Journal of Heuristics

, Volume 22, Issue 4, pp 613–648 | Cite as

Estimating parallel runtimes for randomized algorithms in constraint solving

  • Charlotte TruchetEmail author
  • Alejandro Arbelaez
  • Florian Richoux
  • Philippe Codognet


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.


Constraint solving Parallel processing Performance model Randomized constraint solving 



We acknowledge that some results in this paper have been achieved using the Grid’5000 experimental testbed, being developed under the INRIA ALADDIN development action with support from CNRS, RENATER and several universities as well as other funding bodies. We acknowledge that some other results in this paper have been achieved using the PRACE Research Infrastructure resource JUGENE based in Germany at Jülich Supercomputing Centre. The authors would like to thank the anonymous reviewers for their comments and suggestions that helped to improve the paper. We would like to thank the anonymous reviewers for suggesting to compare our method versus the empirical method depicted in Sect. 7.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Charlotte Truchet
    • 1
    Email author
  • Alejandro Arbelaez
    • 2
  • Florian Richoux
    • 1
  • Philippe Codognet
    • 3
  1. 1.LINA, UMR 6241University of NantesNantesFrance
  2. 2.INSIGHT Centre for Data AnalyticsUniversity College CorkCorkIreland
  3. 3.JFLI - CNRS / UPMCUniversity of TokyoTokyoJapan

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