Estimating parallel runtimes for randomized algorithms in constraint solving

This paper presents a detailed analysis of the scalability and parallelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequentia...

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Published in:	Journal of heuristics Vol. 22; no. 4; pp. 613 - 648
Main Authors:	Truchet, Charlotte, Arbelaez, Alejandro, Richoux, Florian, Codognet, Philippe
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.08.2016 Springer Nature B.V Springer Verlag
Subjects:	Algorithms Artificial Intelligence Boolean Calculus of Variations and Optimal Control; Optimization Combinatorics Computer Science Distributed, Parallel, and Cluster Computing Estimating techniques Management Science Mathematical analysis Mathematics Mathematics and Statistics Methods Operations Research Operations Research/Decision Theory Parallel processing Performance evaluation Propagation Random variables Studies Parallel processing Performance model Randomized constraint solving Constraint solving
ISSN:	1381-1231, 1572-9397
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Abstract	This paper presents a detailed analysis of the scalability and parallelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of a constraint-based Local Search solver (Adaptive Search), two SAT Local Search solvers (namely Sparrow and CCASAT), and a propagation-based constraint solver (Gecode, with a random labeling heuristic). We compare the performance predicted by our model to actual parallel implementations of those methods using up to 384 processes. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of problems, we observe that the experimented solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal. Our results show that the proposed framework estimates the runtime of the parallel algorithm with an average discrepancy of 21 % w.r.t. the empirical data across all the experiments with the maximum allowed number of processors for each technique.
AbstractList	This paper presents a detailed analysis of the scalability and par-allelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of a Constraint-Based Local Search solver (Adaptive Search), two SAT Local Search solvers (namely Sparrow and CCASAT), and a propagation-based constraint solver (Gecode, with a random labeling heuristic). We compare the performance predicted by our model to actual parallel implementations of those methods using up to 384 processes. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of problems, we observe that the experimented solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal. Our results show that the proposed framework estimates the runtime of the parallel algorithm with an average discrepancy of 21% w.r.t. the empirical data across all the experiments with the maximum allowed number of processors for each technique. This paper presents a detailed analysis of the scalability and parallelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of a constraint-based Local Search solver (Adaptive Search), two SAT Local Search solvers (namely Sparrow and CCASAT), and a propagation-based constraint solver (Gecode, with a random labeling heuristic). We compare the performance predicted by our model to actual parallel implementations of those methods using up to 384 processes. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of problems, we observe that the experimented solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal. Our results show that the proposed framework estimates the runtime of the parallel algorithm with an average discrepancy of 21 % w.r.t. the empirical data across all the experiments with the maximum allowed number of processors for each technique. This paper presents a detailed analysis of the scalability and parallelization of Local Search algorithms for constraint-based and SAT (Boolean satisfiability) solvers. We propose a framework to estimate the parallel performance of a given algorithm by analyzing the runtime behavior of its sequential version. Indeed, by approximating the runtime distribution of the sequential process with statistical methods, the runtime behavior of the parallel process can be predicted by a model based on order statistics. We apply this approach to study the parallel performance of a constraint-based Local Search solver (Adaptive Search), two SAT Local Search solvers (namely Sparrow and CCASAT), and a propagation-based constraint solver (Gecode, with a random labeling heuristic). We compare the performance predicted by our model to actual parallel implementations of those methods using up to 384 processes. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of problems, we observe that the experimented solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal. Our results show that the proposed framework estimates the runtime of the parallel algorithm with an average discrepancy of 21 % w.r.t. the empirical data across all the experiments with the maximum allowed number of processors for each technique.
Author	Truchet, Charlotte Richoux, Florian Arbelaez, Alejandro Codognet, Philippe
Author_xml	– sequence: 1 givenname: Charlotte surname: Truchet fullname: Truchet, Charlotte email: charlotte.truchet@univ-nantes.fr organization: LINA, UMR 6241, University of Nantes – sequence: 2 givenname: Alejandro surname: Arbelaez fullname: Arbelaez, Alejandro organization: INSIGHT Centre for Data Analytics, University College Cork – sequence: 3 givenname: Florian surname: Richoux fullname: Richoux, Florian organization: LINA, UMR 6241, University of Nantes – sequence: 4 givenname: Philippe surname: Codognet fullname: Codognet, Philippe organization: JFLI - CNRS / UPMC, University of Tokyo
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SubjectTerms	Algorithms Artificial Intelligence Boolean Calculus of Variations and Optimal Control; Optimization Combinatorics Computer Science Distributed, Parallel, and Cluster Computing Estimating techniques Management Science Mathematical analysis Mathematics Mathematics and Statistics Methods Operations Research Operations Research/Decision Theory Parallel processing Performance evaluation Propagation Random variables Studies
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Title	Estimating parallel runtimes for randomized algorithms in constraint solving
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