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.
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This research was supported by the BSF (Binational Science Foundation, grant no 2008482).
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Rubinstein, R. Stochastic Enumeration Method for Counting NP-Hard Problems. Methodol Comput Appl Probab 15, 249–291 (2013). https://doi.org/10.1007/s11009-011-9242-y
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DOI: https://doi.org/10.1007/s11009-011-9242-y