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Sequential Monte Carlo for Counting Vertex Covers in General Graphs

Author

Listed:
  • Radislav Vaisman

    (Technion, Haifa, Israel)

  • Zdravko Botev

    (University of New South Wales, Sidney, Australia)

  • Ad Ridder

    (VU University Amsterdam)

Abstract

In this paper we describe a Sequential Importance Sampling (SIS) procedure for counting the number of vertex covers in general graphs. The performance of SIS depends heavily on how close the SIS proposal distribution is to a uniform one over a suitably restricted set. The proposed algorithm introduces a probabilistic relaxation technique that uses Dynamic Programming in order to efficiently estimate this uniform distribution. The numerical experiments show that the scheme compares favorably with other existing methods. In particular the method is compared with cachet - an exact model counter, and the state of the art SampleSearch, which is based on Belief Networks and importance sampling.

Suggested Citation

  • Radislav Vaisman & Zdravko Botev & Ad Ridder, 2013. "Sequential Monte Carlo for Counting Vertex Covers in General Graphs," Tinbergen Institute Discussion Papers 13-122/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20130122
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    File URL: https://papers.tinbergen.nl/13122.pdf
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    References listed on IDEAS

    as
    1. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
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    More about this item

    Keywords

    Vertex Cover; Counting problem; Sequential importance sampling; Dynamic Programming; Relaxation; Random Graphs;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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