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Using sequential runtime distributions for the parallel speedup prediction of SAT local search

Published online by Cambridge University Press:  25 September 2013

ALEJANDRO ARBELAEZ ,
CHARLOTTE TRUCHET  and
PHILIPPE CODOGNET
ALEJANDRO ARBELAEZ
Affiliation:
JFLI / Univesity of Tokyo (e-mail: arbelaez@is.s.u-tokyo.ac.jp)
CHARLOTTE TRUCHET
Affiliation:
LINA, UMR 6241/ University of Nantes (e-mail: charlotte.truchet@univ-nantes.fr)
PHILIPPE CODOGNET
Affiliation:
JFLI-CNRS / UPMC / University of Tokyo (e-mail: codognet@is.s.u-tokyo.ac.jp)
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Abstract

This paper presents a detailed analysis of the scalability and parallelization of local search algorithms for the Satisfiability problem. 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 two SAT local search solvers, namely Sparrow and CCASAT, and compare the predicted performances to the results of an actual experimentation on parallel hardware up to 384 cores. We show that the model is accurate and predicts performance close to the empirical data. Moreover, as we study different types of instances (random and crafted), we observe that the local search solvers exhibit different behaviors and that their runtime distributions can be approximated by two types of distributions: exponential (shifted and non-shifted) and lognormal.

Keywords

SATlocal searchparallelismruntime distributionsstatistical analysis
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Special Issue 4-5: 29th International Conference on Logic Programming , July 2013 , pp. 625 - 639
Copyright
Copyright © 2013 [ALEJANDRO ARBELAEZ, CHARLOTTE TRUCHET and PHILIPPE CODOGNET] 

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Footnotes

*

The first author was supported by the Japan Society for the Promotion of Science (JSPS) under the JSPS Postdoctoral Program and the kakenhi Grant-in-aid for Scientific Research.

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