<p>ddd d d </p><p>¨<br>INSTITUT FUR INFORMATIK </p><p>d d d d </p><ul style="display: flex;"><li style="flex:1">d</li><li style="flex:1">d</li></ul><p>d d d d d d d </p><p></p><ul style="display: flex;"><li style="flex:1">¨</li><li style="flex:1">¨</li></ul><p></p><p>d d </p><p>DER TECHNISCHEN UNIVERSITAT MUNCHEN </p><p>Advanced Concepts and Applications of the UB-Tree </p><p>Robert Josef Widhopf-Fenk </p><p>Institut fu¨r Informatik der Technischen Universit¨at Mu¨nchen </p><p>Advanced Concepts and Applications of the UB-Tree </p><p>Robert Josef&nbsp;Widhopf-Fenk </p><p>Vollsta¨ndiger Abdruck der von der Fakult¨at fu¨r Informatik der Technischen Universit¨at Mu¨nchen zur Erlangung des akademischen Grades eines </p><p>Doktors der Naturwissenschaften </p><p>genehmigten Dissertation. </p><ul style="display: flex;"><li style="flex:1">Vorsitzende: </li><li style="flex:1">Univ.-Prof. G. J. Klinker, Ph.D. </li></ul><p>Pru¨fer der Dissertation:&nbsp;1. Univ.-Prof.&nbsp;R. Bayer, Ph.D., emeritiert <br>2. Univ.-Prof.&nbsp;A. Kemper, Ph.D. </p><p>Die Dissertation wurde am 05.08.2004 bei der Technischen Universita¨t Mu¨nchen eingereicht und durch die Fakult¨at fu¨r Informatik am 07.02.2005 angenommen. </p><p>Acknowledgements </p><p>First of all, I want to thank my supervisor Rudolf Bayer for his advice, guidance, support, and patience.&nbsp;Without his invitation to be a Ph.D. student, I would have never been working on database research. <br>I owe my former colleagues in the MISTRAL project many thanks for fruitful discussions, proofreading, inspirations, and motivating me: Volker Markl, Frank Ramsak, Martin Zirkel and our “external” member Roland Pieringer. <br>I like to thank my students, Oliver Nickel, Chris Hodges and Werner Unterhofer contributing to this work by supporting the implementation of algorithms and performing experiments. <br>Special thanks to our project partners at TransAction, Teijin, GfK, and the members of the EDITH project. <br>And last but not least, many thanks to Michael Bauer, Bernd Reiner, and Charlie Hahn for discussions, distraction and small talk.&nbsp;Specifically: to&nbsp;Charlie for the ice cream; to Alex S. for the Gauloise; to Evi Kollmann for all your help, even when you were loaded with other work you always were at hand. Also thanks to everyone I accidently forgot. </p><p>To my love Birgit for your patience, for our children Matilda and Valentin, and for going through this with me! </p><p>Abstract </p><p>The UB-Tree is an index structure for multidimensional point data.&nbsp;By name, it claims to be universal, but this imposes a huge burden, as there are few things which really prove to be universal. This thesis takes a closer look at aspects where the UB-Tree is not universal at a first glance. <br>The first aspect is the discussion of space filling curves (SFC), in particular comparing the Z-curve and the Hilbert-curve.&nbsp;The Z-curve is used to cluster data indexed by the UB-Tree and we highlight its advantages in comparison to other SFCs. While the Hilbertcurve provides better clustering, the Z-curve is superior w.r. to other metrics, i.e., it is significantly more efficient to calculate addresses and the mapping of queries to SFC- segments, and it is able to space efficiently index arbitrary universes. Thus the Z-curve is more universal here. <br>The second aspect are bulk operations on UB-Trees.&nbsp;Especially for data warehousing the bulk insertion and deletion are crucial operations.&nbsp;We present efficient algorithms for incremental insertion and deletion. <br>The third aspect is the comparison of the UB-Tree with bitmap indexes used for an example data warehousing application.&nbsp;We show how performance of bitmap indexes is increased by clustering the base table according to a SFC. Still the UB-Tree proves to be superior. <br>The fourth aspect is the efficient management of data with skewed data distributions. <br>The UB-Tree adapts its partitioning to the actual data distribution, but in comparison to the R-Tree, it suffers from being not able to prune search path leading to unpopulated space (= dead space).&nbsp;This is caused by partitioning the complete universe with separators. We&nbsp;present a novel index structure, the bounding UB-Tree&nbsp;(BUB-Tree), which is a variant of the UB-Tree inheriting its worst case guarantees for the basic operations while efficiently addressing queries on dead space.&nbsp;In comparison to R-Trees, its query performance is similar while offering superior maintenance performance and logarithmic worst case guarantees, thus being more universal than the R<sup style="top: -0.3616em;">∗</sup>-Tree. <br>The last aspect addressed in this thesis is the management of spatial data.&nbsp;The UB-Tree is an index designed for point data, however also spatial objects can be indexed efficiently with it by mapping them to higher dimensional points.&nbsp;We discuss different mapping methods and their performance in comparison to the RI-Tree and R<sup style="top: -0.3615em;">∗</sup>-Tree. </p><p>Our conclusion: The UB-Tree comes closer to being an universal index than any other competing index structure.&nbsp;It is flexible, dynamic, relatively easy to integrate into a DBMS kernel, and provides logarithmic worst case guarantees for the basic operations of insertion, deletion, and update.&nbsp;By extending its concepts to the BUB-Tree it is also able to efficiently support skewed queries on skewed data distributions. </p><p>Contents </p><p></p><ul style="display: flex;"><li style="flex:1">Preface </li><li style="flex:1">1</li></ul><p></p><ul style="display: flex;"><li style="flex:1">1 Introduction </li><li style="flex:1">3</li></ul><p></p><p>344555667778<br>1.1 The&nbsp;Objective: Getting Information Fast&nbsp;. . . . . . . . . . . . . . . . . . . 1.2 The&nbsp;Problem: The Properties of Real World Data&nbsp;. . . . . . . . . . . . . . <br>1.2.1 Complex&nbsp;Structure .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Skewed&nbsp;Data Distribution&nbsp;. . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Huge&nbsp;Data Amounts&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Continuous&nbsp;Change . . . . . . . . . . . . . . . . . . . . . . . . . . . <br>1.3 The&nbsp;Solution: Multidimensional Access Methods . . . . . . . . . . . . . . . 1.4 Objective&nbsp;and Outline of this Thesis&nbsp;. . . . . . . . . . . . . . . . . . . . . 1.5 Related&nbsp;Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . <br>1.5.1 RDBMSs .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Multidimensional&nbsp;Access Methods . . . . . . . . . . . . . . . . . . . <br>1.6 The&nbsp;MISTRAL Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </p><p></p><ul style="display: flex;"><li style="flex:1">2 Terminology&nbsp;and Basic Concepts </li><li style="flex:1">11 </li></ul><p></p><p>2.1 General&nbsp;Notation .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;11 <br>2.1.1 Tuple,&nbsp;Relation, Universe .&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;12 2.1.2 Query,&nbsp;Result Set, and Selectivity&nbsp;. . . . . . . . . . . . . . . . . . .&nbsp;14 <br>2.2 Storage&nbsp;Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;15 2.3 Caching&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;21 2.4 Clustering&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;21 2.5 Access&nbsp;Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;24 <br>2.5.1 Clustering&nbsp;Index, Primary Index, Secondary Index .&nbsp;. . . . . . . . .&nbsp;24 2.5.2 Address&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;25 2.5.3 Accessed&nbsp;Data .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;26 </p><p></p><ul style="display: flex;"><li style="flex:1">3 Space-filling&nbsp;Curves </li><li style="flex:1">29 </li></ul><p></p><p>3.1 Space&nbsp;Filling Curves&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;31 <br>3.1.1 Compound&nbsp;Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;32 3.1.2 Snake-Curve&nbsp;and Zig-Zag-Curve . . . . . . . . . . . . . . . . . . . .&nbsp;33 3.1.3 Fractal&nbsp;Curves .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;33 </p><p>iii iv </p><p>CONTENTS </p><p>3.1.4 Curves&nbsp;created by order preserving Bit-Permutations&nbsp;. . . . . . . .&nbsp;39 <br>3.2 Indexing&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;40 <br>3.2.1 Address&nbsp;calculations .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;41 3.2.2 Indexing&nbsp;a Space Filling Curve&nbsp;. . . . . . . . . . . . . . . . . . . .&nbsp;44 3.2.3 SFC&nbsp;Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;46 <br>3.3 Related&nbsp;Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;49 <br>3.3.1 [Jag90a]&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;52 3.3.2 [MJF<sup style="top: -0.3615em;">+</sup>01] .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;53 3.3.3 [HW02]&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;54 3.3.4 [MAK02]&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;54 3.3.5 [Law00]&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;55 3.3.6 Summary&nbsp;of Related Work . . . . . . . . . . . . . . . . . . . . . . .&nbsp;57 <br>3.4 Comparison&nbsp;of SFC Properties .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;58 <br>3.4.1 Region&nbsp;Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;59 3.4.2 Summary&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;60 </p><p></p><ul style="display: flex;"><li style="flex:1">4 The&nbsp;UB-Tree </li><li style="flex:1">63 </li></ul><p></p><p>4.1 Basic&nbsp;Concepts of UB-Trees&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;63 <br>4.1.1 Z-regions&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;64 4.1.2 Range&nbsp;Query Processing&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;66 <br>4.2 UB-Tree&nbsp;Implementations .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;66 <br>4.2.1 UBAPI&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;67 </p><ul style="display: flex;"><li style="flex:1">4.2.2 Transbase </li><li style="flex:1">Hypercube . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;68 </li></ul><p>4.2.3 RFDBMS&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;68 4.2.4 Summary&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;69 <br>4.3 Bulk&nbsp;Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;71 <br>4.3.1 Introduction&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;71 4.3.2 General&nbsp;Problem Description&nbsp;. . . . . . . . . . . . . . . . . . . . .&nbsp;72 4.3.3 Algorithms .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;73 4.3.4 DBMS-Kernel&nbsp;Integration .&nbsp;. . . . . . . . . . . . . . . . . . . . . .&nbsp;78 4.3.5 Performance&nbsp;Analysis .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;78 4.3.6 Performance&nbsp;Evaluation .&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;80 4.3.7 Conclusion&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;87 <br>4.4 Bulk&nbsp;Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;87 <br>4.4.1 Related&nbsp;Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;88 4.4.2 Algorithm&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;88 4.4.3 Analysis&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;92 <br>4.5 Summary .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;93 </p><p></p><ul style="display: flex;"><li style="flex:1">5 Bitmap-Indexes&nbsp;on Clustered Data </li><li style="flex:1">95 </li></ul><p></p><p>5.1 Introduction&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;96 <br>5.1.1 Encoding&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;96 5.1.2 Query&nbsp;Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;98 </p><p>CONTENTS </p><p>v<br>5.1.3 Compression&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;99 5.1.4 Maintenance&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;101 <br>5.2 Bitmaps&nbsp;on clustered data&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;102 5.3 Evaluation&nbsp;with the GfK DWH&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;103 <br>5.3.1 Maintenance&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;103 5.3.2 Query&nbsp;Performance . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;110 <br>5.4 Summary .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;121 5.5 Multi-User&nbsp;environments . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;122 </p><p></p><ul style="display: flex;"><li style="flex:1">6 The&nbsp;BUB-Tree </li><li style="flex:1">123 </li></ul><p></p><p>6.1 Introduction&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;123 6.2 Related&nbsp;Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;124 6.3 BUB-Tree&nbsp;regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;125 6.4 Point&nbsp;Query . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;128 6.5 Insertion&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;129 6.6 Page&nbsp;Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;130 6.7 Deletion&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;133 6.8 Range&nbsp;Queries .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;133 6.9 Bulk&nbsp;Insertion and Bulk Deletion&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;136 <br>6.9.1 Initial&nbsp;Bulk Loading&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;136 6.9.2 Incremental&nbsp;Bulk Loading&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;136 6.9.3 Bulk&nbsp;Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;137 <br>6.10 Reorganization&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;137 <br>6.10.1 Tightening&nbsp;Bounds .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;138 6.10.2 Optimizing&nbsp;the Index Coverage&nbsp;. . . . . . . . . . . . . . . . . . . .&nbsp;138 6.10.3 Increasing&nbsp;the Page Utilization&nbsp;. . . . . . . . . . . . . . . . . . . .&nbsp;139 <br>6.11 Implementation-Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;139 6.12 Comparison&nbsp;of BUB-Tree and R-Tree&nbsp;. . . . . . . . . . . . . . . . . . . . .&nbsp;141 <br>6.12.1 Related&nbsp;Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;142 6.12.2 {R}-Tree coverage&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;143 6.12.3 Bounding&nbsp;Technique .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;143 6.12.4 Supported&nbsp;Data Types&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;144 6.12.5 Dimensionality&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;144 6.12.6 Multi-User&nbsp;Support . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;144 6.12.7 Page&nbsp;Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;144 6.12.8 Index&nbsp;Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;145 6.12.9 Maintenance&nbsp;Performance .&nbsp;. . . . . . . . . . . . . . . . . . . . . .&nbsp;145 6.12.10Query Performance&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;147 <br>6.13 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;148 <br>6.13.1 Random&nbsp;insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;149 6.13.2 Bulk&nbsp;Loading .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;155 6.13.3 Query&nbsp;Procession . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;166 6.13.4 Point&nbsp;Queries .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;168 6.13.5 Random&nbsp;Range Queries&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;171 6.13.6 Street&nbsp;Section Queries&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;173 <br>6.14 Summary&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;175 </p><p></p><ul style="display: flex;"><li style="flex:1">7 Management&nbsp;of Spatial Objects </li><li style="flex:1">177 </li></ul><p></p><p>7.1 Related&nbsp;Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;178 <br>7.1.1 RDBMS&nbsp;Implementations .&nbsp;. . . . . . . . . . . . . . . . . . . . . .&nbsp;178 7.1.2 Interval&nbsp;Indexing .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;179 7.1.3 Sub-Cube&nbsp;Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;181 7.1.4 Previous&nbsp;UB-Tree based solutions&nbsp;. . . . . . . . . . . . . . . . . . .&nbsp;181 <br>7.2 Mapping&nbsp;Methods .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;181 <br>7.2.1 Approximation&nbsp;by a MBB&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;181 7.2.2 Approximation&nbsp;by SFC-segments&nbsp;. . . . . . . . . . . . . . . . . . .&nbsp;186 7.2.3 Indexing&nbsp;the Parameter Space&nbsp;. . . . . . . . . . . . . . . . . . . . .&nbsp;188 <br>7.3 Experiments:&nbsp;Interval Data&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;189 <br>7.3.1 Artificial&nbsp;Interval Data Sets&nbsp;. . . . . . . . . . . . . . . . . . . . . .&nbsp;189 7.3.2 Artificial&nbsp;Interval Query Sets .&nbsp;. . . . . . . . . . . . . . . . . . . . .&nbsp;190 7.3.3 Interval&nbsp;Index Structures . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;191 7.3.4 Qualitative&nbsp;Comparison of Interval-Index Structures .&nbsp;. . . . . . . .&nbsp;191 7.3.5 Interval&nbsp;Measurement Results&nbsp;. . . . . . . . . . . . . . . . . . . . .&nbsp;192 7.3.6 Clustering&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;195 7.3.7 Real&nbsp;World Data&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;198 7.3.8 GEO&nbsp;Data .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;201 7.3.9 Endpoint&nbsp;Transformation .&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;201 7.3.10 Comparison&nbsp;of Point-Transformation Variants&nbsp;. . . . . . . . . . . .&nbsp;204 7.3.11 Approximation&nbsp;by SFC-segments&nbsp;. . . . . . . . . . . . . . . . . . .&nbsp;204 <br>7.4 Summary .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;205 </p><p></p><ul style="display: flex;"><li style="flex:1">8 Summary </li><li style="flex:1">207 </li></ul><p></p><p>8.1 Conclusion&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;208 </p><p></p><ul style="display: flex;"><li style="flex:1">A Description&nbsp;of the Test System </li><li style="flex:1">209 </li></ul><p></p><p>A.1 System&nbsp;Sunbayer69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;209 A.2 System&nbsp;Sunwibas0 .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;209 A.3 System&nbsp;Atmistral7 .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;210 </p><p></p><ul style="display: flex;"><li style="flex:1">B Real&nbsp;World Data Sets </li><li style="flex:1">211 </li></ul><p></p><p>B.1 GfK&nbsp;Datawarehouse .&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;211 B.2 GEO&nbsp;Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;220 </p><p>C Measures&nbsp;of RFDBMS Bibliography <br>224 239 </p><p>List of Figures </p><p>2.1 Example&nbsp;for a two dimensional Universe and Queries on it&nbsp;. . . . . . . . .&nbsp;15 2.2 Physical&nbsp;Structure of a Hard-Disk&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;18 2.3 Percentage&nbsp;of Positioning Cost with growing Page Size&nbsp;. . . . . . . . . . .&nbsp;19 2.4 Random&nbsp;and sequential Access Times on different Hardware Configurations&nbsp;20 2.5 Different&nbsp;Types of Clustering for Lexical Order and the Interval Query [c, f] 23 </p><p>2.6 Clustering Page-Based Index vs. Secondary Index&nbsp;. . . . . . . . . . . . . .&nbsp;25 </p><p>2.7 Range&nbsp;Query and actually affected Area of the Universe .&nbsp;. . . . . . . . . .&nbsp;27 3.1 Simple&nbsp;SFCs for 8x8 universe with range query .&nbsp;. . . . . . . . . . . . . . .&nbsp;29 3.2 Example&nbsp;relations of ∆<sub style="top: 0.1494em;">M </sub>to ∆<sub style="top: 0.1494em;">S </sub>. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;31 3.3 Universe,&nbsp;quad tree partitioning, and address .&nbsp;. . . . . . . . . . . . . . . .&nbsp;34 3.4 Z-curve&nbsp;for 8x8 universe&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;35 3.5 bit-interleaving&nbsp;for dimensions with differing domains&nbsp;. . . . . . . . . . . .&nbsp;37 3.6 Hilbert-curve&nbsp;for 8x8 universe&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;37 3.7 Hilbert-curve&nbsp;indexing an universe with differing dimension cardinalities .&nbsp;. 38 3.8 Gray-Code-curve&nbsp;for 8x8 universe&nbsp;. . . . . . . . . . . . . . . . . . . . . . .&nbsp;40 3.9 Brother-father-search&nbsp;with Z-curve&nbsp;. . . . . . . . . . . . . . . . . . . . . .&nbsp;43 3.10 Cost&nbsp;of post filtering vs. NJI/NJO calculation&nbsp;. . . . . . . . . . . . . . . .&nbsp;48 3.11 Space&nbsp;partitioning for Z- and Hilbert-curve . . . . . . . . . . . . . . . . . .&nbsp;50 3.12 B-Tree&nbsp;traversal: Page accesses&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;51 3.13 Percentage&nbsp;of segments in SFCs&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;56 3.14 SFC-Regions&nbsp;consisting of disjoint areas in Ω .&nbsp;. . . . . . . . . . . . . . . .&nbsp;60 </p><p>4.1 A&nbsp;UB-Tree Partitioning the World into Z-regions&nbsp;. . . . . . . . . . . . . .&nbsp;64 4.2 Z-regions&nbsp;of a UB-Tree for a given Data Distribution&nbsp;. . . . . . . . . . . .&nbsp;66 4.3 A&nbsp;Bulk Loading Architecture for one dimensional clustering Indexes&nbsp;. . . .&nbsp;73 4.4 Estimated&nbsp;Number of Page Reads and Writes&nbsp;. . . . . . . . . . . . . . . .&nbsp;79 4.5 Changes&nbsp;of UB-Tree Space Partitioning during Incremental Loading&nbsp;. . . .&nbsp;80 4.6 The&nbsp;Bulk Loading Architecture as implemented for UB-Trees .&nbsp;. . . . . . .&nbsp;81 4.7 Data&nbsp;Distribution and Times for Copying resp. Pipe-Lining .&nbsp;. . . . . . . .&nbsp;83 4.8 Address&nbsp;Calculation, Sorting and Loading Performance for GfK DWH .&nbsp;. .&nbsp;83 4.9 Page&nbsp;Statistics for Bulk Loading of GfK DWH&nbsp;. . . . . . . . . . . . . . . .&nbsp;86 4.10 Deleting&nbsp;and Freeing Subtrees&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;91 </p><p>vii viii </p><p>LIST OF FIGURES </p><p>5.1 Query&nbsp;Processing with Bitmap Indexes&nbsp;. . . . . . . . . . . . . . . . . . . .&nbsp;98 5.2 RLE&nbsp;Bitmap Compression&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;100 5.3 Cost&nbsp;for Address Calculation and Sorting .&nbsp;. . . . . . . . . . . . . . . . . .&nbsp;105 5.4 Maintenance&nbsp;Cost for Bitmap Indexesc&nbsp;. . . . . . . . . . . . . . . . . . . .&nbsp;107 5.5 Bitmaps&nbsp;mapped to Images&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;108 5.6 Overall&nbsp;Maintenance Cost&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;110 5.7 PG SERIES: Result Size . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;111 5.8 PG SERIES: Elapsed Time&nbsp;. . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;114 5.9 PG SERIES: Page Accesses w.r. to Query&nbsp;. . . . . . . . . . . . . . . . . .&nbsp;116 5.10 Time&nbsp;per Logical Page Accesses&nbsp;. . . . . . . . . . . . . . . . . . . . . . . .&nbsp;117 5.11 PG SERIES: Page Accesses w.r. to Result Set Size&nbsp;. . . . . . . . . . . . .&nbsp;118 5.12 PG SERIES Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;119 5.13 2Y PG SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .&nbsp;120 </p>