Generic Exact Combinatorial Search at HPC Scale

Exact combinatorial search is essential to a wide range of important applications, and there are many large problems that need to be solved quickly. Searches are extremely challenging to parallelise due to a combination of factors, e.g. searches are non-deterministic, dynamic pruning changes the wor...

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Veröffentlicht in:	International journal of parallel programming Jg. 51; H. 1; S. 83 - 106
Hauptverfasser:	MacGregor, Ruairidh, Archibald, Blair, Trinder, Phil
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.02.2023 Springer Nature B.V
Schlagworte:	C plus plus C++ (programming language) Combinatorial analysis Computer Science Enumeration Graphs Nodes Optimization Processor Architectures Pruning Searching Software Engineering/Programming and Operating Systems Special Issue on High-Level Parallel Programming and Applications (HLPP 2022) Theory of Computation Workload Workloads Combinatorial search Parallel skeletons High performance computing Constraint programming
ISSN:	0885-7458, 1573-7640
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Abstract	Exact combinatorial search is essential to a wide range of important applications, and there are many large problems that need to be solved quickly. Searches are extremely challenging to parallelise due to a combination of factors, e.g. searches are non-deterministic, dynamic pruning changes the workload, and search tasks have very different runtimes. YewPar is a C++/HPX framework that generalises parallel search by providing a range of sophisticated search skeletons.This paper demonstrates generic high performance combinatorial search, i.e. that a variety of exact combinatorial searches can be easily parallelised for HPC using YewPar. We present a new mechanism for profiling key aspects of YewPar parallel combinatorial search, and demonstrate its value. We exhibit, for the first time, generic exact combinatorial searches at HPC scale. We baseline YewPar against state-of-the-art sequential C++ and C++/OpenMP implementations. We demonstrate that deploying YewPar on an HPC system can dramatically reduce the runtime of large problems, e.g. from days to just 100s. The maximum relative speedups we achieve for an enumeration search are near-linear up to 195(6825) compute-nodes(workers), super-linear for an optimisation search on up to 128(4480) (pruning reduces the workload), and sub-linear for decision searches on up to 64(2240) compute-nodes(workers).
AbstractList	Exact combinatorial search is essential to a wide range of important applications, and there are many large problems that need to be solved quickly. Searches are extremely challenging to parallelise due to a combination of factors, e.g. searches are non-deterministic, dynamic pruning changes the workload, and search tasks have very different runtimes. YewPar is a C++/HPX framework that generalises parallel search by providing a range of sophisticated search skeletons.This paper demonstrates generic high performance combinatorial search, i.e. that a variety of exact combinatorial searches can be easily parallelised for HPC using YewPar. We present a new mechanism for profiling key aspects of YewPar parallel combinatorial search, and demonstrate its value. We exhibit, for the first time, generic exact combinatorial searches at HPC scale. We baseline YewPar against state-of-the-art sequential C++ and C++/OpenMP implementations. We demonstrate that deploying YewPar on an HPC system can dramatically reduce the runtime of large problems, e.g. from days to just 100s. The maximum relative speedups we achieve for an enumeration search are near-linear up to 195(6825) compute-nodes(workers), super-linear for an optimisation search on up to 128(4480) (pruning reduces the workload), and sub-linear for decision searches on up to 64(2240) compute-nodes(workers). Exact combinatorial search is essential to a wide range of important applications, and there are many large problems that need to be solved quickly. Searches are extremely challenging to parallelise due to a combination of factors, e.g. searches are non-deterministic, dynamic pruning changes the workload, and search tasks have very different runtimes. YewPar is a C++/HPX framework that generalises parallel search by providing a range of sophisticated search skeletons.This paper demonstrates generic high performance combinatorial search, i.e. that a variety of exact combinatorial searches can be easily parallelised for HPC using YewPar. We present a new mechanism for profiling key aspects of YewPar parallel combinatorial search, and demonstrate its value. We exhibit, for the first time, generic exact combinatorial searches at HPC scale. We baseline YewPar against state-of-the-art sequential C++ and C++/OpenMP implementations. We demonstrate that deploying YewPar on an HPC system can dramatically reduce the runtime of large problems, e.g. from days to just 100s. The maximum relative speedups we achieve for an enumeration search are near-linear up to 195(6825) compute-nodes(workers), super-linear for an optimisation search on up to 128(4480) (pruning reduces the workload), and sub-linear for decision searches on up to 64(2240) compute-nodes(workers).
Author	MacGregor, Ruairidh Trinder, Phil Archibald, Blair
Author_xml	– sequence: 1 givenname: Ruairidh surname: MacGregor fullname: MacGregor, Ruairidh organization: School of Computing Science, University of Glasgow – sequence: 2 givenname: Blair surname: Archibald fullname: Archibald, Blair email: blair.archibald@glasgow.ac.uk organization: School of Computing Science, University of Glasgow – sequence: 3 givenname: Phil surname: Trinder fullname: Trinder, Phil organization: School of Computing Science, University of Glasgow
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Cites_doi	10.1145/3107239 10.1007/BF01098364 10.1090/mcom/3075 10.5281/zenodo.4270336 10.1145/2742359 10.1016/j.jpdc.2014.09.007 10.1007/978-3-642-40627-0_45 10.1090/dimacs/026 10.1007/978-3-030-51372-6_19 10.1007/978-3-030-49432-2_3 10.1007/3-540-45706-2_132 10.3390/a6040618 10.1007/978-3-540-72521-3_18 10.1007/978-3-030-19212-9_2 10.3390/a5040545 10.1145/2676870.2676883 10.1145/3332466.3374537 10.1007/s10766-015-0356-7 10.1613/jair.5456 10.48550/ARXIV.2207.06902
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References	Alba, E., et al.: MALLBA: a library of skeletons for combinatorial optimisation. In: Euro-Par, Paderborn, Germany, August, 2002, Proceedings (2002) Galea, F., Le Cun, B.: Bob++: a framework for exact combinatorial optimization methods on parallel machines. In: International Conference High Performance Computing and Simulation (HPCS) (2007) Knizikevičius, I., Trinder, P., Archibald, B., Yan, J.: Parallel Flowshop in YewPar. arXiv preprint arXiv:2207.06902 (2022) McCreeshCProsserPThe shape of the search tree for the maximum clique problem and the implications for parallel branch and boundTOPC201510.1145/27423591328.90127 OttenLDechterRAND/OR branch-and-bound on a computational gridJ. Artif. Intell. Res.20175935143510.1613/jair.54561418.68189 Archibald, B., et al.: Sequential and parallel solution-biased search for subgraph algorithms. In: CPAIOR 16th Thessaloniki, Greece, June 2019 (2019) Knizikevičius, I., Trinder, P., Archibald, B., Yan, J.: Parallel flowshop in YewPar (2022). https://doi.org/10.48550/ARXIV.2207.06902 Régin, J., Rezgui, M., Malapert, A.: Embarrassingly parallel search. In: Schulte, C. (ed.) Principles and Practice of Constraint Programming—19th International Conference, CP 2013, Uppsala, Sweden, Sept 16–20, vol. 8124, pp. 596–610. Springer, Berlin (2013). https://doi.org/10.1007/978-3-642-40627-0_45 KehrerSBlochingerWFergusonDMuñozVMPahlCHelfertMDevelopment and operation of elastic parallel tree search applications using TASKWORKCloud Computing and Services Science–9th International Conference, CLOSER 2019, Heraklion, Crete, Greece, May 2–4, 2019, Revised Selected Papers. Communications in Computer and Information Science2019BerlinSpringer426510.1007/978-3-030-49432-2_3 MenouerTMixing static and dynamic partitioning to parallelize a constraint programming solverInt. J. Parallel Program.201610.1007/s10766-015-0356-7 Johnson, D.J., Trick, M.A. (eds.): Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October, 1993. American Mathematical Society (1996) Archibald, B., et al.: YewPar: skeletons for exact combinatorial search. In: PPoPP’20:, San Diego, California, USA, February, 2020. ACM (2020) FromentinJHivertFExploring the tree of numerical semigroupsAm. Math. Comput.2016853012553256810.1090/mcom/30751344.20075 Maher, S.J., Ralphs, T.K., Shinano, Y.: Assessing the effectiveness of (parallel) branch-and-bound algorithms. arXiv preprint arXiv:2104.10025 (2021) The GAP Group: GAP - Groups, Algorithms, and Programming, Version 4.8.7 (2017), https://www.gap-system.org/Releases/4.8.7.html Archibald, B.: Skeletons for Exact Combinatorial Search at Scale. Ph.D. thesis, University of Glasgow (2018) http://theses.gla.ac.uk/id/eprint/31000 KleinAStormeLApplications of finite geometry in coding theory and cryptographyInf. Secur. Cod. Theory Rel. Comb.20112938581366.94509 HeuleMJHKullmannOThe science of brute forceCommun. ACM2017608707910.1145/3107239 McCreesh, C.: Sequential MCsa1 Maximum Clique Implementation (2018). https://github.com/ciaranm/sicsa-multicore-challenge-iii/c++ PietracaprinaASpace-efficient parallel algorithms for combinatorial search problemsJ. Parallel Distrib. Comput.201576586510.1016/j.jpdc.2014.09.007 PardalosPXueJThe maximum clique problemJ. Global Optim.1994430132810.1007/BF010983640797.90108 BarucciVMaximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains1997ProvidenceAmerican Mathematical Society0868.13003 ProsserPExact algorithms for maximum clique: a computational studyAlgorithms201210.3390/a50405451461.90162 Kaiser, H., et al.: HPX: A Task Based Programming Model in a Global Address Space. In: ICPGASPM 2014, Eugene, OR, USA, Oct. 2014 (2014) McCreesh, C., Prosser, P., Trimble, J.: The glasgow subgraph solver: Using constraint programming to tackle hard subgraph isomorphism problem variants. In: Gadducci, F., Kehrer, T. (eds.) Graph Transformation—13th International Conference, ICGT 2020, Held as Part of STAF 2020, Bergen, Norway, June 25–26, 2020, Proceedings. Lecture Notes in Computer Science, vol. 12150, pp. 316–324. Springer, Berlin (2020). https://doi.org/10.1007/978-3-030-51372-6_19 ArchibaldBMaierPStewartRTrinderPImplementing YewPar: A Framework for Parallel Tree Search2019GottingenEuro-Par Poldner, M., Kuchen, H.: Algorithmic skeletons for branch & bound. In: ICSOFT, Setúbal, Portugal, Sept. 2006 (2006) Olivier, S., Huan, J., Liu, J., Prins, J., Dinan, J., Sadayappan, P., Tseng, C.W.: UTS: an unbalanced tree search benchmark. In: International Workshop on Languages and Compilers for Parallel Computing, pp. 235–250. 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References_xml	– reference: McCreeshCProsserPMulti-threading a state-of-the-art maximum clique algorithmAlgorithms20136461863510.3390/a60406181461.05215 – reference: McCreeshCProsserPThe shape of the search tree for the maximum clique problem and the implications for parallel branch and boundTOPC201510.1145/27423591328.90127 – reference: Kaiser, H., et al.: HPX: A Task Based Programming Model in a Global Address Space. In: ICPGASPM 2014, Eugene, OR, USA, Oct. 2014 (2014) – reference: KehrerSBlochingerWFergusonDMuñozVMPahlCHelfertMDevelopment and operation of elastic parallel tree search applications using TASKWORKCloud Computing and Services Science–9th International Conference, CLOSER 2019, Heraklion, Crete, Greece, May 2–4, 2019, Revised Selected Papers. Communications in Computer and Information Science2019BerlinSpringer426510.1007/978-3-030-49432-2_3 – reference: Knizikevičius, I., Trinder, P., Archibald, B., Yan, J.: Parallel flowshop in YewPar (2022). https://doi.org/10.48550/ARXIV.2207.06902 – reference: BarucciVMaximality Properties in Numerical Semigroups and Applications to One-Dimensional Analytically Irreducible Local Domains1997ProvidenceAmerican Mathematical Society0868.13003 – reference: MenouerTMixing static and dynamic partitioning to parallelize a constraint programming solverInt. J. Parallel Program.201610.1007/s10766-015-0356-7 – reference: Archibald, B., et al.: Sequential and parallel solution-biased search for subgraph algorithms. In: CPAIOR 16th Thessaloniki, Greece, June 2019 (2019) – reference: HeuleMJHKullmannOThe science of brute forceCommun. ACM2017608707910.1145/3107239 – reference: Maher, S.J., Ralphs, T.K., Shinano, Y.: Assessing the effectiveness of (parallel) branch-and-bound algorithms. arXiv preprint arXiv:2104.10025 (2021) – reference: PardalosPXueJThe maximum clique problemJ. Global Optim.1994430132810.1007/BF010983640797.90108 – reference: FromentinJHivertFExploring the tree of numerical semigroupsAm. Math. Comput.2016853012553256810.1090/mcom/30751344.20075 – reference: Johnson, D.J., Trick, M.A. (eds.): Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October, 1993. American Mathematical Society (1996) – reference: KleinAStormeLApplications of finite geometry in coding theory and cryptographyInf. Secur. Cod. Theory Rel. Comb.20112938581366.94509 – reference: McCreesh, C.: Solving hard subgraph problems in parallel. Ph.D. thesis, University of Glasgow (2017) – reference: Archibald, B.: Skeletons for Exact Combinatorial Search at Scale. 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Snippet	Exact combinatorial search is essential to a wide range of important applications, and there are many large problems that need to be solved quickly. Searches...
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SubjectTerms	C plus plus C++ (programming language) Combinatorial analysis Computer Science Enumeration Graphs Nodes Optimization Processor Architectures Pruning Searching Software Engineering/Programming and Operating Systems Special Issue on High-Level Parallel Programming and Applications (HLPP 2022) Theory of Computation Workload Workloads
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Title	Generic Exact Combinatorial Search at HPC Scale
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