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Positive-instance driven dynamic programming for treewidth

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  • Hisao Tamaki

    (Meiji University)

Abstract

Consider a dynamic programming scheme for a decision problem in which all subproblems involved are also decision problems. An implementation of such a scheme is positive-instance driven (PID), if it generates positive subproblem instances, but not negative ones, building each on smaller positive instances. We take the dynamic programming scheme due to Bouchitté and Todinca for treewidth computation, which is based on minimal separators and potential maximal cliques, and design a variant (for the decision version of the problem) with a natural PID implementation. The resulting algorithm performs extremely well: it solves a number of standard benchmark instances for which the optimal solutions have not previously been known. Incorporating a new heuristic algorithm for detecting safe separators, it also solves all of the 100 public instances posed by the exact treewidth track in PACE 2017, a competition on algorithm implementation. We describe the algorithm, prove its correctness, and give a running time bound in terms of the number of positive subproblem instances. We perform an experimental analysis which supports the practical importance of such a bound.

Suggested Citation

  • Hisao Tamaki, 2019. "Positive-instance driven dynamic programming for treewidth," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1283-1311, May.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:4:d:10.1007_s10878-018-0353-z
    DOI: 10.1007/s10878-018-0353-z
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    Cited by:

    1. Niels Lindner & Julian Reisch, 2022. "An analysis of the parameterized complexity of periodic timetabling," Journal of Scheduling, Springer, vol. 25(2), pages 157-176, April.
    2. Tom C. van der Zanden & Hans L. Bodlaender & Herbert J. M. Hamers, 2023. "Efficiently computing the Shapley value of connectivity games in low-treewidth graphs," Operational Research, Springer, vol. 23(1), pages 1-23, March.

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