Threshold Behaviour of WalkSAT and Focused Metropolis Search on Random 3-Satisfiability

  • Sakari Seitz
  • Mikko Alava
  • Pekka Orponen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)


An important heuristic in local search algorithms for Satisfiability is focusing, i.e. restricting the selection of flipped variables to those appearing in presently unsatisfied clauses. We consider the behaviour on large randomly generated 3-SAT instances of two focused solution methods: WalkSAT and Focused Metropolis Search. The algorithms turn out to have qualitatively quite similar behaviour. Both are sensitive to the proper choice of their “noise” and “temperature” parameters, but with appropriately chosen values, both achieve solution times that scale linearly in the number of variables even for clauses-to-variables ratios α > 4.2. This is much closer to the satisfiability transition threshold α c ≈ 4.267 than has generally been assumed possible for local search algorithms.


Local Search Solution Time Local Search Algorithm Local Search Method Satisfying Assignment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sakari Seitz
    • 1
    • 2
  • Mikko Alava
    • 2
  • Pekka Orponen
    • 1
  1. 1.Laboratory for Theoret. Computer Science
  2. 2.Laboratory of PhysicsHelsinki University of TechnologyFinland

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