based, 355–382, 803, 805–811 bucket PR k-d tree, xxiii, 74, 75, 82, 97, 409, 411n, 782 object-based, 382–399, 812–813 110, 116, 160, 164, 171 generalized. See generalized bintree surface-based, 399–408, 814 bucket PR octree MX. See MX bintree bounded embedding space, 3 triangulation, 241 PR. See PR bintree bounded quadtree (BQT), 476, 482 bucket PR quadtree, xxiii, 45–46, 45, 61, restricted. See restricted bintree space requirements, 477–478 97, 164, 169–170, 182, 187, 581 bintree bounding-box cell-tree pyramid, window query, 477–478 bucket PR-CIF k-d tree, 476–478, 476, 306 bounded-index extendible hashing, 730 482–483 bioinformatics database, xvi, 164, 609, 692 bounding box, 195 construction cost, 482 biquadratic patches, 373 ellipse. See ellipse bounding box deletion, 480 bisector tree, 599, 617–622, 617, 856–857 bounding-box cell-tree pyramid, 305, 305, insertion, 480 eccentric child, 618 310–311 one-dimensional. See one-dimensional gh-tree bintree. See bintree bounding-box bucket PR-CIF k-d tree range query, 618 cell-tree pyramid space requirements, 477–478, 482 bit concatenation, 90, 94, 142, 159, 716, generalized k-d tree. See generalized k-d two-dimensional. See two-dimensional 871 tree bounding-box cell-tree pyramid bucket PR-CIF k-d tree range query, 91 point quadtree. See point quadtree window query, 477–478, 480 reversed. See reversed bit concatenation bounding-box cell-tree pyramid bucket pseudo quadtree, 62–63 bit interleaving, 90, 93–95, 97, 142, 159, bounding-box pyramid, 310–311 bucket rectangle PM quadtree, xxiii, 477, 172, 199, 215, 410, 716, 731, 737, irregular grid. See irregular grid 481, 481–483 871 bounding-box pyramid space requirements, 481 Gray code, 93–95 bounds array, 57, 461 window query, 481–482 partial range query, 93–95, 768 BOXTREE, 398 bucket rectangle quadtree, 481. See also range query, 91, 93 Boyce-Codd normal form, 329 bucket rectangle PM quadtree B-tree, 92, 95, 768 branch and bound neighbor finding strategy, buddy page, 113, 113 binary search tree, 91–92, 95 489, 517, 554 buddy system, 731 reversed. See reversed bit interleaving BRep. See boundary model buddy-tree, 97, 110, 112–113, 116 bit manipulation, 245 bs-tree. See bisector tree range query, 116 buffer, 402

971 buffer tree, 299–301, 794 cell-based decomposition. See image-based CLIPLINES, 804 bulk insertion decomposition clipping, 366 grid file. See grid file cell-based query. See location-based query clique, 622 object-tree pyramid. See object-tree cell-tree pyramid, 267–269, 267, 305 close-reinsert, 290 pyramid bintree bounding-box. See bintree closest pairs. See all closest pairs query R-tree. See object-tree pyramid bounding-box cell-tree pyramid cluster, 598 bulk loading, 165 bounding-box. See bounding-box cluster center, 598 grid file. See grid file cell-tree pyramid cluster detection, 62, 269 object-tree pyramid. See object-tree generalized k-d tree bounding-box. See cluster preservation ratio (CPR), 696 pyramid generalized k-d tree bounding-box clustering-based distance-based indexing R-tree. See object-tree pyramid cell-tree pyramid methods, 598–599, 625 BV-tree, 12, 82, 97, 107n, 116–129, 141n, point quadtree bounding-box. See point CMAT. See corner medial axis 167, 187, 770–773 quadtree bounding-box cell-tree transformation (CMAT) construction, 120–122, 770–771 pyramid cnode record deletion, 122, 771 CENTER field MX-CIF quadtree, 470 directory node, 117 square record in PM quadtree, 367 code, 90 exact match query, 122–125, 771–772 centroid shrink operation in balanced box- collapsing point page, 117 decomposition tree (BBD-tree), MX quadtree. See MX quadtree space requirements, 125–127, 772 84 MX-CIF quadtree. See MX-CIF quadtree CF, 319 PR quadtree. See PR quadtree C CFFCCW, 321 collision detection, xix, 392–393, 398, 567 C field CFFCCW field collision set rectangle record in MX-CIF quadtree, edge-edge record in oriented winged- locality sensitive hashing (LSH). See 470 edge data structure, 326 locality sensitive hashing (LSH) C programming language, xx, 743, 745 CFFCW, 321 color table, 411, 415, 814 C++, xx, 743 CFFCW field column order, 200, 278 CAD. See computer-aided design (CAD) edge-edge record in oriented winged- combined index, 5–6, 5 Caltech Intermediate Form (CIF) quadtree, edge data structure, 326 partial range query, 6, 13, 747 466 chain, 243 common partition elimination, 228 canonical cut, 64, 70 chain code, xxii, 313, 416–417, 816–817 compact, 315n canonical region, 64 chain tree, 243 compaction methods Cantor-diagonal order, 199–202, 199, CHAINID field difference-based. See difference-based 776–778 TYPE field value gap compaction methods Cartesian tree, 19n, 27, 27, 438, 751 ldnode record in layered dag, 252 companion half-edge, 328 CCF, 319 Chamfer metric, 210, 210, 779 companion transition, 331 CCFFCCW, 321 change-based runlength encoding, 409, complete containment rule, 261, 261n CCFFCCW field 414, 416 complete quadtree, 402, 424 edge-edge record in oriented winged- Chessboard metric, 779 complete sector tree, 380 edge data structure, 326 CHILD field complete t-ary tree, 30n CCFFCW, 321 bnode record in MX-CIF quadtree, 470 component CCFFCW field cnode record in MX-CIF quadtree, 470 eight-connected. See eight-connected edge-edge record in oriented winged- node record in MX quadtree for points, component edge data structure, 326 41 four-connected. See four-connected CCQUAD, 35 node record in PM quadtree, 367 component CCV, 319 node record in point k-d tree, 52 COMPRESS, 784 CCVVEND, 321 node record in point quadtree, 30 compressed bitmap representation, 6,9 CCVVEND field node record in PR quadtree, 46 Compressed DFT. See Compressed Discrete edge-edge record in oriented winged- CHILDTYPE function Fourier Transform (CDFT) edge data structure, 326 point k-d tree, 52 Compressed Discrete Fourier Transform CCVVSTART, 321 point quadtree, 31 (CDFT), 680–681, 680, 683–684 CCVVSTART field CHOOSECHILD, 180 compressed quadtree, 410, 581 edge-edge record in oriented winged- CIF. See Caltech Intermediate Form (CIF) COMPRESSTREE, 784 edge data structure, 326 quadtree computational geometry, xv, xix, xxii, 427 CCW, 319 CIFCOMPARE, 827 computer graphics, xv–xvi, xviii–xix, xxii CDT. See convex difference tree (CDT) CIFDELETE, 830 computer vision, xv–xvii, xx, xxii, 425 cell, 449 CIFINSERT, 829 computer-aided design (CAD), xv, xvii, 260 address. See address of a cell in space CIFSEARCH, 828 COND, 744 black, 202 circle property, 347, 347–348, 351 condensing point, 514 location. See location of a cell in space City Block distance, 32. See also Manhattan cone tree, 380–382, 380, 811 white, 202 distance Boolean set operations, 381 cell pyramid, 266, 266–267, 272, 304 City Block metric, 779 contact point. See contact point cell tree, 312 clevel, 118 rotation, 381

972 scaling, 381 corner* lath data structure, 342 data mining, 164 translation, 381 correctness criterion, 498, 520 data organization methods, 3, 28, 49, 77, conflation problem, 486 corridor, 402 95, 184–185, 188, 190, 455 CONFLICT, 237 cost-based unbalanced R-tree (CUR-tree), data-dependent strategy conforming Delaunay triangulation, 351, 302 LSD tree. See LSD tree 351 COUNTCHILDS, 176 database, xxii conforming mesh, 401, 403, 405–406 cover fieldtree, 257–259, 257, 475, 480. bioinformatics. See bioinformatics conjugation tree, 88–89, 88, 767–768 See also loose quadtree database connected component labeling, 200n coverage, 274 constraint. See constraint database connected objects, 191n coverage-based splitting, 255–260, 255, dynamic. See dynamic database connectivity table, 355, 355, 802 789 moving object. See moving object constrained Delaunay triangulation, 351, covers, 430 database 351, 394 CQUAD, 35 multimedia. See multimedia database constraint database, xix, 445 cracks, 402 spatial. See spatial database constructive solid geometry (CSG), 314, create, 743 spatiotemporal. See spatiotemporal 314, 372, 374, 393, 409, 417–418, CREATEPNODE, 756 database 453, 809 criterion 1 (one), 32 static. See static database contact point criterion 2 (two), 32 database management systems (DBMS), cone tree, 381 cross-hairs, 63 xv, xxii sector tree, 377 CROSSAXIS, 828 DBMS. See database management systems containment hierarchy, 117, 119 CSG. See constructive solid geometry (DBMS) level. See level (CSG) dC, 210, See also Chamfer metric containment query, 427, 444 CSG tree, 372 dead area, 274 one-dimensional. See one-dimensional well behaved, 372 decimation containment query cube, 232 surface. See surface simplification representative point rectangle cubetree, 297, 298 DECODE2DRE, 815 representation. See representative CUR-tree. See cost-based unbalanced DECODE2DRE2, 816 point rectangle representation R-tree (CUR-tree) decomposition two-dimensional interval tree. See curse of dimensionality, xvi–xvii, 486–489, image-based. See image-based two-dimensional interval tree 486, 561, 563, 592n, 663, 669 decomposition two-dimensional segment tree. See CV, 319 object-based. See object-based two-dimensional segment tree CVVEND, 321 decomposition containment set, 444 CVVEND field quaternary hierarchical triangular. See interval tree. See interval tree edge-edge record in oriented winged- quaternary hierarchical triangular priority search tree. See priority search edge data structure, 326 decomposition tree CVVSTART, 321 regular. See regular decomposition segment tree. See segment tree CVVSTART field ternary hierarchical triangular. See continuous multiresolution model, 399 edge-edge record in oriented winged- ternary hierarchical triangular contractive embedding, 664, See also edge data structure, 326 decomposition contractive mapping; pruning CW, 319 decomposition hierarchy, 117 property decoupling, 165–167, 165 contractive mapping, 664, See also D deferred splitting, 98, 98n, 283, 285, 289, contractive embedding; pruning D-CEL data structure, 323–324, 323, 329, 308, 719 property 343 Delaunay graph, 346–348, 352–353, 598, convex difference tree (CDT), 262–264, D-CEL-face. See D-CEL-face data 629, 629n, 630–633, 637–639, 641, 790 structure 858 convex hull, 195 D-CEL-face-vertex. See D-CEL-face- nearest neighbor query, 630, 650 convex polygon, 503 vertex data structure Las Vegas algorithm, 712 COORD field D-CEL-vertex. See D-CEL-vertex data Delaunay tetrahedralization, xxii, 352–353, node record in point k-d tree, 52 structure 352 coordinate, 1n D-CEL-face data structure, 324, 324, 343 Delaunay triangulation (DT), xxii, 241, corner lath data structure, 333, 335–346, D-CEL-face-vertex data structure, 324, 322, 347–354, 347, 367, 377, 400, 799 329, 796 402, 584, 629n, 631–632, 638–641, corner medial axis transformation (CMAT), D-CEL-vertex data structure, 324, 324, 343 640n, 643, 788, 799–802, 861–862 208, 210 D-Euclidean conforming. See conforming Delaunay corner stitching, 459–460, 459, 826 metric. See D-Euclidean metric triangulation point query, 460–461 D-Euclidean metric, 210 constrained. See constrained Delaunay solid tile. See solid tile d-heap, 20n triangulation space tile. See space tile D-tree, 68–69, 68, 224 nondegenerate. See nondegenerate window query, 460–461 data bucket, 103 Delaunay triangulation corner table, 354, 355 DATA field DEM. See Digital Elevation Model (DEM) corner transformation, 454, 670 edgelist record in PM quadtree, 368

973 density-based splitting, 255, 260–264, 790. sorted. See Sorted Discrete Fourier ldnode record in layered dag, 252 See also bucket methods Transform (SDFT) TYPE field value gap depth-first k nearest neighbors query. See k subtrail, 681 ldnode record in layered dag, 252 nearest neighbor finding trail, 681 DQP. See Dynamically Quantized Pyramid DEQUEUE, 518 unitary matrix, 680 (DQP) DF-expression, 410, 411, 414, 814 value, 683 DQS. See Dynamically Quantized Space DFT. See Discrete Fourier Transform variance. See Variance Discrete Fourier (DQS) (DFT) Transform (VDFT) DR-tree, 303 DFTRAV, 519 discrete multiresolution model, 399 DT. See Delaunay triangulation (DT) DFTRAVFARTHEST, 521, 836 discrete Voronoi diagram, 490 DTM. See Digital Terrain Model (DTM) DIAGONALNEIGHBOR, 781 discriminator zone expression (DZE), 80 dual contraction, 396 diameter of a point set, 699, 699, 867 disjoint object pyramid, 310–312, 310 dual graph, 322 DICTIONARY field disk-resident data, 2 dual mesh, 322 node record in PM quadtree, 367 distance dynamic database, 2 difference neighborhood graph (DNG), bidistance. See bidistance function dynamic hashing, 730, 730 642, 642, 860 edit. See edit distance dynamic interval tree, 438, 439, 821 difference-based compaction methods, Hamming. See Hamming edit distance rectangle intersection problem, 438 408–423, 814–819 Hausdorff. See Hausdorff distance spatial join query, 439, 821 Digital Elevation Model (DEM), 262, 400 Levenshtein. See Levenshtein edit dynamic multipaging, 136, 147n, 154, 159 digital geometry, xx distance dynamic p hashing, 151 digital searching, 2 multi. See multidistance function range query, 152 Digital Terrain Model (DTM), 262, 400 network, 487 dynamic programming, 136, 783 digital tree, 2 pseudo-Euclidean. See pseudo-Euclidean dynamic pseudo k-d tree Dijkstra’s shortest-path algorithm, 509, distance regions, 224 513–515 distance browsing, 491 dynamic storage allocation, 731 dimension, 1n distance field, 363 dynamic z hashing, 140, 150–152, 151, 774 dimension reduction methods, 662–685, distance join, 489 range query, 151–152 697, 709, 864–867 distance matrix methods, 598, 643–650, Dynamically Quantized Pyramid (DQP), Discrete Fourier Transform (DFT). See 862 62–64, 62, 186, 269 Discrete Fourier Transform (DFT) distance metric, 488 cross-hairs. See cross-hairs representative point, 670–671 distance scan, 491 space requirements, 64 Singular Value Decomposition (SVD). distance semijoin, 486, 490, 658 warping process. See warping process See Singular Value Decomposition distance-based indexing methods, 598–662, Dynamically Quantized Space (DQS), (SVD) 855–864 62–64, 62 using only one dimension, 668–670, 865 clustering-based. See clustering-based space requirements, 64 directed Hausdorff distance, 392n, 392n distance-based indexing methods directory hierarchy, 117 pivot-based. See pivot-based distance- E level. See level based indexing methods Earth, 231 directory merging distance-preserving embedding, 687–689 Earth’s curvature, 231 EXCELL. See EXCELL distortion, 687, 688 ECDF tree, 7, 13 grid file. See grid file distribution-dependent strategy range query, 14, 748 directory node LSD tree. See LSD tree ranking, 14, 748 BV-tree. See BV-tree divide-and-conquer methods, xvii, xxii space requirements, 14, 748 PK-tree. See PK-tree divided k-d tree, 65 edge directory page, 103 divided-leaf octal tree, 370 oriented. See oriented edge EDGE field external. See external directory page Dk, 518 internal. See internal directory page dlevel, 118 edge_orientation_pair record in Dirichlet domain. See Voronoi diagram dodecahedron, 232 ORIENTEDFACEEDGETABLE and DISC field dominance merge, 461 ORIENTEDVERTEXEDGETABLE, node record in point k-d tree, 52 dominance relation, 461, 503 326 disc property, 347, 347, 351, 640, 800 double balance, 753 TYPE field value edge Discrete Cosine Transform (DCT), 676 double Gray order, 94, 94, 199–202, 199, ldnode record in layered dag, 252 Discrete Fourier Transform (DFT), 216, 776–779 edge quadtree, 359–362, 360, 364–365, 803 676–685, 866–867 partial range query, 94–95, 768 edge record adjoint of a unitary matrix, 680 range query, 95 layered dag, 252 coefficients, 676 doubly chained tree (DCT), 6–8, 7 edge-based object representations using compressed. See Compressed Discrete exact match query, 7, 13, 747 winged-edges, 317–329, 345, Fourier Transform (CDFT) doubly linked list, 432 795–796 ith harmonic, 683 Douglas-Peucker line generalization edge-EXCELL, 365, 370 Parseval’s theorem. See Parseval’s algorithm, 383–384, 390, 393 edge-face relation, 316, 317 theorem DOWN field multiple shells and multiply connected TYPE field value edge faces, 317

974 edge-lath table, 332 ENCW(e) edge around a vertex, 319n explicit representation, 194 edge-loop relation, 317 ENCW(e) edge in a face, 319n explicit winged-edge data structure. See edge-ordered dynamic tree, 253 endif, 744 non-oriented winged-edge data edge-ordering property, 243 ENQUEUE, 518 structure edge-vertex relation, 317 envelope, 395 exponent of a floating-point number, 2 edgelist record EPCCW(e) edge around a vertex, 319n extended binary tree, 98, 98n, 102–103, PM quadtree, 368 EPCCW(e) edge in a face, 319n 105–106, 718n, 751, 872 edge_orientation_pair record EPCW(e) edge around a vertex, 319n extended neighborhood (EN), 638–639, 641 oriented winged-edge data structure, 326 EPCW(e) edge in a face, 319n extended octree, 370 edit distance, 488 EPICT. See efficient pixel interleaving extended pyramid technique, 589 Hamming. See Hamming edit distance compression technique extendible hashing, 46, 135, 140, 730 Levenshtein. See Levenshtein edit epsilon query, 664, See also range query bounded-index. See bounded-index distance ε-nearest neighbor, 580–581 extendible hashing efficient pixel interleaving compression equator, 231–232 Extensible and Flexible Library (XXL), 271 technique (EPICT), 215, 215, 219, equivalence relation extension parameters, 454, 455 781 approximate k nearest neighbor finding. extent-based object aggregation techniques, eight-connected, 200n See approximate k nearest neighbor 282–289, 791–792 eight-connected component, 200n finding external directory page, 103 eight-connected region. See eight-connected fuzzy logic. See fuzzy logic external methods in SP-GiST, 188 component error-bound method, 256, 257 external searching, 717 Elias algorithm, 593 Escher staircase, 218 EXTRACTEDGESINCIDENTATVERTEX, ellipse bounding box, 383 Euclidean distance, 55 795 else, 744 Euclidean embedding, 687 EXTRACTEDGESOFFACE, 322 elseif, 744 Euclidean matching problem, 190, 473, 776 EXTRACTORIENTEDEDGESINCIDENTAT- embedding, 687 Euler’s formula, 242, 789 VERTEX, 796 Euclidean. See Euclidean embedding exact match query, 3, 192, 428 EXTRACTORIENTEDEDGESOFFACE, 326 isometric. See isometric embedding BANG file. See BANG file Lipschitz. See Lipschitz embedding BD-tree. See BD-tree F embedding methods, 489, 515, 598, 601, doubly chained tree (DCT). See doubly face decimation, 395–399 612, 623, 647, 685–716, 867–871 chained tree (DCT) face octree, 361–362, 361, 365, 371, 803 distance-preserving. See distance- grid file. See grid file space requirements, 362, 373, 809 preserving embedding kB-tree. See kB-tree face simplification, 395 distortion. See distortion LSD tree. See LSD tree face-based object representations using Euclidean. See also Euclidean embedding multidimensional B-tree (MDBT). See laths, 330, 344 isometric. See isometric embedding multidimensional B-tree (MDBT) face-edge octree, 362, 362 Lipschitz. See Lipschitz embedding multidimensional extendible hashing space requirements, 362 proximity-preserving. See proximity- (MDEH). See multidimensional face-edge relation, 316, 317 preserving embedding extendible hashing (MDEH) multiple shells and multiply connected weakly proximity preserving. See weakly nested interpolation-based grid file faces, 317 proximity preserving embedding (NIBGF). See nested interpolation- face-edge table, 318 embedding space, 2 based grid file (NIBGF) face-lath table, 332 bounded. See bounded embedding space point k-d tree. See point k-d tree face-loop relation, 317 embedding space organization methods, 3, quintary tree. See quintary tree FACEEDGETABLE, 320 10, 28, 49, 77, 95, 184–185, 188, sequential list. See sequential list fair-split tree, 58–59, 186 190, 455, 489n Spatial Approximation tree (sa-tree). See false dismissal, 663 empirical cumulative distribution function Spatial Approximation tree (sa-tree) false hit, 273, 663 tree (ECDF tree). See ECDF tree EXCELL, xxii–xxiii, 46, 130–131, 135, far-reinsert, 290 EN. See extended neighborhood (EN) 137–140, 153n, 160–163, 186–189, farthest neighbor query, 667 ENCCW(e) edge around a vertex, 319n 370, 775–776 approximate. See approximate farthest ENCCW(e) edge in a face, 319n bucket merging, 140 neighbor query enclosure query, 427, 444 directory merging, 140 incremental algorithm. See incremental interval tree. See interval tree excluded middle vantage point forest, 612 farthest neighbor finding priority search tree. See priority search EXHASH, 137, 140, 163 k farthest. See k farthest neighbor finding tree expanded MX-CIF quadtree, 256, 481, 481, farthest-point clustering, 623 representative point rectangle 483 Fast Fourier Transform (FFT), 684, 867 representation. See representative construction cost, 481, 483 fast nearest-neighbor classifier, 486. See point rectangle representation rectangle intersection problem, 481, 483 also nearest neighbor query; nearest two-dimensional interval tree. See space requirements, 481, 483 object query two-dimensional interval tree window query, 483 FastMap, 686, 690, 695–711, 867–871 two-dimensional segment tree. See expansion index, 148 deriving first coordinate value, 699–700, two-dimensional segment tree explicit aggregation. See explicit 867–868 enclosure set. See containment set representation

975 FastMap (continued) FORMNODEFORMINENCLOSINGBLOCK- Generalized Search Tree (GiST), 189, 271, deriving remaining coordinate values, WITHKITEMS, 175 590 701–703, 868–869 four-connected, 200n geographic information system (GIS), xv, expansion of distances, 707–708, 707, four-connected component, 200n xix, xxii, 164 870–871 four-connected region. See four-connected geometree, 370 farthest pair of objects. See diameter of a component geometric join query, 428 point set four-dimensional representative point geometric modeling, xix heuristics for non-Euclidean metrics, rectangle representation, 460–463, Geometric Near-neighbor Access Tree 708–709 826–827 (GNAT), 529, 591–592, 616–617, pivot object selection, 698–699, 867 balanced four-dimensional k-d tree. See 622–624, 622n, 630, 646, 856 pivot objects, 697 balanced four-dimensional k-d tree Dirichlet domain, 617 projected distance, 700–701 grid file. See grid file incremental nearest neighbor query, 617 pruning property, 703–707, 869–870 k-d tree. See k-d tree range query, 617 spread between pivot objects, 698 LSD tree. See LSD tree split point, 616 fat region, 64, 580 fq-array. See fixed-queries array geometric probability, 369, 376 FCCW(e), 319 fq-tree. See fixed-queries tree geometric simplification. See surface FCW(e), 319 fractional cascading simplification feature detection, 425 point location query, 127, 251, 435n GETNETWORKDISTINTERVAL, 511 feature extraction, 425 dynamic, 253 GG. See Gabriel graph (GG) feature query, 191 front-to-back algorithm, 236, 787 gh-tree, xxiii, 599, 609, 616–619, 621–622, feature vector, 485 FRONTPRIORITYQUEUE, 501 630, 636n, 649 feature-based query, 192 fuzzy logic augmented. See augmented gh-tree Fibonacci heap, 20n approximate k nearest neighbor finding, incremental nearest neighbor query, Fibonacci number, 223, 767 651 614–616 field, 1n equivalence relation, 651 peer-to-peer (P2P), 614 fieldtree, 259 range query, 614, 616 cover. See cover fieldtree G search hierarchy, 614–615 partition. See partition fieldtree g-degrees rotated x-range, 64n, 195 GIS. See geographic information system file, 1 Gabriel graph (GG), 640, 640–643, (GIS) filial set, 7,8 860–862 GiST. See Generalized Search Tree (GiST) filter tree, 255, 255–256, 259 nearest neighbor query, 643 global, 743 filter-and-refine method, xvii, 663 game programming, xv, xvii, xix, xxii, 259 GNAT. See Geometric Near-neighbor nearest neighbor finding, 666 gap, 245 Access Tree (GNAT) filtering, 663 gap tree, 245, 245, 248–254, 788–789 GPU. See graphics processing unit (GPU) FINDCANDIDATE, 753 point location query, 246–248, 788–789 graph FINDCHILD, 175 GBI. See Generalized Bulk Insertion (GBI) object. See object graph FINDDMINIMUM, 53, 762 GBT. See generalized balanced ternary planar. See planar graph FINDFATHER, 763 (GBT) graph drawing, 64 findpath problem, 425 generalization, 383 graphical search-and-replace operation, 459 FINDY, 252 generalized balanced ternary (GBT), 231 graphics processing unit (GPU), xviii finite metric space, 598 Generalized BD-tree (GBD-tree), 82 Gray code, 93–95, 93n, 212 finite-element analysis, xv, 211, 425 generalized bintree, 71, 221, 222, 782 gray level, 424 first normal form (1nf), 317n Generalized Bulk Insertion (GBI), 297–298, gray node, 214 fixed-grid method, xxiii, 10–12, 14, 57, 66, 298 Gray order, 94, 94, 199–202, 199, 216, 91, 136, 186, 189, 776 window query, 298 776–779 fixed-height fixed-queries tree, 611–613, generalized hyperplane partitioning, 598, partial range query, 95, 768 611 598, 603, 613–624, 856–858 range query, 95 fixed-queries array, 601, 611, 612–613 generalized hyperplane tree. See gh-tree GRAY value fixed-queries tree, 601, 611, 612–613, 856 generalized k-d tree, 50 NODETYPE field FLEX, xx, 743 regions, 224–225, 305, 311 node record in MX quadtree for points, floating-point arithmetic, 197 generalized k-d tree bounding-box cell-tree 41 floating-point representation pyramid, 306, See also k-d-B-tree node record in PM quadtree, 367 exponent. See exponent of a floating-point for regions node record in PR quadtree, 46 generalized k-d trie, 71, 110, 112–113 number + greedy insertion technique, 393 mantissa. See mantissa of a floating-point generalized k -d tree, 98, 102–103, greedy set cover algorithm, 716 105–108, 108n, 110, 768–769 240 number + greedy triangulation, FNDFTRAV, 523 generalized k -d trie, 112n grid cell, 130 FNDFTRAVFARTHEST, 529, 839 generalized pseudo k-d tree, 58, 61, 70, grid directory, 12, 96, 130 foldover, 397 97–98, 103, 129, 186 grid file. See grid file forced reinsertion, 285, 289–290, 289, deletion, 65 grid directory methods, 130–163, 773–775 292n, 293–294, 300, 303 range query, 65 grid file, xxii–xxiii, 46, 110n, 115, 130– forest, 722n

976 137, 140, 146–148, 160, 162–163, separate chaining method. See separate Hilbert packed R-tree, 276, 276–278, 280– 186–189, 210, 594, 773, 776 chaining method 281, 280n, 294, 296–297, 301, bucket merging, 135 spiral. See spiral hashing 587 buddy system, 135 Hausdorff distance, 392, 392n, 488 Hilbert R-tree, 275n, 280, 280, 280n, 285 merging threshold, 135 directed. See directed Hausdorff distance Hilbert tree, 280n neighbor system, 135 hB-tree, 12, 82, 97, 106–110, 114, 116– hinted quadtree, 482–483 bulk insertion, 136 118, 125, 128–129, 167, 171, 187, construction cost, 482 bulk loading, 136 581, 768–769 hinted distance, 482 directory merging, 135 hB-tree, 108n, 108n, 109 owner pointer, 482 exact match query, 136 sibling pointer. See sibling pointer space requirements, 482 four-dimensional representative point heap, 20n, 187 window query, 483 rectangle representation, 462 binary. See binary heap hole, 200n grid directory, 131 binomial. See binomial heap holey brick tree (hB-tree). See hB-tree grid refinement, 134 d-heap. See d-heap homogeneous image, 423 linear scale. See linear scale Fibonacci. See Fibonacci heap homogeneous k-d tree, 58n multilayer. See multilayer grid file sequential. See sequential heap horizontal rectangle, 449 partial range query, 134, 136 HEAPMAX field Hough Transform, xxii, 62–63, 70 range query, 132, 136 node record in priority search tree, 21 HV/VH tree, 476, See also bucket PR-CIF rectangle intersection problem, 462 height-balanced binary search tree, 7–8, 66, k-d tree space requirements, 136 280n hybrid k-d trie, 74 two-level. See two-level grid file exact match query, 13, 747 hybrid tree, 101–102, 295, 465, 572–573, grid refinement hexagonal grid. See hexagonal tiling 585, 592, 610n grid file. See grid file hexagonal tiling, 197, 198, 205, 230–231 grid-partition index, 582 4-shape. See 4-shape I grouping process, 165 7-shape. See 7-shape icosahedron, 231 growth factor, 735 9-shape. See 9-shape IER nearest neighbor algorithm. See guard, 118 hexahedron, 232 Incremental Euclidean Restriction HICHILD field (IER) nearest neighbor algorithm H node record in point k-d tree, 52 if, 744 H-rectangle, 449 hidden-line elimination, 423 image, 196 h-refinement, 405 hidden-surface elimination, 234, 236, 423, homogeneous. See homogeneous image Haar Transform, 676 787 image processing, xv, xx, xxii, 423 HAL tree. See hierarchical approximation hierarchical approximation and localization image understanding, 424 and localization tree (HAL tree) tree (HAL tree), 389–391, 389, 813 image-based decomposition, 191 half-edge, 328 construction, 391, 813 image-based query. See location-based companion. See companion half-edge polysurface. See polysurface query half-edge data structure, 328, 331, 333, space requirements, 391, 813 image-space methods, 183, 191 343–345 hierarchical Delaunay triangulation (HDT), iMinMax method, 589–592, 589, 854 half-edge-face. See half-edge-face data 402, 402 window query, 591 structure hierarchical face clustering, 395–399, 395 implicit aggregation. See implicit half-edge-vertex. See half-edge-vertex circularity. See irregularity in hierarchical representation data structure face clustering implicit representation, 195 nonmanifold object, 316 irregularity. See irregularity in implicit winged-edge data structure. See half-edge lath data structure. See split-vertex hierarchical face clustering oriented winged-edge data structure lath data structure hierarchical probe model, 377 INCFARTHEST, 507, 835 half-edge-face data structure, 328, 329 hierarchical rectangular decomposition. See INCFARTHESTDUP, 507, 835 half-edge-vertex data structure, 328, 329, quaternary hierarchical rectangular inclusion set. See containment set 346, 796, 799 decomposition INCNEAREST, 494 half-quad data structure, 343 hierarchical space indexing method, 370 INCNEARESTDUP, 500 halfplanar range query, 88 hierarchical triangular decomposition INCNEARESTSPATIALNETWORK, 512 halfspace quaternary. See quaternary hierarchical Incremental Euclidean Restriction (IER) linear. See linear halfspace triangular decomposition nearest neighbor algorithm, 509, halting point, 429 ternary. See ternary hierarchical 514 Ham-Sandwich cut, 89, 768 triangular decomposition incremental farthest neighbor finding, 502 Ham-Sandwich Theorem, 88 hierarchy vp-tree. See vp-tree Ham-Sandwich tree, 88 ordinary. See ordinary hierarchy incremental nearest neighbor finding, Hamming edit distance, 488n, 603 reflection. See reflection hierarchy 490–517, 833–835 Hamming space, 712 rotation. See rotation hierarchy AESA. See AESA Hamming space mapping, 712 High variable duplicate object instances, 499–502, hashing, 466 layered dag, 252 834–835 linear. See linear hashing high-energy physics, 211 PM quadtree, 499 linear probing. See linear probing Hilbert B-tree, 280n PMR quadtree, 500

977 incremental nearest neighbor INSERTL, 519 ISAM. See indexed-sequential file finding (continued) INSERTNODE, 176 organization (ISAM) duplicate object instances (continued) INSERTQUADRANT, 35 isohedral tiling, 197 region quadtree, 499 instantiation methods, 170–171, 183–184 isolated vertex, 368 R+-tree, 499–500 integrated polytree, 371 isometric embedding, 688, See also general, 493–499, 833–834 interface parameters in SP-GiST, 188 distance-preserving embedding r-optimal. See r-optimal algorithm interior-based object representation, 192, ISPOINT, 180 space requirements, 495–496 193–312, 776–794 iterative end-point fit method. See Douglas- Geometric Near-neighbor Access arbitrary objects, 254–264, 789–790 Peucker line generalization Tree (GNAT). See Geometric blocks, 204–232, 778–787 algorithm Near-neighbor Access Tree (GNAT) hierarchical, 264–312, 790–794 gh-tree. See gh-tree disjoint object-based, 304–312, 794 J kNN graph. See kNN graph image-based, 266–270, 790 Java, xx, 743 LAESA. See LAESA object-based, 270–303, 790–794 Johnson-Lindenstrauss Lemma, 715, 871 M-tree. See M-tree nonorthogonal blocks, 232–254, 787–789 join maximum distance, 502, 507 unit-size cells, 194–204, 776–778 all nearest neighbor. See all nearest maximum result, 502, 507. See also k internal directory page, 103 neighbor join (ANN join) nearest neighbor finding intersection query, 427 distance. See distance join minimum distance, 502, 507 intersection vertex, 514 spatial. See spatial join query monotonous bisector tree (mb-tree). See INTERSECTLINESQUARE, 368 K monotonous bisector tree (mb-tree) interval tree, xxii–xxiii, 434–439, 445–447, k farthest neighbor finding mvp-tree. See mvp-tree 473–474, 820–823 depth-first algorithm R-tree. See R-tree containment set, 446 basic, 520–521, 836 search hierarchy, 492–493, 666–667, 833 definition as a Cartesian tree, 438 MINFARTHESTDIST, 548, 846 MX-CIF quadtree. See MX-CIF deletion, 437 pruning rules, 529, 839 quadtree dynamic. See dynamic interval tree k nearest neighbor finding R-tree. See R-tree enclosure query, 439, 820 AESA. See AESA Spatial Approximation tree (sa-tree). See insertion, 437 best-first algorithm, 502, 507 Spatial Approximation tree (sa-tree) one-dimensional containment query, basic, 548–550 spatial network, 508–516, 835 439, 820 MAXNEARESTDIST, 550–552 Incremental Euclidean Restriction primary structure. See primary structure space requirements, 548 (IER) nearest neighbor algorithm. rectangle intersection problem, 244n, depth-first algorithm, 517–557, 835–848 See Incremental Euclidean 434–439, 442, 460, 820–821 basic, 518–521, 835–836 Restriction (IER) nearest neighbor secondary structure. See secondary MAXNEARESTDIST, 538–548, algorithm structure 845–847 Incremental Network Expansion (INE) spatial join query, 439, 820 point k-d tree. See point k-d tree nearest neighbor algorithm. See stabbing counting query, 439, 820 pruning rules, 521–529, 836–840 Incremental Network Expansion stabbing query, 439, 820 space requirements, 548 (INE) nearest neighbor algorithm tertiary structure. See tertiary structure M-tree. See M-tree TLAESA. See TLAESA two-dimensional. See two-dimensional k-center, 623 vp-tree. See vp-tree interval tree approximate. See approximate k-center vpsb-tree. See vpsb-tree window query, 444 k-center problem, 623 Incremental Network Expansion (INE) inverse priority search tree, 190, 776, 821 k-cut, 65 nearest neighbor algorithm, intervals k-cuttable, 65, 70 513–514 one-dimensional containment query, k-d tree, xxii–xxiii, 11, 14, 37, 48–89, independent vertex, 238 443, 821 761–768. See also point k-d tree index, xv points, 23, 443 adaptive. See adaptive k-d tree indexed-sequential file organization inverted file, 5, 5, 37, 134 balanced four-dimensional. See balanced (ISAM), 717 partial range query, 136 four-dimensional k-d tree indirect uniform grid, 211 range query, 5, 136 bucket PR. See bucket PR k-d tree INE nearest neighbor algorithm. See inverted list, 5, 37, 65, 91, 186–187, 189, bucket PR-CIF. See bucket PR-CIF k-d Incremental Network Expansion 755, 776 tree (INE) nearest neighbor algorithm IQ-tree, 592, 595–597 exact match query, 51 influence set, 658 irregular cell-tree pyramid, 63 four-dimensional representative point inherent dimensionality, 488 irregular grid, 210–211, 210 rectangle representation, 462 initial network distance interval, 511 irregular grid array pyramid, 269 generalized. See generalized k-d tree inner approximation, 378 irregular grid bounding-box pyramid, 304, minimum-ambiguity. See minimum- inner box in balanced box-decomposition 304–305 ambiguity k-d tree tree (BBD-tree), 83 irregular grid pyramid, 269, 304 MX. See MX k-d tree INRANGE, 17 irregularity in hierarchical face clustering, MX-CIF. See MX-CIF k-d tree INSERTAXIS, 829 397 INSERTCHILDSOFNODE, 176

978 open-sliding midpoint. See open-sliding neighborhood of. See neighborhood of a lath data structure midpoint k-d tree K-vertex companion transition. See companion path-compressed PR. See path- Karhunen-Loeve` Transform (KLT), 591, transition compressed PR k-d tree 671–673, 685–686, 690, 697–698, corner lath data structure. See corner lath path-level compressed PR. See path-level 704, 710 data structure compressed PR k-d tree VA +-file. See VA +-file half-edge lath data structure. See peer-to-peer (P2P), 49 kB-tree, 6, 8–9, 66n split-vertex lath data structure PK PR. See PK PR k-d tree exact match query, 136 manifold objects, 331–336, 797 PMR. See PMR k-d tree partial range query, 9, 136 meshes with boundaries, 336–340, point. See point k-d tree range query, 136 797–799 PR. See PR k-d tree kB+-tree, 9 primitive transition. See primitive skip list. See skip list KD2-tree, 68, 68, 464n, 610n transition sliding-midpoint. See sliding-midpoint KD2B-tree, 68, 68 split-edge lath data structure. See k-d tree KDCOMPARE, 761 split-face lath data structure spatial. See spatial k-d tree KDDELETE, 762 split-face lath data structure. See superkey. See superkey KDDELETE1, 762 split-face lath data structure VAMSplit. See VAMSplit k-d tree KDINSERT, 761 split-vertex lath data structure. See k+-d tree key, 1n split-vertex lath data structure generalized . See generalized k+-d tree primary retrieval. See primary key layered dag, xxii, 69, 224, 248–254, 248, k-d trie, 49, 71, 110, 112n, 142 retrieval 347, 789 bucket generalized. See bucket secondary retrieval. See secondary key ldnode. See ldnode generalized k-d trie retrieval map overlay problem, 254, 789 generalized. See generalized k-d trie KFARTHEST, 521, 836 point location query, 250–254 hybrid. See hybrid k-d trie Klein bottle, 316, 353, 372n three-dimensional point location query, k-d-B-tree, 12, 93, 96–103, 106, 110, 112, KLT. See Karhunen-Loeve` Transform 254 112n, 114, 116, 127–130, 187, 295, (KLT) x-interval. See x-interval 768 KNEAREST, 519 layered tree, 823 point page, 98 kNN graph, 582, 599, 637–643, 637, 658, LAYEREDDAGPOINTLOCATION, 252 region page, 98 662, 859–862 ldnode record regions, 224, 306–311, 306 extended neighborhood (EN), 638 layered dag, 251 resplitting. See k-d-B-tree resplitting k nearest neighbor query, 641 LEAF value space requirements, 312, 794 best-first algorithm, 641 NODETYPE field k-d-B-tree resplitting, 309–310, 309 nearest neighbor query, 638–639, 714, node record in PM quadtree, 367 k-d-B-trie, 12, 110–116, 110, 129, 183–184, 716 least recently used (LRU) page replacement 187, 769–770 best-first algorithm, 639 policy, 723 point page, 110 incremental algorithm, 641 least square quadtree, 360 range query, 112 Monte Carlo algorithm, 711 LEFT field region page, 110 range query, 641 line record in PM quadtree, 367 k-deinstantiated node, 170 reverse. See reverse kNN graph node record in one-dimensional range k-DOP, 195 seed, 638 tree, 15 k-instantiable node. See k-instantiated node τ-closer, 638 node record in priority search tree, 21 k-instantiated node, 168–170 node record in two-dimensional range k-instantiation methods, 183 L tree, 16 k-instantiation value, 164 L field TYPE field value vertex k-mean, 623 rectangle record in MX-CIF quadtree, ldnode record in layered dag, 251 k-means problem, 533, 594 470 Lemma 2.1 of Feustel and Shapiro, 525 k-median problem, 623 LAESA, 599, 601, 623, 643, 646–650, Lemma 2.2 of Feustel and Shapiro, 528, K-structure, xxii, 69, 224, 237–242, 250, 650n, 862 See also Pruning Rule 2 for k = 1 347, 394, 787–788 incremental nearest neighbor query, 647 Lemma 4.1, 600 construction algorithm, 238–239 search hierarchy, 646, 650 Lemma 4.2, 601 dynamic edge insertion, 239 lambda problem. See range query Lemma 4.3, 602 independent vertex. See independent Lambert’s cylindrical projection, 232 Lemma 4.4, 603 vertex landmark, 515 LEN field K-vertex. See K-vertex Las Vegas randomized algorithm, 711 square record in PM quadtree, 367 map overlay problem, 242, 788–789 approximate k nearest neighbor finding level compression, 77, 169, 183 neighborhood of a K-vertex. See SASH (Spatial Approximation Sample level decompression, 79 neighborhood of a K-vertex Hierarchy), 712 Level of Detail (LOD) methods, xix, 391 point location query, 239–241 nearest neighbor query Levenshtein edit distance, 488n, 603 visible vertex. See visible vertex Delaunay graph, 712 lexicographic ordering, 200 K-vertex, 238, 241 LATERALNEIGHBOR, 218 LHRBC. See linear hashing with reversed independent. See independent vertex lath, 330 bit concatenation (LHRBC)

979 LHRBI. See linear hashing with reversed locality sensitive hashing (LSH), 490, 664, layered dag. See layered dag bit interleaving (LHRBI) 686 PM quadtree. See PM quadtree limited tiling, 197, 198 approximate k nearest neighbor finding, mapping. See embedding line intersection problem, 445 711–716, 871 mark, 430 line quadtree, 356–357, 356, 803 Monte Carlo randomized algorithm, MAT. See medial axis transformation revised. See revised line quadtree 713 (MAT); multiattribute tree line record collision set, 714 matrix manipulation PM quadtree, 367 localization, 389, 392 MX k-d tree. See MX k-d tree Linear Approximating and Eliminating location of a cell in space, 192, 195 MX quadtree. See MX quadtree Search Algorithm (LAESA). See location parameters, 454, 455 MAXDIST, 526 LAESA location query, 191 axis-aligned minimum bounding linear halfspace, 67n location-based query, 192 hyperrectangle, 840 linear hashing, xxii–xxiii, 130–131, 137, locational code, 72, 115, 166–167, 172, SR-tree, 840 140–146, 152, 157–163, 187–188, 183, 187, 214, 255–256, 479, 510, MAXDISTINTER, 840 735, 739, 773–775 587 MAXDISTOBJECT, 535 asymptotic analysis, 734, 874 LOCHILD field MAXDISTSR, 840 basics, 729–734, 873–874 node record in point k-d tree, 52 maximal block, 208 merging, 731, 733, 874 LOD methods. See Level of Detail (LOD) maximal leaf node, 779 overflow bucket. See overflow bucket methods maximum clique problem, 448, 452, 776, primary bucket. See primary bucket loop on a face, 316 824 recursive. See recursive linear hashing loop-edge relation, 317 region quadtree. See region quadtree reversed bit concatenation. See loop-face relation, 317, 794 segment tree. See segment tree linear hashing with reversed bit loose octree, 259 maximum distance query. See nearest concatenation (LHRBC) loose quadtree, 257–259, 257, 475. See also neighbor query reversed bit interleaving. See linear cover fieldtree maximum result query. See nearest neighbor hashing with reversed bit Low variable query interleaving (LHRBI) layered dag, 252 MAXMINDIST, 535n splitting, 731 LRU. See least recently used (LRU) page MAXNEARESTDIST, 526 storage utilization factor. See storage replacement policy axis-aligned minimum bounding utilization factor LSD tree, 12, 61, 97, 102–106, 110, 110n, hyperrectangle, 840 linear hashing with partial expansions 129–130, 187, 585, 768 minimum bounding hypersphere, 530 (LHPE), 140, 152, 774 collection of rectangles, 103n minimum bounding spherical shell, 531 linear hashing with reversed bit data-dependent strategy, 103, 463 SR-tree, 841 concatenation (LHRBC), 143, distribution-dependent strategy, 103, 463 MAXPRIORITYQUEUE, 519 146n, 148, 150, 152 exact match query, 102 mb-tree, xxiii. See monotonous bisector linear hashing with reversed bit interleaving four-dimensional representative point tree (mb-tree) (LHRBI), 142–146, 142, 148, 150, rectangle representation, 463 mb∗-tree. See monotonous bisector∗ tree 152, 160–162, 773, 775 paged. See paged LSD tree (mb∗-tree) range query, 143, 146 regions, 224, 308, 312 MD-tree, 98n linear homogeneity heuristic, 228 LSDh tree, 592 MDBT. See multidimensional B-tree linear least squares problem, 671 LSH. See locality sensitive hashing (LSH) (MDBT) linear prefix, 415, 415, 815 MDEH. See multidimensional extendible linear probing, 740 M hashing (MDEH) linear programming problem M-tree, 529, 533, 540, 547, 551, 553, 557, mean gray level, 424 minimum bounding hyperspheres, 852 561, 592, 599, 609, 622, 624–629, mean square error, 690 Voronoi site reconstruction problem, 801 841, 845, 854 MEANORPIVOTDIST, 522 linear scale, 11, 130, 131, 186, 210 covering radius, 624 measure problem, 428, 447–453, 447, linear scan method. See sequential scan incremental nearest neighbor query, 823–824 method 626–629 multidimensions, 448–451 linear tree, 411, 415, 814–815 k nearest neighbor query, 628–629 segment tree. See segment tree link-cut tree, 253 parent object, 624 medial axis transformation (MAT), 6n, Lipschitz embedding, 515, 608, 686, range query, 626 208–210, 208, 212, 364 690–697, 691, 709–711, 716 routing object, 624 medical image processing, 425 reference sets of the embedding. See search hierarchy, 626–627 merging, 779 reference sets MAKENODEANDADDASCHILD, 175 linear hashing. See linear hashing LISP, 743–744 Manhattan distance, 32. See also City Block spiral hashing. See spiral hashing list, 194n distance mesh, 400 list, 743 manifold with boundary, 396 conforming. See conforming mesh LITMAX, 92 mantissa of a real number, 2 mesh generation, 425 Lloyd’s algorithm, 594 map, 356 metric, 488 Local Split Decision tree (LSD tree). See map overlay problem, 241 Chamfer. See Chamfer metric LSD tree K-structure. See K-structure City Block. See City Block distance

980 Euclidean. See Euclidean distance molecular tile, 197 multidimensional range tree, 5–6, 9, 14, 18, Manhattan. See Manhattan distance monotonous bisector tree (mb-tree), 580, 187, 190, 776 Minkowski. See Minkowski distance 599, 618–622, 618, 649, 856–857 construction cost, 18, 750 metric Lp incremental nearest neighbor query, 621 range query, 18, 750 Octagonal. See Octagonal metric range query, 621 space requirements, 18, 187, 750 metric space monotonous bisector∗ tree (mb∗-tree), 618 multidimensional scaling (MDS), 689–690 finite. See finite metric space Monte Carlo randomized algorithm, 711, multidimensional searching, xix, xxii metric tree, 598 716 multidimensional trie, 3 ball partitioning. See vp-tree approximate k nearest neighbor finding multidistance function, 640 generalized hyperplane partitioning. See locality preserving hashing (LSH), 713 multilayer grid file, 256, 256 gh-tree SASH (Spatial Approximation Sample multilevel grid file, 97, 110, 113–116, 115n, MetricMap, 697, 711, 711 Hierarchy), 712 465 pseudo-Euclidean distance. See nearest neighbor query multilist, 5 pseudo-Euclidean distance kNN graph, 711 multimedia database, xv–xvii, xix, xxi–xxii reference objects, 711 Morton block, 215, 510 multiobject BSP tree, 233 Metro system, 392 Morton location ordering, 412–416, 412, multipaging, 10–11, 10, 130, 136–137, 136 MIDRANGE field 816 axial array. See axial array node record in one-dimensional range Morton number, 93, 199, 410, 479 dynamic. See dynamic multipaging tree, 15 Morton order, 93, 150–152, 172, 199–203, static. See static multipaging node record in priority search tree, 21 199, 216, 256, 275, 277, 280, 280n, multiple coverage problem, 128 node record in two-dimensional range 296, 301, 303, 410, 413, 423, 469, multiple posting problem, 108, 125, 128 tree, 16 670, 776–779, 815, 818. See also N multiple resolution, 255, 424 MINDIST, 524 order; Z order multiple storage quadtree, 481 axis-aligned minimum bounding pruning property, 670, 865 multiresolution. See multiple resolution hyperrectangle, 840 Morton packed R-tree, 277, 280 multiresolution model, 391, 394, 399 SR-tree, 840 Morton size ordering, 410, 410, 412–414, continuous. See continuous MINDISTINTER, 840 814 multiresolution model MINDISTOBJECT, 535 most recently used (MRU) page replacement discrete. See discrete multiresolution MINDISTSR, 840 policy, 724n model MINFARTHESTDIST, 839 moving objects database, xvii, xix, 286, multiresolution radiosity, 398 axis-aligned minimum bounding 445, 487, 567 multiresolution representation, 266 hyperrectangle, 842 MRU. See most recently used (MRU) page multitriangulation, 399 minimum bounding hypersphere, 842 replacement policy multiway tree, 8, 97–98, 717 minimum bounding spherical shell, 842 MST. See minimal spanning tree (MST) mutual intersection rule, 261, 261, 261n SR-tree, 843 multi-level order preserving linear hashing mvp-tree, 608–609, 608, 611, 613, 856 minimal spanning tree (MST), 639, (MLOPLH), 162–163, 162, 775 incremental nearest neighbor query, 609 641–643, 859, 861 Multi-scale Line Tree, 384, 384 range query, 609 nearest neighbor query, 643 multiattribute tree, 6–7, 6, 9, 208n MWT. See minimum-weight triangulation minimax facilities location problem, 852 multibody problem, 426. See also N-body (MWT) minimum angle property, 347 problem MX bintree, 72 minimum bounding box. See bounding box multicolored quadtree, 211 MX k-d tree minimum bounding n-corner, 195 multidimensional B-tree (MDBT), 6, 8–9, points, 72, 182 minimum bounding object. See bounding 8, 14, 66, 748 matrix manipulation, 72 box exact match query, 136 MX octree, xxiii minimum bounding polybox, 195 partial range query, 8–9, 14, 136, 748 regions, 357, 361, 363, 369–370, 803 minimum distance query. See nearest range query, 8, 136, 748 MX quadtree, xxiii, 369 neighbor query multidimensional directory (MDD), 9–10, PK-tree. See PK MX quadtree minimum-ambiguity k-d tree, 58–61, 70 9, 66 points, 11, 38–42, 38, 72, 172, 174– approximate nearest neighbor query, 70, hybrid variant, 10 175, 180, 182, 186, 188–189, 473, 763 multidimensional extendible hashing 756–758, 776 minimum-weight triangulation (MWT), (MDEH), 140, 146–150, 152–153, collapsing, 40 240 153n, 155–156, 159–162, 774–775 comparison with point quadtree, Minkowski distance metric Lp, 64 exact match query, 150 47–48, 761 two dimensions, 209n partial expansion, 152 comparison with PR quadtree, 47–48, MINMAXDIST, 535n range query, 150–151 761 MINNETWORKDISTBLOCK, 511 multidimensional histogramming, 62, 269 deletion, 40–41, 756–757 MINPRIORITYQUEUE, 836 multidimensional measure problem insertion, 39–41, 756 MLOPLH. See multi-level order preserving region quadtree. See region quadtree matrix manipulation, 40, 42, 72, linear hashing (MLOPLH) trellis. See trellis 757–758 mobility, 260 multidimensional order-preserving linear range query, 40–42, 757 Mobius¨ strip, 316, 353, 372 hashing with partial expansion space requirements, 48 modified empty circle property, 351 (MOLHPE), 152, 152 splitting, 40

981 MX quadtree (continued) ε. See ε-nearest neighbor two-dimensional range tree, 16 regions, 40, 357–360, 357, 803 feature, 485 NODETYPE field space requirements, 357–359, 376, Gabriel graph (GG). See Gabriel graph node record in MX quadtree for points, 803 (GG) 41 MX quadtrie, 38 incremental algorithm. See incremental node record in PM quadtree, 367 MX-CIF k-d tree, 475–476 nearest neighbor finding node record in PR quadtree, 46 MX-CIF quadtree, xxiii, 115, 255–257, k nearest neighbors. See k nearest non-oriented winged-edge data structure, 259, 466–476, 466, 478–479, 481, neighbor finding 324 827–830, 832 kNN graph. See kNN graph nondegenerate Delaunay triangulation, 347 axes. See axes minimal spanning tree (MST). See nondegenerate Voronoi diagram, 347, 367 axis lines. See axis lines minimal spanning tree (MST) nonhomogeneous k-d tree, 58n collapsing, 468 partial match. See partial match nearest nonleaf node, 214 construction cost, 481, 483 neighbor query nonmanifold object deletion, 468–471, 830 probably approximately correct (PAC). half-edge data structure. See half-edge expanded. See expanded MX-CIF See probably approximately correct data structure quadtree (PAC) nearest neighbor query partial-entity structure. See partial-entity insertion, 468, 470–471, 829, 832 relative neighborhood graph (RNG). See structure one-dimensional. See one-dimensional relative neighborhood graph (RNG) radial-edge data structure. See radial-edge MX-CIF quadtree reverse. See reverse nearest neighbor data structure overlap test, 470, 828–829 query (RNN) nonpolygonal tiling, 377–380 overlay query, 469 R∗-tree. See R∗-tree nonprimitive topological entities, 316 peer-to-peer (P2P), 259, 517 sequential scan method. See sequential NP problem, 206n range query, 469, 472 scan method NP-complete problem, 206n rectangle intersection problem, 481, 483 vector approximation file (VA-file). See Steiner point tetrahedralization. See expected cost, 473 vector approximation file (VA-file) Steiner point tetrahedralization plane-sweep methods, 469, 473 X-tree. See X-tree problem tree traversal, 469 nearest object query, 192, See nearest traveling salesman. See traveling search hierarchy, 493, 833 neighbor query salesman problem space requirements, 481, 483 ordered R-tree. See ordered R-tree splitting, 468 R-tree. See R-tree O window query, 469, 472, 474, 480 neighbor finding in a region quadtree OBB. See oriented bounding box (OBB) MXCOMPARE, 756 diagonal neighbor, 220, 781–782 OBBTree, 195, 386, 389, 393, 398 MXDELETE, 756 lateral neighbor, 217 object aggregation techniques, 271–272, MXINSERT, 756 neighborhood of a K-vertex, 238 274–275 nested interpolation-based grid file extent-based. See extent-based object N (NIBGF), 115, 115, 479 aggregation techniques N order, 200, See also Morton order; Z exact match query, 116, 769 ordering-based. See ordering-based order 509 object aggregation techniques network distance, + N-body problem, 59, 426. See also network distance interval, 511 object B -tree, 279, 279–280, 283, 301 multibody problem NEWROOT, 504, 754 object graph, 316 N-tree, 93 NEXT field object hierarchy, 189 NAME field edgelist record in PM quadtree, 368 object number, 275 rectangle record in MX-CIF quadtree, node record in one-dimensional range object pyramid, 272, 272, 274, 304 470 tree, 15 object representation natural correspondence between a forest NEXTVERTEXSHORTESTPATH, 511 boundary-based. See boundary-based and a binary tree, 7, 722, 722n node object representation nearest common ancestor, 435 directory. See directory node interior-based. See interior-based object nearest foreign neighbor problem, 577 gray. See gray node representation nearest neighbor query, 192n. See also post k-deinstantiated. See k-deinstantiated object-based decomposition, 191 office problem node object-based query. See feature-based query approximate. See approximate nearest k-instantiable. See k-instantiated node object-space methods, 183, 191 neighbor query k-instantiated. See k-instantiated node object-tree pyramid, 272, 273–274, 275n, augmented Gabriel graph (AGG). See nonleaf. See nonleaf node 276–279, 282–283, 294, 296, augmented Gabriel graph (AGG) separator. See separator node 298–299, 301, 304 best-first incremental algorithm. See node record bulk insertion, 296–299, 297 incremental nearest neighbor MX quadtree for points, 41 bulk loading, 297, 299–301, 794 finding one-dimensional range tree, 15 Octagonal metric, 210 best-first k nearest neighbors. See k PM quadtree, 367 octahedron, 232 nearest neighbor finding point k-d tree, 52 octree, 211, 393 Delaunay graph. See Delaunay graph point quadtree, 30 extended. See extended octree depth-first k nearest neighbors. See k PR quadtree, 46 face. See face octree nearest neighbor finding priority search tree, 21 MX. See MX octree

982 regions. See MX octree Morton. See Morton order probably correct. See probably correct PM. See PM octree N. See N order os-tree PM1. See PM1 octree Peano-Hilbert. See Peano-Hilbert order overlapping pyramid, 257, 424 PM2. See PM2 octree R-tree. See R-tree overlay query PM3. See PM3 octree row. See row order MX-CIF quadtree. See MX-CIF quadtree region. See region octree row-prime. See row-prime order PR quadtree. See PR quadtree vector. See vector octree spiral. See spiral order oversized shelf, 567 OLAP. See online analytic processing stable. See stable order overwork, 37, 37, 755 (OLAP) U. See U order , xx Z. See Z order P 65 P-tree, 195, 570 one-cut, order preserving linear hashing (OPLH), + one-dimensional bucket PR-CIF k-d tree, 142, 148, 150, 152–153, 153n, 162 p -order, 151, 151–152 476–478, 480, 482 partial expansion, 152 P1 field one-dimensional containment query ordered R-tree, 301, 303 line record in PM quadtree, 367 interval tree. See interval tree nearest object query, 303 P2 field inverse priority search tree point query, 303 line record in PM quadtree, 367 intervals. See inverse priority search rectangle intersection problem, 303 PAC. See probably approximately correct tree window query, 303 (PAC) nearest neighbor query priority search tree ordered R-tree node-splitting policies packed R-tree, 277, 277–278, 281, intervals. See priority search tree seed-picking 296–297, 301 one-dimensional MX-CIF quadtree, 255, linear cost, 303 Hilbert. See Hilbert packed R-tree 467, 470, 473–475 quadratic cost, 303 Morton. See Morton packed R-tree comparison, 470–471, 828, 832 ordering point query, 296 one-dimensional ordering, 90–95, 187, 768 partial. See partial ordering window query, 296 one-dimensional partial overlap query total. See total ordering page, 3, 12 priority search tree ordering-based object aggregation buddy. See buddy page intervals. See priority search tree techniques, 275–281, 790–791 directory. See directory page one-dimensional point quadtree, 474–475 representative point, 275 external directory. See external directory one-dimensional PR quadtree, 474–475 ordinary hierarchy, 197 page one-dimensional R-file, 478 organization method internal directory. See internal directory one-dimensional range tree, 5, 9, 14, 19–20, data. See data organization methods page 433, 440–441, 444–446, 821 embedding space. See embedding space point. See point page range query, 14–15 organization methods region. See region page rectangle intersection problem, 433 ORIENT field page fault, 717 online analytic processing (OLAP), 297 edge_orientation_pair record in paged LSD tree, 105 OPDIRECTION, 470 ORIENTEDFACEEDGETABLE and parallel data structure, 49 open-sliding midpoint k-d tree, 74, 74, 766 ORIENTEDVERTEXEDGETABLE, parallel processing, xviii space requirements, 74, 77, 764–766 326 parametric R-tree, 286, 445 OPLH. See order preserving linear hashing oriented bounding box (OBB), 195 Pareto operator, 503 (OPLH) oriented bounding box tree (OBBTree). See Parseval’s theorem, 680 OPQUAD, 32 OBBTree partial expansion OPTBFTRAV, 550 oriented edge, 324 multidimensional extendible hashing OPTBFTRAVFARTHEST, 553, 847 oriented winged-edge data structure, (MDEH). See multidimensional OPTDFTRAV, 541 324–329, 325, 331, 343–344 extendible hashing (MDEH) OPTDFTRAVFARTHEST, 548, 846 ORIENTEDFACEEDGETABLE, 325 order preserving linear hashing (OPLH). optimized k-d tree, 58, 65–66, 69, 763 ORIENTEDVERTEXEDGETABLE, 325 See order preserving linear hashing deletion, 65 orphan object, 652, 659n, 661–662 (OPLH) range query, 65 orthogonal partition tree, 450, 452 partial match nearest neighbor query, 844 optimized point quadtree, 30, 30–31, 58, orthogonal polygon, 409n partial match query. See partial range query 65, 190, 752–753, 776 os-tree. See overlapped-split tree (os-tree) partial ordering, 506, 506n construction cost, 31, 752 OTHERAXIS, 470 skyline query. See skyline query total path length (TPL), 31, 752 outer approximation, 378 partial range query, 3 OPTINSERTL, 542 outer box in balanced box-decomposition BD-tree. See BD-tree order tree (BBD-tree), 83 bit interleaving. See bit interleaving admissible. See admissible order OUTOFRANGEY, 22 combined index. See combined index B-tree. See B-tree overflow bucket, 130, 731 double Gray order. See double Gray B+-tree. See B+-tree overflow file, 733 order Cantor-diagonal. See Cantor-diagonal overlap, 274 Gray order. See Gray order order overlapped-split tree (os-tree), 68, 573–575, grid file. See grid file column. See column order 610n inverted file. See inverted file double Gray. See double Gray order cover, 573 kB-tree. See kB-tree Gray. See Gray order failure probability, 575

983 partial range query (continued) PK MX quadtree, 172, 172 bucket rectangle. See bucket rectangle multidimensional B-tree (MDBT). See PK point k-d tree, 184, 775 PM quadtree multidimensional B-tree (MDBT) PK point quadtree, 184, 775 edge-based, 365, 375 point k-d tree. See point k-d tree PK PR k-d tree, 168, 169–171, 183 map overlay problem, 369 point quadtree. See point quadtree PK PR octree, 170 vertex-based, 365–366, 374 PR k-d tree. See PR k-d tree PK PR quadtree, 168, 168–170, 173–174, PM1 quadtree, xxiii, 365, 365–369, PR quadtree. See PR quadtree 177–178, 181 372–377, 513, 516, 809–810 quintary tree. See quintary tree PK pseudo k-d tree, 775 bucket. See bucket PM1 quadtree U order. See U order PK pseudo quadtree, 775 deletion, 368–369, 805–806 partial-entity structure, 316 PK-tree, xxiii, 12, 117, 127n, 164–185, insertion, 368, 803–805 partition fieldtree, 257–259, 257, 401, 475, 190, 216, 775 point location query, 369, 808–809 480 deletion, 176, 178–181, 775 space requirements, 376 partition number, 146 directory node, 117, 167 vertex-based, 366 partition process, 165 insertion, 172–178 PM2 quadtree, xxiii, 366, 367, 369, 371, partitioning box in balanced box- MX quadtree. See PK MX quadtree 375–377, 584–585, 801, 810, 853 decomposition tree (BBD-tree), point k-d tree. See PK point k-d tree bucket. See bucket PM2 quadtree 83 point node, 117, 167 deletion, 369, 807 PASCAL, xx, 743 point quadtree. See PK point quadtree insertion, 369, 806–807 path compression, 76, 169, 182–183 PR k-d tree. See PK PR quadtree vertex-based, 366 path planning, 373 PR octree. See PK PR octree PM3 quadtree, xxiii, 366, 367, 370–372, path-compressed PR k-d tree, 75–82, 76, PR quadtree. See PK PR quadtree 375–376, 809–810 169, 182, 188, 581, 619, 765–766 pseudo k-d tree. See PK pseudo k-d tree bucket. See bucket PM3 quadtree space requirements, 76–77, 766 pseudo quadtree. See PK pseudo quadtree deletion, 369, 808 path-level compressed PR k-d tree, 77–79, space requirements, 183 insertion, 369, 807–808 78, 82, 165, 169, 182, 767 PKDELETE, 180 vertex-based, 366 path-level compression, 78 PKINSERT, 176 PM-CSG tree, 373 Patricia trie, 76, 183, 188 plan, 424 PM1CHECK, 804 pattern matching, 425 planar graph, 315 PM2CHECK, 806 pattern recognition, xv, xx, 423 adjacent faces, 315 PM3CHECK, 807 PCA. See Principal Component Analysis face, 315 PMDELETE, 805 (PCA) frontier of a face, 315 PMINSERT, 803 Peano-Hilbert location ordering, 415–416 Planar Straight Line Graph (PSLG), 351, PMR k-d tree, xxiii, 74–75, 182–183 Peano-Hilbert order, 145, 151–152, 172, 352, 352n PMR polygon quadtree, 262, 262 199–202, 199, 216, 275–277, 280– plane-sweep methods, xxiii, 291, 428–453, PMR quadtree, xxiii, 74n, 182–183, 262, 281, 296–297, 301, 303, 410, 423, 428, 819–824 366, 369, 374–377, 375, 513, 516 670, 768, 774, 776–779, 793, 815 skyline query. See skyline query deletion, 377 Peano-Hilbert size ordering, 410, 414 plane-sweep triangulation, 238 insertion, 377 peer-to-peer (P2P) Platonic solids, 232 polygon. See PMR polygon quadtree gh-tree. See gh-tree PLC. See Piecewise Linear Complex (PLC) space requirements, 376 k-d tree. See k-d tree PLOP hashing. See piecewise linear order PMR rectangle k-d tree, xxiii MX-CIF quadtree. See MX-CIF quadtree preserving (PLOP) hashing PMR rectangle quadtree, xxiii. See also R-tree. See R-tree PM octree, xxiii, 363, 369–374, 369, PMR rectangle quadtree perfect point quadtree, 37, 57, 755 808–809, 809 point bucket, 97 perimeter computation problem black hole, 371 point dominance problem, 88, 444. See also segment tree. See segment tree Boolean node, 372 dominance relation persistent search trees, 445 Boolean set operations, 370–372 POINT field phasing, 46, 46 conversion between boundary model, node record in priority search tree, 21 PHYSICAL, 874 370 node record in two-dimensional range piano movers problem, 425 nasty node, 371 tree, 17 pick query in computer graphics, 4, 192, nearby node, 372 point k-d tree, xxiii, 49–72, 50, 88, 96, 98, 486. See also nearest neighbor space requirements, 373 101, 183, 186, 189, 418, 576, 585, query; nearest object query terminal gray node, 371 761–764, 776 Piecewise Linear Complex (PLC), 352, PM1 octree, 369, 371–373, 808 bounds array. See bounds array 352n point location query, 374 bucket adaptive. See bucket adaptive k-d piecewise linear order preserving (PLOP) space requirements, 373, 809 tree hashing, 146, 153–156, 159, 161, PM2 octree, 371–373, 371 bucket generalized pseudo. See bucket 187–188, 774 black hole, 372 generalized pseudo k-d tree pivot, 521, 598, See also pivot object PM3 octree, 371, 372 deletion, 52–55, 65, 762–763 pivot object, 598, See also pivot PM quadtree, xxiii, 363, 365–369, 481, analogy to binary search tree deletion, pivot-based distance-based indexing 584, 801, 803–808 52–53 methods, 598–599, 625 bucket. See bucket PM quadtree depth-first k nearest neighbor algorithm, pixel, 192 538, 844

984 divided. See divided k-d tree single rotation, 31, 753 post office tree, 609 double rotation, 52 space requirements, 48 PR bintree, 71 generalized pseudo. See generalized total path length (TPL), 30–31, 34–35, PR k-d tree, xxiii, 70–74, 71, 76, 80, 82–84, pseudo k-d tree 755 110, 112–114, 168–171, 182–183, homogeneous. See homogeneous k-d tree point quadtree bounding-box cell-tree 186, 189, 619, 764, 776 insertion, 50–52, 761 pyramid, 306 bucket. See bucket PR k-d tree MX-CIF. See MX-CIF k-d tree point query partial range query, 72, 764 nonhomogeneous. See nonhomogeneous feature, 485 path-compressed. See path-compressed k-d tree objects, 428 PR k-d tree optimized. See optimized k-d tree balanced four-dimensional k-d tree. path-level compressed. See path-level partial range query, 56–57, 72, 763–764 See balanced four-dimensional k-d compressed PR k-d tree PK-tree. See PK point k-d tree tree PK-tree. See PK PR k-d tree pseudo. See pseudo k-d tree corner stitching. See corner stitching regions, 221 range query, 55–57, 65, 763 ordered R-tree. See ordered R-tree two-dimensional representative point regions, 223–225, 260, 305, 314, 783 packed R-tree. See packed R-tree rectangle representation, 464 search, 55–57, 763 R-file. See R-file point query, 464 single rotation, 52 R-tree. See R-tree PR octree, 170 spatial. See spatial k-d tree representative point rectangle PK-tree. See PK PR octree total path length (TPL), 52–53, 58, 65, representation. See representative PR quadtree, xxiii, 11, 38, 42–47, 42, 70– 762 point rectangle representation 71, 80, 163, 166, 168–173, 175, trie-based. See trie-based k-d tree R+-tree. See R+-tree 178, 180–183, 186, 188–189, 366, VAMSplit k-d tree. See VAMSplit k-d points, 192, 428. See exact match query 368, 511, 580, 599, 619, 758–761, tree two-dimensional representative point 776 point location problem. See point location rectangle representation bucket. See bucket PR quadtree query PR k-d tree. See PR k-d tree collapsing, 43 point location query, 192, 435n, 489 PR quadtree. See PR quadtree comparison with MX quadtree, 47–48, fractional cascading. See fractional spatial k-d tree. See spatial k-d tree 761 cascading point record comparison with point quadtree, 47–48, gap tree. See gap tree layered dag, 252 761 K-structure. See K-structure PM quadtree, 367 deletion, 43, 47, 759–760 layered dag. See layered dag two-dimensional range tree, 17 four-dimensional representative point PM1 quadtree. See PM1 quadtree point set query, 428 rectangle representation, 458 R-tree. See R-tree pointer, 743 insertion, 43, 47, 758–759 separating chain. See gap tree polar coordinates, 377–380, 740 one-dimensional. See one-dimensional point node polar quadtree, 379–380, 379 PR quadtree PK-tree. See PK-tree pole, 231–232 overlay query, 45 point page polygon partial range query, 48, 761 BV-tree. See BV-tree convex. See convex polygon PK-tree. See PK PR quadtree k-d-B-tree, 103. See also k-d-B-tree polygon quadtree range query, 44, 47, 761 k-d-B-trie. See k-d-B-trie bucket. See bucket polygon quadtree skip list. See skip list point quadtree, xxiii, 11, 14, 28–37, 57, PMR. See PMR polygon quadtree space requirements, 44, 47–48, 760 70, 88, 96, 164, 183, 186–189, 269, vertex bucket. See vertex bucket polygon splitting, 43 418, 425, 751–755, 775–776 quadtree triangulation, 241 comparison with MX quadtree, 47–48, polygon representation, 313 two-dimensional representative point 761 polygon tree, 36, 37 rectangle representation, 458, 464 comparison with PR quadtree, 47–48, polygonal map, 261, 356 point query, 464 761 regularization. See regularization PR quadtrie, 42, 163 construction cost, 31, 753 y-monotone subdivision. See y-monotone PR-file, 384 deletion, 31–36, 504, 753–754 subdivision PRCOMPARE, 758 analogy to binary search tree deletion, polygonal tiling, 197–199, 776 PRDELETE, 759 31 polyhedral approximation, 362, 386–389, precision, 664, 664 double rotation, 31, 753 813 predictive region quadtree construction. See insertion, 28–31, 751–752 adjustment step, 387–388, 813 region quadtree one-dimensional. See one-dimensional polyline, 68, 224, 313 preference function, 505 point quadtree polysurface, 390 prefix B+-tree, 415, 726, 815 optimized. See optimized point quadtree polytree, 370 preload, 743 partial range query, 37, 48, 755, 761 population, 45 preprocessing cone, 424 PK-tree. See PK point quadtree population model, 45–46 PREV field pseudo. See pseudo quadtree POSSIBLEPM1MERGE, 806 node record in one-dimensional range range query, 36–37, 755 POSSIBLEPM23MERGE, 807 tree, 15 region query, 37 post office problem, 4, 486. See also nearest primary bucket, 731 regions, 222–223, 260, 305, 782–783 neighbor query primary key, 91

985 primary key retrieval, 1n,5 See also contractive embedding; irregular grid array. See irregular grid primary structure, 435, 435 contractive mapping array pyramid active node, 436 space-ordering methods. See space- irregular grid bounding-box. See irregular inactive node, 436 ordering methods grid bounding-box pyramid prime meridian, 232 Pruning Rule 1 object. See object pyramid primitive topological entities, 316 k farthest neighbors, 529, 838 overlapping. See overlapping pyramid primitive transition, 331 k nearest neighbors, 524, See also point quadtree bounding-box cell-tree. principal axis, 66 Lemma 4.2 See point quadtree bounding-box principal axis tree (PAT), 9, 66 Pruning Rule 2 cell-tree pyramid Principal Component Analysis (PCA), k farthest neighbors region representation, 424–425 398, 591, 671–673, 685–686, 690, nonobjects, 548, 846 truncated-tree. See truncated-tree 697–698, 704, 710 objects, 529, 838 pyramid probably correct os-tree. See probably k nearest neighbors. See also Lemma 4.1 pyramid technique, 587–592, 587, 854 correct os-tree nonobjects, 540 extended. See extended pyramid PRINSERT, 758 objects, 524 technique priority queue, 20, 493 Pruning Rule 3 pyramid value, 588 priority R-tree, 286n k farthest neighbors, 529, 838 window query, 591 priority search tree, xxii–xxiii, 6, 9, 13, 19– k nearest neighbors, 524, See also 27, 19, 187, 189–190, 439–443, Lemma 4.2 Q 447, 750–751, 776, 821 Pruning Rule 4 q-edge, 366 containment set, 446 k farthest neighbors q-face, 366, 370 intervals, xxiii, 435n, 439–443, 821 nonobjects, 548, 846 Q-tree, 423 enclosure query, 443, 821 objects, 529, 838 QLQT. See quad list quadtree (QLQT) one-dimensional containment query, k nearest neighbors. See also Lemma 4.1 QMAT. See quadtree medial axis transform 443, 821 nonobjects, 540 (QMAT) one-dimensional partial overlap query, objects, 524 QSF-tree 443, 821 Pruning Rule 5 simple. See simple QSF-tree rectangle intersection problem, farthest neighbor, 529, 839 quad list quadtree (QLQT), 482–483 439–443, 821 k nearest neighbors, 541, 541, 543–546 construction cost, 483 stabbing query, 443, 821 nearest neighbor, 526, See also space requirements, 477–478, 482–483 inverse. See inverse priority search tree Lemma 4.2 window query, 477–478, 482–483 points, xxiii, 19–27, 440, 750–751 pseudo k-d tree, 58, 65–66, 69 quad-edge data structure, 322–324, 322, construction cost, 19, 26, 750 PK-tree. See PK pseudo k-d tree 329–330, 341–343, 345, 353–354 semi-infinite range query, 20–23, pseudo quadtree, 34, 34, 36, 58, 65, 69, 88, quadgrid, 165, 165, 170 25–26, 440, 750 190, 755, 775–776 quadtree, xviii, 211, 423 space requirements, 19, 25, 750 PK-tree. See PK pseudo quadtree 0-balanced. See 0-balanced quadtree two-dimensional range query, 19 pseudo-Euclidean distance, 711 1-balanced. See 1-balanced quadtree two-dimensional. See two-dimensional PSLG. See Planar Straight Line Graph 1-irregular. See 1-irregular quadtree priority search tree (PSLG) adaptive. See adaptive quadtree PRIORITYSEARCH, 21 PTCOMPARE, 751 balanced. See balanced quadtree PRIORITYSEARCH2, 26 PTDELETE, 753 binary. See binary quadtree prism tree, 362, 386–389, 387, 391, 393, PTINSERT, 752 bounded. See bounded quadtree (BQT) 398, 401–402, 813 PTINSQUARE, 368 bucket PM. See bucket PM quadtree object intersection, 389 puzzletree, 66, 225–230, 225, 260, 572, bucket PM1. See bucket PM1 quadtree regular. See regular prism tree 783–786. See also treemap; X-Y bucket PM2. See bucket PM2 quadtree probably approximately correct (PAC) tree bucket PM3. See bucket PM3 quadtree nearest neighbor query, 561–563, pyramid, xvi, xx, 63, 266–270, 384, 424, bucket polygon. See bucket polygon 562, 579, 596–597 776, 790 quadtree probably correct os-tree, 574–580, 575, 853 array. See array pyramid bucket pseudo. See bucket pseudo Principal Component Analysis (PCA), bintree bounding-box cell-tree. See quadtree 575–576, 580 bintree bounding-box cell-tree bucket rectangle. See bucket rectangle support vector machines (SVM) method, pyramid PM quadtree 576–577, 579 bounding-box cell-tree. See bounding- bucket rectangle PM. See bucket support vectors, 576 box cell-tree pyramid rectangle PM quadtree projection space, 712 cell. See cell pyramid edge. See edge quadtree property sphere, 231 cell-tree. See cell-tree pyramid expanded MX-CIF. See expanded proximity query, 4 disjoint object. See disjoint object MX-CIF quadtree proximity search, 36 pyramid hinted. See hinted quadtree proximity-preserving embedding, 686–687 generalized k-d tree bounding-box least square. See least square quadtree proximity-preserving property, 665, 665, cell-tree. See generalized k-d tree line. See line quadtree 667, 687, 864–865 bounding-box cell-tree pyramid multicolored. See multicolored quadtree pruning property, 664–665, 664, 667. irregular grid. See irregular grid pyramid

986 multiple storage. See multiple storage farthest neighbor. See farthest neighbor point query, 479 quadtree query two-dimensional. See two-dimensional MX. See MX quadtree feature. See feature query; feature-based R-file MX-CIF. See MX-CIF quadtree query window query, 480 expanded. See expanded MX-CIF geometric join. See geometric join query r-optimal algorithm, 494, 497–498 quadtree intersection. See intersection query R-tree, xvi, xviii, xxii–xxiii, 12, 61, 68, 96– PK MX. See PK MX quadtree location. See location query; location- 97, 101, 112, 117, 127–130, 165, PK point. See PK point quadtree based query 171, 187, 189, 280n, 282–290, 282, PK PR. See PK PR quadtree maximum distance. See nearest neighbor 292–296, 301–302, 308, 376, 382, PK pseudo. See PK pseudo quadtree query 398, 427, 488–489, 509–511, 515, PM. See PM quadtree maximum result. See nearest neighbor 535, 537–538, 548, 556, 566–574, PM1. See PM1 quadtree query 579, 585, 595–596, 604, 606, 614, PM2. See PM2 quadtree measure problem. See measure problem 622, 624–626, 629, 663, 674–676, PM3. See PM3 quadtree minimum distance. See nearest neighbor 685, 791–792, 841 PMR. See PMR quadtree query bulk insertion. See object-tree pyramid PMR polygon. See PMR polygon nearest neighbor. See nearest neighbor bulk loading. See object-tree pyramid quadtree query deletion, 287, 791 point. See point quadtree nearest object. See nearest object query Hilbert. See Hilbert R-tree polar. See polar quadtree partial match. See partial range query incremental nearest neighbor finding, PR. See PR quadtree partial match nearest neighbor. See 494–495, 666–667 pseudo. See pseudo quadtree partial match nearest neighbor query insertion, 287 quad list (QLQT). See quad list quadtree partial range. See partial range query nearest object query, 289, 792 (QLQT) pick in computer graphics. See nearest node-splitting policies. See R-tree rectangle. See rectangle quadtree object query node-splitting policies region. See region quadtree point order, 282 restricted. See restricted quadtree objects. See point query ordered. See ordered R-tree revised line. See revised line quadtree points. See exact match query overflow, 283 shortest path. See shortest-path quadtree point set. See point set query packed. See packed R-tree trie-based. See trie-based quadtree probably approximately correct (PAC) parametric. See parametric R-tree uniform. See uniform quadtree nearest neighbor. See probably peer-to-peer (P2P), 271 vector. See vector quadtree approximately correct (PAC) nearest point location query, 61 vertex bucket polygon. See vertex bucket neighbor query point query, 288 polygon quadtree proximity. See proximity query priority. See priority R-tree Quadtree Complexity Theorem, 357–359, range. See range query rectangle intersection problem, 289 358, 376, 803 range aggregation. See range aggregation restructuring quadtree medial axis transform (QMAT), query incremental refinement, 302, 302 212, 212, 220, 257, 365, 365n, 425, rectangle intersection. See rectangle postoptimization, 302, 302 782 intersection problem search hierarchy, 492–493, 666–667, 833 quadtree skeleton, 212, 220, 782 reverse nearest neighbor (RNN). See skyline query, 505 quadtrie, 423 reverse nearest neighbor query spatial sampling, 780 MX. See MX quadtrie (RNN) underflow, 283 PR. See PR quadtrie skyline. See skyline query Voronoi diagram, 573 quantile hashing, 153–156, 155n, 159, 161, spatial join. See spatial join query window query, 289 187–188, 774 stabbing. See stabbing query rectangular, 289, 792 quaternary hierarchical decomposition, 403 stabbing counting. See stabbing counting R∗-tree, 283, 285, 289–296, 289, 300– rectangle. See quaternary hierarchical query 303, 465, 488, 548, 566–570, 572, rectangular decomposition window. See window query 586, 629, 674–675, 681–682, 685, triangle. See quaternary hierarchical quicksort, 661 791–793 triangular decomposition QUILT quadtree GIS, xviii forced reinsertion. See forced reinsertion quaternary hierarchical rectangular quintary tree, 6–9, 7 nearest neighbor query, 594 decomposition, 402–405, 408 construction cost, 13, 748 reinsertion quaternary hierarchical triangular exact match query, 13, 748 close-reinsert. See close-reinsert decomposition, 400, 402–405, 407 partial range query, 7, 13, 748 far-reinsert. See far-reinsert query range query, 13, 748 R+-tree, 12, 96, 130, 311–312, 311, 376, all closest pairs. See all closest pairs space requirements, 8, 13, 747 382, 773 query deletion, 312 Boolean. See Boolean query R insertion, 312 containment. See containment query R-file, 115, 256, 478–480 point query, 312 containment set. See containment set deletion, 480 rectangle intersection problem, 312 enclosure. See enclosure query insertion, 480 space requirements, 312, 794 epsilon. See epsilon query one-dimensional. See one-dimensional window query, 312 exact match. See exact match query R-file

987 R-tree node-splitting policies, 284–289, multidimensional extendible hashing grid file. See grid file 791–792 (MDEH). See multidimensional interval tree. See interval tree exhaustive, 284–285, 291 extendible hashing (MDEH) MX-CIF quadtree. See MX-CIF quadtree reducing overlap, 285–288, 291, 294 mvp-tree. See mvp-tree one-dimensional range tree. See seed-picking, 285 MX-CIF quadtree. See MX-CIF quadtree one-dimensional range tree linear cost, 285, 287–288, 290–292, one-dimensional range tree. See ordered R-tree. See ordered R-tree 294, 296 one-dimensional range tree priority search tree. See priority search quadratic cost, 285, 287–288, optimized k-d tree. See optimized k-d tree 290–292, 294, 296, 793 tree R-tree. See R-tree radial-edge data structure, 316 priority search tree. See priority search representative point rectangle radix searching, 2 tree representation. See representative random access structure, 202 quintary tree. See quintary tree point rectangle representation random lines model, 369, 376 SASH (Spatial Approximation Sample R+-tree. See R+-tree randomized algorithm, 711 Hierarchy). See SASH (Spatial segment tree. See segment tree Las Vegas. See Las Vegas randomized Approximation Sample Hierarchy) tile tree. See tile tree algorithm semi-infinite. See semi-infinite range rectangle placement problem, 449, 452 Monte Carlo. See Monte Carlo query rectangle quadtree, xxiii, 480, 481 randomized algorithm Spatial Approximation tree (sa-tree). See rectangle record range aggregation query, 485n Spatial Approximation tree (sa-tree) MX-CIF quadtree, 470 range priority tree, 9, 23–25, 23, 187 two-dimensional range tree. See rectangular coding, 208 construction cost, 23, 27, 751 two-dimensional range tree RECTINTERSECT, 470 space requirements, 23, 27, 751 U order. See U order recursive linear hashing, 733–734, 733, 874 two-dimensional range query, 25–27, uniform grid. See uniform grid overflow file. See overflow file 751 vp-tree. See vp-tree red-black balanced binary tree, 19, updates, 23, 27 vpsb-tree. See vpsb-tree 440–443, 722–723, 726–727, 873 range query, 3, 4. See also window query range tree, xxii–xxiii, 5, 13–18, 187, 2-3 tree, 722, 722n, 726, 872. See also AESA. See AESA 189–190, 749–750, 776 2-3 tree aggregation. See range aggregation query multidimensional. See multidimensional bottom-up insertion algorithm, BD-tree. See BD-tree range tree 722–723, 726 bisector tree. See bisector tree one-dimensional. See one-dimensional deletion, 726 bit concatenation. See bit concatenation range tree top-down insertion algorithm, 726 bit interleaving. See bit interleaving range query 2-3-4 tree, 722, 722n, 726, 872. See also buddy-tree. See buddy-tree one-dimensional range tree. See 2-3-4 tree double Gray order. See double Gray one-dimensional range tree bottom-up insertion algorithm, 723, order two-dimensional range tree. See 726 dynamic p hashing. See dynamic p two-dimensional range tree deletion, 726 hashing space requirements, 15 top-down insertion algorithm, 726–727 dynamic z hashing. See dynamic z two-dimensional. See two-dimensional black edge, 722 hashing range tree red edge, 722 ECDF tree. See ECDF tree RANGESEARCH, 15 reduced combined index, 6 feature, 485 RANGETREE field Reduced Overhead AESA (ROAESA). See generalized pseudo k-d tree. See node record in two-dimensional range ROAESA generalized pseudo k-d tree tree, 17 reduction factor, 65 Geometric Near-neighbor Access ranking reference, 743 Tree (GNAT). See Geometric ECDF tree. See ECDF tree reference sets, 691 Near-neighbor Access Tree (GNAT) raster data, 367 selection, 692–693 gh-tree. See gh-tree raster-scan order, 779, See also row order refinement, 511, 663 Gray order. See Gray order RASTERTOVLIST, 421, 423, 818 surface. See surface simplification grid file. See grid file ray tracing, 398–399 REFLECT, 218 inverted file. See inverted file recall, 664, 664 reflection hierarchy, 198 k-d-B-trie. See k-d-B-trie recognition cone, 424 region, 200n kB-tree. See kB-tree RECT field α-balanced. See α-balanced region kNN graph. See kNN graph bnode record in MX-CIF quadtree, 470 aspect ratio. See aspect ratio of region linear hashing with reversed bit rectangle intersection problem, 428–445, canonical. See canonical region interleaving (LHRBI). See 428, 819–822 eight-connected. See eight-connected linear hashing with reversed bit balanced four-dimensional k-d tree. See component interleaving (LHRBI) balanced four-dimensional k-d tree fat. See fat region M-tree. See M-tree bin method. See bin method four-connected. See four-connected monotonous bisector tree (mb-tree). See dynamic interval tree. See dynamic component monotonous bisector tree (mb-tree) interval tree nonobject (white), 200n multidimensional B-tree (MDBT). See expanded MX-CIF quadtree. See object, 200n multidimensional B-tree (MDBT) expanded MX-CIF quadtree skinny. See skinny region

988 region bucket, 97 LSD tree. See LSD tree runlength encoding, 42, 205, 206, 409–417, region capacity, 476 point query, 456, 458 409, 420, 422, 814–816 region octree, 211–220, 212, 314, 358, PR quadtree. See PR quadtree change-based. See change-based 361, 363, 370, 399, 409, 418, 425, rectangle intersection problem, 456 runlength encoding 779–782 window query, 456, 458 Morton order, 414 Boolean set operations, 372 location parameters. See location Peano-Hilbert order, 414 space requirements, 373 parameters value-based. See value-based runlength region page polar coordinates, 453 encoding k-d-B-tree, 103. See also k-d-B-tree two-dimensional point runlength representation. See runlength k-d-B-trie. See k-d-B-trie BANG file. See BANG file encoding region quadtree, xvii, 37, 44, 141n, 211– PR k-d tree. See PR k-d tree 223, 211, 226–227, 233, 257, 259, PR quadtree. See PR quadtree S 266–267, 305, 314, 356, 358, spatial k-d tree. See spatial k-d tree S-tree, 301, 303, 411, 411, 411n, 414 skew factor. See skew factor 380–381, 399, 402, 409–415, 423– resolution ∗ See S -tree, 412 425, 448, 466, 473, 510, 515–516, multiple. multiple resolution + 779–782, 803, 815–816 restricted bintree, 64, 406–408, 406, 814 S -tree, 411–412, 411, 414–415, 815 construction restricted d-dimensional quadtree, 408 sa-tree. See Spatial Approximation tree bottom-up, 779 restricted quadtree, 64, 381–382, 405–408, (sa-tree) predictive, 779 405 SAIL, xx, 743 top-down, 779 restricted rectangle quadtree. See restricted SAND Internet Browser, xviii maximum clique problem, 449, 452 quadtree SASH, 651 multidimensional measure problem, 448, restricted triangular quadtree, 408 SASH (Self Adaptive Set of Histograms), 452–453 RETURNTREETOAVAIL, 806 650n surface area, 452 reverse kNN graph, 658, 662, 864 SASH (Spatial Approximation Sample optimal position, 219, 780 reverse nearest neighbor query (RNN), 658, Hierarchy), 557, 582, 599, 650–662, spatial sampling, 780 658n 863–864 translation, 425 influence set. See influence set approximate k nearest neighbor finding, region tree, 243 reversed bit concatenation, 143 655–658, 662, 716, 863 separator node. See separator node reversed bit interleaving, 140, 142, 146, 159 Las Vegas randomized algorithm, 712 regular B-partition, 112 revised line quadtree, 357, 357, 803 Monte Carlo randomized algorithm, regular decomposition, 3, 211 RIGHT field 712 regular prism tree, 389, 389 line record in PM quadtree, 367 construction, 651–653 regular tiling, 197 node record in one-dimensional range orphan object. See orphan object regularization tree, 15 range query, 662 polygonal map, 242, 244, 247–249 node record in priority search tree, 21 SATREEINCNEAREST, 634 plane-sweep, 788 node record in two-dimensional range Schonhardt¨ Twisted Prism, 353 regularized Boolean set operations, 314n, tree, 16 SDFT. See Sorted Discrete Fourier 393 TYPE field value vertex Transform (SDFT) relative neighborhood graph (RNG), ldnode record in layered dag, 251 search hierarchy. See nearest neighbor 639–643, 639, 859–861 RMD-tree, 98n query nearest neighbor query, 643 RNG. See relative neighborhood graph AESA. See AESA REMOVECHILDSOFNEWNODEFROM- (RNG) gh-tree. See gh-tree FATHER, 176 RNN. See reverse nearest neighbor query LAESA. See LAESA REMOVENODEFROMFATHER, 176 (RNN) M-tree. See M-tree REMOVEPRIORITYQUEUE, 518n ROAESA, 649, 649–650 MX-CIF quadtree. See MX-CIF quadtree REPARTITION, 786 alive, 649 R-tree. See R-tree representative point, 99n, 103n, 453 not alive, 649 vp-tree. See vp-tree representative point rectangle robot, 425 searching, xix representation, 453–466, 824–827 robotics, xv, 373, 425 second normal form (2nf), 329 Cartesian coordinates, 453 rosette, 231 secondary key, 91 Cartesian product, 454 rotation secondary key retrieval, 1n extension parameters. See extension point k-d tree. See point k-d tree secondary structure, 435, 435 parameters point quadtree. See point quadtree sector tree, 377–381, 378, 811 four-dimensional point, 454–463, rotation hierarchy, 198 complete. See complete sector tree 824–827 routing object, 521 intersection, 379 balanced four-dimensional k-d tree. row order, 199–202, 200, 278, 296, 423, rotation, 380–381 See balanced four-dimensional k-d 776–778, 779, 818–819 scaling, 379 tree row-prime order, 199–202, 199, 776–778 translation, 380 union, 379 containment query, 456, 458 RR1 quadtree, 261 segment tree, xxii–xxiii, 430–434, 445–447, enclosure query, 456, 458 RR2 quadtree, 261 grid file. See grid file runlength code, 42. See also runlength 451–452, 473, 819–823 k-d tree. See k-d tree encoding containment set, 444–445

989 segment tree (continued) simplicial complex, 353, 353, 354n, 869 sort-tile-recurse method (STR method), deletion, 432 simplification 277–278 insertion, 432 view-dependent. See view-dependent Sorted DFT (SDFT). See Sorted Discrete maximum clique problem, 449, 452 simplification Fourier Transform (SDFT) measure problem, 447, 452 simplification envelope method, 395 Sorted Discrete Fourier Transform (SDFT), multidimensional. See multidimensional simplification methods, 391, See surface 684, 684 segment tree simplification sorting, xv perimeter computation problem, 447, SIMULA, xx, 743 SP-GiST. See spatial partitioning 452 single balance, 753 generalized search tree (SP-GiST) rectangle intersection problem, 430–434, Singular Value Decomposition (SVD), space hierarchy, 189 439, 460, 819–820 xvii, 66n, 591, 671–677, 672, 681, space planning, 425 space requirements, 432 683–686, 683n, 690, 697–698, 704, space requirements stabbing counting query, 434 710–711, 866 balanced four-dimensional k-d tree. See stabbing query, 434, 822 Approximate SVD transform matrix. See balanced four-dimensional k-d tree two-dimensional. See two-dimensional Approximate SVD transform matrix bounded quadtree (BQT). See bounded segment tree transform matrix, 672 quadtree (BQT) window query, 444 site, 69, 346, 581, 658n bucket PR-CIF k-d tree. See bucket segmentation, 424 SIZE, 518 PR-CIF k-d tree selectivity estimation, 259 size-bound method, 256, 257, 259 bucket rectangle PM quadtree. See bucket semi-infinite range query, 19, 440 skeleton, 208–209, 209 rectangle PM quadtree semiclosed boundary, 429 adaptively sampled distance field (ADF). expanded MX-CIF quadtree. See semijoin See adaptively sampled distance expanded MX-CIF quadtree distance. See distance semijoin field (ADF) hinted quadtree. See hinted quadtree separate chaining method, 729, 729n quadtree. See quadtree skeleton quad list quadtree (QLQT). See quad list separating chain, 69, 224, 242–254, 243, skew factor, 302 quadtree (QLQT) 788–789 skinny region, 64 segment tree. See segment tree dynamic edge insertion, 245–246, 248, skip list, 27n, 661 space tile, 459, 460 789 k-d tree space-filling curve, 90, 199, 444n, 776 point location query. See gap tree half-space range query, 27n space-ordering methods, 199–202, 275, separation factor, 582 PR quadtree 776–778 separator node, 243 approximate nearest neighbor query, admissible. See admissible order septree, 231 27n pruning property, 669–670 sequential heap, 106 approximate range query, 27n stable. See stable order sequential list, 5, 185, 776 point location, 27n sparse matrix, 423 exact match query, 5, 13, 747 skycube, 503n SparseMap, 686, 690, 694–697, 709–710 sequential scan method, 592–597, 854 skyline cube, 503n cluster preservation ratio (CPR). See nearest neighbor query, 594 skyline points, 503 cluster preservation ratio (CPR) serial data structure, 49 skyline query, 502–507, 503 greedy resampling, 694 set, 194n block-nested loop strategy, 503–504 Spatial Approximation tree (sa-tree), 598– set cover algorithm divide-and-conquer strategy, 503 599, 629–637, 639, 641, 643, greedy. See greedy set cover algorithm partial ordering, 506–508 858–859 shading, 197 plane-sweep methods, 504–507 ancestor neighbors, 634 SHAREPM12VERTEX, 804 preference function. See preference exact match query, 633 SHAREPM3VERTEX, 808 function incremental nearest neighbor query, shell in an object, 316 R-tree. See R-tree 634–637 shortest-path algorithm sort-first block-nested loop strategy, 503, nearest neighbor query, 650 Dijkstra. See Dijkstra’s shortest-path 505 neighbor set, 631 algorithm top-k. See top-k skyline query range query, 633–634 shortest-path map, 510 total ordering, 502–506 spatial database, xv–xvi, xix, xxii, 164, 166 shortest-path quadtree, 510 slab, 449 spatial distance, 510 shrink operation in balanced box- slice, 146 spatial indexing, 366 decomposition tree (BBD-tree), slice-and-dice, 225 spatial join query, xx, 428, 438, 465, 485 83 sliding-midpoint k-d tree, 72–74, 77, dynamic interval tree. See dynamic shuffle order, 143 764–766 interval tree sibling pointer, 108n space requirements, 74, 76–77, 766 interval tree. See interval tree sign language, 40 sliding-midpoint rule, 72 spatial k-d tree, 62, 68, 101, 464, 610n silhouette, 361 Slim-tree, 625 space requirements, 102 similar tiling, 197 Slim-down algorithm, 625 two-dimensional representative point similarity retrieval. See similarity searching Small-Tree-Large-Tree (STLT) method, rectangle representation, 464 similarity searching, xv, xvii, 164, 485, 685 297–298 point query, 464 simple QSF-tree, 465 solid modeling, xv–xvi, xix, xxii, 425 spatial network, 508, 516 simplex, 353, 353, 354n solid tile, 459 incremental nearest neighbor finding.

990 See incremental nearest neighbor squarecode, 208 symmetric structure, 317 finding SR-tree, 164, 195, 533, 569–573 spatial partitioning generalized search tree SS-tree, 561, 567–572, 622, 625, 674–675, T (SP-GiST), 188–190, 271, 590 852 (t,ε)-AVD, 581–585, 581 external methods. See external methods stabbing counting query, 434 telephonic transmission, 40 in SP-GiST interval tree. See interval tree telescoping vector. See TV-tree interface parameters. See interface segment tree. See segment tree ternary hierarchical triangular parameters in SP-GiST stabbing query, 434 decomposition, 400, 401–402 spatial range query. See window query interval tree. See interval tree tertiary structure, 435, 436 spatial sampling multidimensional segment tree. See tessellation, 237, See also polygonal tiling R-tree. See R-tree multidimensional segment tree hexagonal. See hexagonal tiling region quadtree. See region quadtree priority search tree. See priority search test-concatenation techniques, 79 spatiotemporal database, xvii, xix, 445 tree tetrahedralization sphere tree, 195, 383, 389, 567–568, 622, segment tree. See segment tree Delaunay. See Delaunay 625 two-dimensional interval tree. See tetrahedralization Spherical Pyramid Technique (SPY-TEC), two-dimensional interval tree tetrahedron, 232 587 two-dimensional segment tree. See tetrahedron table, 354 spherical triangle, 231 two-dimensional segment tree then, 744 spiral hashing, xxii, 130–131, 153, stable order, 199 Thiessen polygon. See Voronoi diagram 156–160, 187–188, 190, 774 standard deviation, 423 third normal form (3nf), 329 asymptotic analysis, 742, 875 star-vertex data structure, 355 threshold, 423 basics, 735–742, 874–875 static database, 2 TID, 208 growth factor. See growth factor static multipaging, 136 tile merging, 735, 741, 874 statistical analysis, 46 atomic. See atomic tile overflow bucket. See overflow bucket Steiner point tetrahedralization problem molecular. See molecular tile primary bucket. See primary bucket NP-complete, 353 solid. See solid tile splitting, 735 Steiner point, 262, 352–353 space. See space tile storage utilization factor. See storage STLT method. See Small-Tree-Large-Tree tile tree, 435, 435n, 438n, 473–474 utilization factor (STLT) method rectangle intersection problem, 438n spiral order, 199–202, 199, 776–778 storage utilization factor, 731 tiling spiral storage, 130. See also spiral hashing STR method. See sort-tile-recurse method adjacency number. See adjacency number split operation in balanced box- (STR method) of a tiling decomposition tree (BBD-tree), streaming, 451 hexagonal. See hexagonal tiling 83 stress, 689–690, 689 isohedral. See isohedral tiling split-and-merge segmentation algorithm, strip tree, 360, 362, 382–386, 382, 389, limited. See limited tiling 424 395, 812–813 nonpolygonal. See nonpolygonal tiling grouping step, 424 area, 385 polygonal. See polygonal tiling merge step, 424 area-area intersection, 386 regular. See regular tiling pyramid. See pyramid construction similar. See similar tiling split step, 424 bottom-up, 385 square. See square tiling split-edge lath data structure. See split-face top-down, 382, 385, 812 trapezoidal. See trapezoidal tiling lath data structure curve-area intersection, 385 triangular. See triangular tiling split-face lath data structure, 333, 336–344, curve-curve intersection, 385 uniform orientation. See uniform 797 three-dimensional, 388 orientation of a tiling split-quad data structure, 343 subSASH, 651 uniformly adjacent. See uniformly split-vertex lath data structure, 333–344, subset relation, 427 adjacent tiling 798 subsubSASH, 651 unlimited. See unlimited tiling SPLITPMNODE, 805 subsumed, 220 time-parametric rectangle, 286 splitting subsumption property, 220 time-series databases, 681–683, 685 linear hashing. See linear hashing superface algorithm, 398 TLAESA, 618, 649, 649–650 MX quadtree. See MX quadtree superkey, 50, 52, 54, 59 incremental nearest neighbor query, 650 MX-CIF quadtree. See MX-CIF quadtree surface decimation, 393–399 top-down region quadtree construction. See PR quadtree. See PR quadtree face decimation. See face decimation region quadtree spiral hashing. See spiral hashing vertex clustering. See vertex clustering top-k skyline query, 504, 505–506 splitting threshold, 75, 375, 375 vertex decimation. See vertex decimation topological entities SPY-TEC. See Spherical Pyramid surface simplification, 238, 391–399, 813 primitive. See primitive topological Technique (SPY-TEC) decimation, 392, See surface decimation entities SQUARE field geometric, 392 topological simplification. See surface node record in PM quadtree, 367 refinement, 392, 393 simplification square record topological, 392 topological sort, 243 PM quadtree, 367 SVD. See Singular Value Decomposition total grid partition, 141 square tiling, 197 (SVD)

991 total ordering, 506, 506n plane-sweep. See plane-sweep uniformly adjacent tiling, 198 skyline query. See skyline query triangulation union neighborhood graph (UNG), 642, total path length (TPL) PR quadtree. See PR quadtree 642, 860 k-d tree. See k-d tree trie, 2, 6, 142, 423, 467, 729–730 unit-segment tree, 430, 430, 434, 448 optimized point quadtree. See point k-d. See k-d trie unit-size cells quadtree quad. See quadtrie array access structure, 202–203 point quadtree. See point quadtree trie-based k-d tree, 70–87, 764–767 tree access structure, 203–204 touching rule, 261, 261, 261n trie-based quadtree, 37–47, 756–761 unlimited tiling, 197 TPR-tree, 286, 445, 488 trie-based representations, 184, 189 UP field ∗ TPR -tree, 286, 445, 488 trie-based searching methods, 2 TYPE field value edge trafficability, 260 trivial split, 72 ldnode record in layered dag, 252 training set, 60 truncated-tree pyramid, 268 TYPE field value gap transformation method, 671 TRYTOMERGEPM1, 806 ldnode record in layered dag, 252 trapezoidal tiling, 197 TRYTOMERGEPM23, 807 traveling salesman problem, 202 TR∗-tree, 303 V NP-complete, 202 TV-tree, 572, 572 V-rectangle, 449 treap, 27n, See also Cartesian tree twin grid file, 137, 137, 773 VA-file. See vector approximation file tree directory, 12, 96 two-dimensional bucket PR-CIF k-d tree, (VA-file) tree directory methods, 96–130, 165, 476–478, 480, 482 value, 743 768–773 two-dimensional interval tree, 446 VALUE field tree-based representations, 184, 189 containment query, 446 node record in one-dimensional range tree-based searching methods, 2 enclosure query, 446 tree, 15 treemap, 66, 225–226, 225, 572. See also stabbing query, 446 value-based runlength encoding, 409, 414, puzzletree; X-Y tree window query, 446 416 trellis, 449, 452 two-dimensional priority search tree, 447 VAMSplit k-d tree, 58–59, 129, 129–130, multidimensional measure problem, two-dimensional R-file, 478 186–187, 773 449–452 two-dimensional range tree, xxiii, 15–18, VAMSplit R-tree, 129–130, 130, 187, 279, 455 568, 570–571, 586 tri-cell, , 462 444, 821, 823 + triacon hierarchy, 232, 401 construction cost, 16, 18, 749 VAMSplit R -tree, 130 trial midpoint split operation in balanced range query, 16, 18, 749–750 vantage object, 688 box-decomposition tree (BBD-tree), space requirements, 16, 18, 749 vantage point, 598 84 two-dimensional representative point vantage point tree (vp-tree). See vp-tree triangle collapse, 394 rectangle representation, 463–464, variable resolution, 424 triangle decimation, 394 827 variable-resolution representation, 266 triangle inequality, 514–515, 599, 650, 658 BANG file. See BANG file Variance DFT (VDFT). See Variance triangle intersection problem, 447 PR k-d tree. See PR k-d tree Discrete Fourier Transform (VDFT) triangle measure problem, 453 PR quadtree. See PR quadtree Variance Discrete Fourier Transform triangle strip, 399 spatial k-d tree. See spatial k-d tree (VDFT), 684, 684 triangle table, 353–355, 354, 367, 584, 802 two-dimensional runlength encoding, VASCO. See Visualization and Animation triangular cell. See tri-cell 413–416, 413, 815–816 of Spatial Constructs and Operations 445 (VASCO) triangular decomposition two-dimensional segment tree, , + hierarchical 446–447 VA -file, 592, 594–597, 594 quaternary. See quaternary hierarchical containment query, 446 Karhunen-Loeve` Transform (KLT), 594, triangular decomposition enclosure query, 446 596–597 ternary. See ternary hierarchical stabbing query, 446 VDFT. See Variance Discrete Fourier triangular decomposition window query, 446 Transform (VDFT) Triangular Irregular Network (TIN), 400, two-level grid file, 132 vector approximation file (VA-file), 400 two-manifold surface, 315n, 372 592–597, 592, 854 triangular tiling, 197, 231–232 TYPE field nearest neighbor query, 594 triangulation, 262, 367 ldnode record in layered dag, 251 vector data, 366 bucket PR octree. See bucket PR octree vector octree, 367 conforming Delaunay. See conforming U vector quadtree, 367 Delaunay triangulation U order, 94, 199–202, 199, 216, 776–779 vector quantization problem, 486. See also constrained Delaunay. See constrained partial range query, 95, 768 nearest neighbor query; nearest Delaunay triangulation range query, 95 object query Delaunay. See Delaunay triangulation unambiguous boundary model, 316 VEND, 319 (DT) uniform extendible array of exponential vertex greedy. See greedy triangulation varying order (UXAE), 147n cone, 418 hierarchical uniform grid, 10, 10, 210, 393 vertex representation, 418 adaptive. See adaptive hierarchical range query, 10, 14, 749 weight. See weight of a vertex triangulation (AHT) uniform hashing, 653 vertex bucket polygon quadtree, 262, 264, minimum weight. See minimum-weight uniform orientation of a tiling, 198 376–377, 809–810 triangulation (MWT) uniform quadtree. See PR quadtree vertex clustering, 393–394

992 vertex decimation, 394–395 incremental nearest neighbor query, 330, 318, 342–345, 353, 367, 584, triangle decimation. See triangle 606–607 795–796 decimation correctness criterion, 607 explicit. See non-oriented winged-edge vertex removal. See vertex removal range query, 606–607 data structure vertex simplification. See vertex search hierarchy, 606 implicit. See oriented winged-edge data simplification vps-tree, 607 structure vertex enlargement, 263–264, 263, 790 vpsb-tree, 607–608, 608, 612, 855 non-oriented. See non-oriented winged- vertex list, 421–423, 421, 818 incremental nearest neighbor query, 608 edge data structure vertex removal, 394, 394 range query, 608 oriented. See oriented winged-edge data vertex representation, 195, 417–423, VSTART, 319 structure 817–819 winged-edge-face data structure, 319, 322, vertex. See vertex W 324, 329, 341 vertex simplification, 394–395, 394 warping process, 63 winged-edge-vertex data structure, 319, memoryless, 395 wavelets, 676 322, 324, 329, 341 optimal placement, 394 weakly edge visible polygons, 239 vertex-based object representations using weakly proximity preserving embedding, X laths, 329–346, 796–799 686 x-discriminator, 50 vertex-edge relation, 317 weight balancing, 7 x-interval, 248 vertex-edge table, 318 weight of a vertex, 418, 418 x-partition, 476 vertex-lath table, 332 weighted randomized search tree, 27n X-tree, 164, 301, 566–567, 587, 589, VERTEXEDGETABLE, 320 well-separated pair decomposition (WSPD), 595–596 vertical rectangle, 449 582, 582 nearest neighbor query, 594 very large-scale integration (VLSI), xvii, well-separation, 582 supernode, 566 WHITE xxii, 211, 260, 417, 427, 443, value X-Y tree, 66, 225–230, 225, 260, 572, 481–482 NODETYPE field 783–786. See also puzzletree; view-dependent simplification, 399 node record in MX quadtree for points, treemap visibility number, 236, 787 41 XCOORD field visible vertex, 238 node record in PR quadtree, 46 node record in point quadtree, 31 visual computing, xix WHITEBLOCKS, 816 node record in PR quadtree, 46 visualization, xviii window query, 36, 192, 428, 444, 444 point record in layered dag, 252 Visualization and Animation of Spatial balanced four-dimensional k-d tree. See point record in PM quadtree, 367 Constructs and Operations balanced four-dimensional k-d tree point record in two-dimensional range (VASCO), xviii, 271 bounded quadtree (BQT). See bounded tree, 17 VLSI. See very large-scale integration quadtree (BQT) XVAL field (VLSI) bucket PR-CIF k-d tree. See bucket TYPE field value vertex volume computation problem, 448 PR-CIF k-d tree ldnode record in layered dag, 251 volume graphics, 363 bucket rectangle PM quadtree. See bucket XXL. See Extensible and Flexible Library volume rendering, 363 rectangle PM quadtree (XXL) Voronoi cell, 346 corner stitching. See corner stitching Y Voronoi Diagram, xxii, 69, 322, 346–348, Generalized Bulk Insertion (GBI). See y-discriminator, 50 346, 350, 352–354, 367, 486, 515, Generalized Bulk Insertion (GBI) y-monotone subdivision, 69, 242 563, 566, 573–580, 598, 603, 616, hinted quadtree. See hinted quadtree y-partition, 476 623, 629–631, 633, 658n, 799, 853 iMinMax method. See iMinMax method YCOORD field approximate. See approximate Voronoi interval tree. See interval tree node record in point quadtree, 31 diagram (AVD) MX-CIF quadtree. See MX-CIF quadtree node record in PR quadtree, 46 discrete. See discrete Voronoi diagram ordered R-tree. See ordered R-tree point record in layered dag, 252 nondegenerate. See nondegenerate packed R-tree. See packed R-tree point record in PM quadtree, 367 Voronoi diagram pyramid technique. See pyramid point record in two-dimensional range R-tree. See R-tree technique tree, 17 site. See site quad list quadtree (QLQT). See quad list YSEARCH, 22 site reconstruction problem, 350, quadtree (QLQT) R-tree. See R-tree 800–802 Z representative point rectangle Voronoi graph, 629n z buffer algorithm, 236 representation. See representative Voronoi property, 630, 630, 858 Z order, 93–94, 172, 200, See also Morton point rectangle representation Voronoi region, 346 order; N order R+-tree. See R+-tree Voronoi tree, 618, 621–622, 622, 857 z+-order, 150–152, 150, 774 segment tree. See segment tree voxel, 192 zkd Btree, 93, 97, 257 two-dimensional interval tree. See vp-tree, xxiii, 555, 599, 604–614, 616, zkd tree, 93 621–622, 636n, 855 two-dimensional interval tree approximate nearest neighbor query, 607 two-dimensional segment tree. See dynamic, 605 two-dimensional segment tree incremental farthest neighbor query, 607 winged-edge data structure, xxii, 317–

993