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Estimating parallel runtimes for randomized algorithms in constraint solving

Author

Listed:
  • Charlotte Truchet

    (University of Nantes)

  • Alejandro Arbelaez

    (University College Cork)

  • Florian Richoux

    (University of Nantes)

  • Philippe Codognet

    (University of Tokyo)

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.

Suggested Citation

  • Charlotte Truchet & Alejandro Arbelaez & Florian Richoux & Philippe Codognet, 2016. "Estimating parallel runtimes for randomized algorithms in constraint solving," Journal of Heuristics, Springer, vol. 22(4), pages 613-648, August.
    • Handle: RePEc:spr:joheur:v:22:y:2016:i:4:d:10.1007_s10732-015-9292-3
    DOI: 10.1007/s10732-015-9292-3
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    References listed on IDEAS

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    1. Bernard Gendron & Teodor Gabriel Crainic, 1994. "Parallel Branch-and-Branch Algorithms: Survey and Synthesis," Operations Research, INFORMS, vol. 42(6), pages 1042-1066, December.
    2. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
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    Cited by:

    1. Sultan Almotairi & Elsayed Badr & Mustafa Abdul Salam & Hagar Ahmed, 2023. "Breast Cancer Diagnosis Using a Novel Parallel Support Vector Machine with Harris Hawks Optimization," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    2. Alejandro Arbelaez & Deepak Mehta & Barry O’Sullivan & Luis Quesada, 2018. "A constraint-based parallel local search for the edge-disjoint rooted distance-constrained minimum spanning tree problem," Journal of Heuristics, Springer, vol. 24(3), pages 359-394, June.

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