Width-Based Algorithms for SAT and CIRCUIT-SAT

  • Elizabeth Broering
  • Satyanarayana V. Lokam
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2919)

Abstract

We investigate theoretical and practical aspects of algorithms for CIRCUIT-SAT and SAT based on combinatorial parameters. Two such algorithms are given in [1] and [4] based on branch-width of a hypergraph and cut-width of a graph respectively. We give theoretical generalizations and improvements to the cut-width-based algorithm in [4] in terms of many other well-known width-like parameters. In particular, we have polynomial-time backtrack search algorithms for logarithmic cut-width and path-width, nO(logn)-time backtrack search algorithms for logarithmic tree-width and branch-width, and a polynomial-time regular resolution refutation for logarithmic tree-width. We investigate the effectiveness of the algorithm in [1] on practical instances of CIRCUIT-SAT arising in the context of Automatic Test Pattern Generation (ATPG).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alekhnovich, M., Razborov, A.: Satisfiability, Branch-width, and Tseitin Tautologies. In: 43rd Symp. Foundations of Computer Science (FOCS), pp. 593–603 (2002)Google Scholar
  2. 2.
    Bodlaender, H.L.: A Partial k-arboretum of Graphs with Bounded Treewidth. Theoretical Computer Science 209, 1–45 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cook, W., Seymour, P.: Tour Merging via Branch-Decompistion (December 18, 2002) (manuscript)Google Scholar
  4. 4.
    Prasad, M.R., Chong, P., Keutzer, K.: Why is Combinatorial ATPG Efficiently Solvable for Practical VLSI Circuits? Journal of Elecrtonic Testing: Theory and Applications 17, 509–527 (2001)CrossRefGoogle Scholar
  5. 5.
    Diestel, R.: Graph Theory, 2nd edn. Graduate Texts in Mathematics, vol. 173. Springer, Heidelberg (2000)Google Scholar
  6. 6.
    Robertson, N., Seymour, P.D.: Graph Minors X - Obstructions to Treedecomposition. Jl. Combinatorial Theory, Series B 52, 153–190 (1991)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Elizabeth Broering
    • 1
  • Satyanarayana V. Lokam
    • 1
  1. 1.EECS DepartmentUniversity of MichiganAnn ArborUSA

Personalised recommendations