List of Algorithms 1.1 A Generic Local Search Algorithm ............................ 6 1.2 The DPLL Algorithm . ..................................... 7 1.3 The CDCL Algorithm . ..................................... 8 2.1 The General Framework of the Procedure CreateCubes ........... 39 2.2 The Procedure CreateCubes∗ with the Cutoff Mechanism . ...... 41 2.3 The Pseudo-Code of SolveCubes Using the Partition . .......... 43 3.1 Linear Search SAT-UNSAT Algorithm . ........................ 67 3.2 Linear Search UNSAT-SAT Algorithm . ........................ 68 3.3 WMSU3 Algorithm ......................................... 69 3.4 Fu-Malik for Weighted MaxSAT Algorithm . ................... 70 4.1 Pseudocode of QCDCL .....................................109 4.2 Splitting Algorithm for QBF Evaluation ........................112 5.1 The CS-SDSMT Algorithm . .................................150 5.2 An Interpolation-based Reconciliation Algorithm . ..............159 7.1 Naive Computation of the Least Model ........................241 7.2 Basic SMODELS Procedure . .................................243 7.3 Parallel Grounding on Beowulf Cluster (from [6]) . ..............248 7.4 Component Level Parallelism ................................249 7.5 Rule Level Parallelism (adapted from [68]) . ...................250 7.6 Single-Rule Level Parallelism (adapted from [68]) ...............251 7.7 Overall Structure of a Parallel Search ASP Computation ..........256 7.8 Naive Lookahead . ..........................................263 7.9 Parallel Lookahead .........................................263 7.10 GPU-ASP-Computation .................................267 7.11 Stratified Datalog Computation . ............................272 8.1 A Generic Tree Search Algorithm . ............................284 8.2 A Generic Branch-and-Bound Algorithm . ...................287 8.3 Basic Racing Algorithm .....................................309 8.4 Static Load-Balancing Algorithm . ............................310 8.5 Master (Master-Worker) .....................................312 8.6 Worker (Master-Worker) .....................................312 © Springer International Publishing AG, part of Springer Nature 2018 667 Y. Hamadi und L. Sais (eds.), Handbook of Parallel Constraint Reasoning, https://doi.org/10.1007/978-3-319-63516-3 668 Alejandro Arbelaez, Deepak Mehta, Barry O’Sullivan, and Luis Quesada 8.7 Supervisor (Supervisor-Worker) . ............................314 8.8 Worker (Supervisor-Worker) .................................315 8.9 Master (Master-Hub-Worker) .................................316 8.10 Hub Master (Master-Hub-Worker) ............................317 8.11 Worker (Master-Hub-Worker) ................................318 8.12 Self Coordination Algorithm .................................318 11.1 A* .......................................................423 11.2 Simple Parallel A* (SPA*) . .................................427 11.3 Decentralized A* with Local OPEN/CLOSED lists ..............428 12.1 Depth-First Search Algorithm ................................474 12.2 Sequential Emptiness Check for Weak TGBAs Based on DFS .....476 12.3 Nested Depth-First Search Algorithm . ........................477 12.4 SCC-Based Emptiness Check ................................480 12.5 A Parallel Search Algorithm for Checking the Emptiness of Terminal Automata .........................................482 12.6 A parallel DFS algorithm for checking emptiness of weak automata 483 12.7 CNDFS, a Multi-Core Algorithm for LTL Model Checking . .....486 12.8 Concurrent Union-Find Data Structure . ........................489 12.9 Swarmed SCC-Based Algorithm . ............................490 12.10 UFSCC Algorithm: Improved Swarmed SCC Algorithm ..........491 12.11 OWCTY Algorithm .........................................495 12.12 MAP Algorithm . ..........................................496 13.1 The BDD Algorithm and, with the BDDs x and y as Parameters . 515 13.2 The Algorithm (left) is Implemented (right) Using SPAWN, SYNC and CALL .................................................520 13.3 The Implementation of Work-Stealing Using Leapfrogging when Waiting for a Stolen Task to Finish, i.e., steal from the thief . .....522 13.4 Parallelized BDD Algorithm exists, with the BDD x and V the Cube of Variables that are Abstracted via Existential Quantification . 523 13.5 The Parallel Algorithm relnext, which Given the BDDs S (representing a set of states), R (representing a transition relation) and V (the cube of interleaved variables x ∪ x ) Computes the Set of Successor States Defined on x, i.e., ∃x: (S ∧ R) [x := x].We Assume that all Variables in R are also in V .....................524 13.6 Algorithm for Parallel find-or-insert of the Hash Table, with 512 Buckets per Region. The Variable myregion is a Thread-Specific Variable .....................................530 13.7 The cache-put Algorithm .................................532 13.8 The cache-get Algorithm .................................533 14.1 Tree Search Algorithm . .....................................552 14.2 HS-TREE ALGORITHM ....................................553 14.3 PROCESSNODE ............................................554 14.4 DIAGNOSELW: Level-Wise Parallelization . ...................563 14.5 DIAGNOSEFP: Full Parallelization ............................564 14.6 QUICKXPLAIN (QXP) .....................................567 17 Parallel Constraint-Based LS: An Application to Designing Resilient LRPON 669 14.7 MERGEXPLAIN (MXP) ....................................568 15.1 Portfolio Configuration Procedure GLOBAL ....................599 15.2 Portfolio Configuration Procedure PARHYDRA ..................600 15.3 Portfolio Configuration Procedure PARHYDRAb .................605 17.1 Iterated Constraint-Based Local Search (move-op, s) .............638 17.2 Constraint-Based Local Search (move-op, {T1,...,T|M |}).........646 17.3 Random Independent set(fcg, card)............................648 17.4 Iterated Constraint-based Parallel Local Search (move-op, t).......649 Index ω-regular language, 463 grounder, 239, 247–252 antecedent clause, 39, 109 A* search algorithm, 423, 562 Aquarius, 180, 181, 202, 207 abstraction ASlib, 591 algorithm, 295 asserting clause, 110 communication, 306 assignment cache, 121 implementation, 296 assignment tree, 103, 106, 108, 109, 113, 119 interface, 295 associative-commutative symbol, 208, 209 accepting run assumption-based reasoning, 121 definition, 464 automatic construction of parallel portfolios, lasso-shaped, 467 585, 596 accepting SCC, 468 automaton ACPP: Global, 599 Büchi, 463 ACPP: ParHydra, 600 degeneralization, 465 ACPP: parHydrab, 605 terminal, 471 adaptivity, 298 weak, 471 admissible heuristic, 424 agent-based modeling, 398 backjumping, 9, 121, 212, 246 algorithm backtrack, 8, 108, 184, 255, 339, 445, 474 abstract parallel, 308 backward contraction, 186–188, 190, 195–197, abstraction, 295 203, 205–208, 213 comparison, 326 Beowulf, 248 correctness, 290 binary decision diagram, 458, 509–541, 618, deterministic, 17, 85, 290, 304, 319 620 effectiveness, 290, 291 bisimulation, 510, 535 framework, 295, 308, 321 bisimulation minimization, 537 integration, 295 blocking, 209 parallel, 290, 326 bloqqer, 117–119, 126, 128 phase, 292 bounded expansion, 104 separation, 298 bounding, 286, 288, 299 sequential, 286, 325 branching, 8, 16, 36, 39, 51, 79, 287–289, underlying sequential, 293 319–322, 325, 340–342, 538 algorithm configuration, 596, 597 method, 288 algorithm parameters, 595 pseudocost, 299 answer set, 242 strategy, 285, 288 computation, 246, 256, 267 strong, 297 constraint, 243, 275 breadth-first search, 433, 474, 492, 553 © Springer International Publishing AG, part of Springer Nature 2018 671 Y. Hamadi und L. Sais (eds.), Handbook of Parallel Constraint Reasoning, https://doi.org/10.1007/978-3-319-63516-3 672 Index C-reduction, 183 degeneralization, 465 caching, 126, 183, 184, 473, 532 delta debugging, 131 callback, 320 dependency graph, 243, 244, 247, 249, 250, caqe, 115, 116, 118, 125 253, 265 cardinality constraints, 66 DepQBF, 115–121 CDCL, 7, 81, 103, 104, 108, 109, 212, 213, depth-first search, 8, 184, 358, 474, 487, 575 215–217 determinism, 87, 303, 304, 319, 364 CEGAR, 125, 129 deterministic parallelism CL-SDSAT, 214 strong, 304 clasp, 239, 247, 267, 270 weak, 305 claspfolio, 274 deterministic solver, 85 clausal simplification, 185, 186, 189, 206 diagnosis, 551 clause diffusion, 180, 181, 190, 202–212, 214, parallel algorithms 215 Boolean-HS-Tree, 577 clause learning, 33, 81, 108, 128, 212, 255 evaluation, 569–574 clause sharing, 16, 17, 22–24, 44, 61, 72, 81, full parallelization, 564 82, 93, 594, 598, 602, 603, 609 hybrid strategy, 575 clingo, 247 join relation, 576 column generation, 319 leading diagnoses, 574 communication protocol level-wise parallelization, 563 MPI, 307 MapReduce, 576 OpenMP, 307 node and conflict search, 567 PVM, 307 parallel random depth-first search, 575 completion procedure, 187, 192, 196, 208 parallelization strategies computational platform, see platform node processing, 559 concurrent rewriting, 192 tree decomposition, 561 configuration space, 596 window-based processing, 560, 562 conflict, 81, 245, 267–270, 552 distributed fairness, 206, 207 analysis, 121, 269, 289 distributed global contraction, 206, 207 graph, 289 distributed proof reconstruction, 206, 207 MERGEXPLAIN, 568 distributed search, 93, 191, 198, 202, 203, 206, QUICKXPLAIN, 567 208–211, 213, 215, 217 search algorithms, 566–567 distributed-memory algorithms, 9, 257, 315, conflict clause, 35, 39, 50,