Solving Boolean Satisfiability Using Local Search Guided by Unit Clause Elimination

  • Hirsch Edward A. 
  • Arist Kojevnikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)


In this paper we present a new randomized algorithm for SAT combining unit clause elimination and local search. The algorithm is inspired by two randomized algorithms having the best current worst- case upper bounds ([9]and [11],[12]). Despite its simplicity, our algorithm performs well on many common benchmarks (we present results of its empirical evaluation). It is also probabilistically approximately complete.


Boolean satisfiability local search empirical evaluation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Dantsin, E.A. Hirsch, S. Ivanov,and M. Vsemirnov. Algorithms for SAT and upper bounds on their complexity.ECCC Technical Report 01-012,
  2. 2.
    J. Gu, P.W. Purdom, J. Franco, and B.W. Wah. Algorithms for satisfiability (SAT)problem:A survey.DIMACS DM and TCS 35,1997,pages 19–152.Google Scholar
  3. 3.
    H.H. Hoos.On the run-time behaviour of stochastic local search algorithms for SAT. In Proc.AAAI’99,pages 661–666.Google Scholar
  4. 4.
    H.H. Hoos. Stochastic Local Search-Method,Models,Applications.PhD thesis, Department of Computer Science, Darmstadt University of Technology,1998.Google Scholar
  5. 5.
    H.H. Hoos and T. Stützle. SATLIB.
  6. 6.
    H.H. Hoos and T. Stützle. Local search algorithms for SAT:An empirical evaluation. Journal of Automated Reasoning,24(4):421–481,2000.zbMATHCrossRefGoogle Scholar
  7. 7.
    D.S. Johnson and M.A. Tricks,editors. Cliques,Coloring and Satisfiability, volume 26 of DIMACS DM and TCS.AMS,1996.Google Scholar
  8. 8.
    D. McAllester, B. Selman,and H. Kautz. Evidence in invariants for local search. In Proc.AAAI’97,pages 321–326.Google Scholar
  9. 9.
    R. Paturi, P. Pudl ák, M.E. Saks,and F. Zane. An improved exponential-time algorithm for k-SAT. In Proc.FOCS’98,pages 628–637.Google Scholar
  10. 10.
    S.D. Prestwich. Local search and backtracking vs non-systematic backtracking. In AAAI 2001 Fall Symposium on Using Uncertainty within Computation.To appear.Google Scholar
  11. 11.
    U. Schöning. A probabilistic algorithm for k-SAT and constraint satisfaction problems. InProc.FOCS’99,pages 410–414.Google Scholar
  12. 12.
    R. Schuler, U. Schöning,and O. Watanabe. An improved randomized algorithm for 3-SAT. Technical Report TR-C146, Dept.of Math.and Comp.Sci.,Tokyo Inst.of Tech.,2001.Google Scholar
  13. 13.
    D. Schuurmans and F. Southey. Local search characteristics of incomplete SAT procedures. In Proc.of AAAI’2000,pages 297–302.Google Scholar
  14. 14.
    B. Selman, H. A. Kautz, and B. Cohen. Noise strategies for improving local search. In Proc.AAAI’94,pages 337–343.Google Scholar
  15. 15.
    B. Selman, H. Levesque, and D. Mitchell. A new method for solving hard satisfiability problems. In Proc.AAAI’92,pages 440–446.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hirsch Edward A. 
    • 1
  • Arist Kojevnikov
    • 2
  1. 1.Steklov Institute of Mathematics at St.PetersburgSt.PetersburgRussia
  2. 2.Department of Mathematics and MechanicsSt.Petersburg State UniversitySt.PetersburgRussia

Personalised recommendations