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Journal of Combinatorial Optimization

, Volume 32, Issue 1, pp 51–66 | Cite as

Performances of pure random walk algorithms on constraint satisfaction problems with growing domains

  • Wei Xu
  • Fuzhou Gong
Article

Abstract

The performances of two types of pure random walk (PRW) algorithms for a model of constraint satisfaction problem with growing domains (called Model RB) are investigated. Threshold phenomenons appear for both algorithms. In particular, when the constraint density \(r\) is smaller than a threshold value \(r_d\), PRW algorithms can solve instances of Model RB efficiently, but when \(r\) is bigger than the \(r_d\), they fail. Using a physical method, we find out the threshold values for both algorithms. When the number of variables \(N\) is large, the threshold values tend to zero, so generally speaking PRW does not work on Model RB. By performing experiments, we show that PRW strategy cannot do better than other fundamental strategies.

Keywords

Constraint satisfaction problems Model RB Random walk  Local search algorithms 

Notes

Acknowledgments

Partially supported by NSFC 61370052 and 61370156.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  2. 2.Institute of Applied Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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