A comparative runtime analysis of heuristic algorithms for satisfiability problems

  • Authors:

  • Yuren Zhou;Jun He;Qing Nie

  • Affiliations:

  • School of Computer Science and Engineering, South China University of Technology, Guangzhou 510640, China and Department of Mathematics, University of California, Irvine, CA 92697-3875, USA;Department of Computer Science, University of Wales, Aberystwyth, Ceredigion, SY23 3DB, UK;Department of Mathematics, University of California, Irvine, CA 92697-3875, USA

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2009

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Abstract

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic algorithms: RandomWalk, (1+1) EA, and hybrid algorithm. The runtime analysis of these heuristic algorithms on two 2-SAT instances shows that the expected runtime of these heuristic algorithms can be exponential time or polynomial time. Furthermore, these heuristic algorithms have their own advantages and disadvantages in solving different SAT instances. It also demonstrates that the expected runtime upper bound of RandomWalk on arbitrary k-SAT (k=3) is O((k-1)^n), and presents a k-SAT instance that has @Q((k-1)^n) expected runtime bound.