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Stochastic Enumeration Method for Counting NP-Hard Problems

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  • Reuven Rubinstein

    (Israel Institute of Technology)

Abstract

We present a new generic sequential importance sampling algorithm, called stochastic enumeration (SE) for counting #P-complete problems, such as the number of satisfiability assignments and the number of perfect matchings (permanent). We show that SE presents a natural generalization of the classic one-step-look-ahead algorithm in the sense that it: Runs in parallel multiple trajectories instead of a single one; Employs a polynomial time decision making oracle, which can be viewed as an n-step-look-ahead algorithm, where n is the size of the problem. Our simulation studies indicate good performance of SE as compared with the well-known splitting and SampleSearch methods.

Suggested Citation

  • Reuven Rubinstein, 2013. "Stochastic Enumeration Method for Counting NP-Hard Problems," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 249-291, June.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:2:d:10.1007_s11009-011-9242-y
    DOI: 10.1007/s11009-011-9242-y
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    References listed on IDEAS

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    1. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    2. Reuven Rubinstein, 2009. "The Gibbs Cloner for Combinatorial Optimization, Counting and Sampling," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 491-549, December.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin & Tim Zajic, 1999. "Multilevel Splitting for Estimating Rare Event Probabilities," Operations Research, INFORMS, vol. 47(4), pages 585-600, August.
    4. Zdravko I. Botev & Dirk P. Kroese, 2008. "An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 471-505, December.
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    Cited by:

    1. Alathea Jensen, 2018. "Stochastic Enumeration with Importance Sampling," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1259-1284, December.

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