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Statistical Mechanics of an NP-complete Problem: Subset Sum

T. Sasamoto·T. Toyoizumi·H. Nishimori
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Abstract

We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and has been studied in the physics literature. The asymptotic expressions for the number of solutions are obtained. These results applied to the number partitioning problem as a special case are compared with those which were previously obtained by a different method. We discuss the limit of applicability of the techniques of statistical mechanics to the present problem.

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BibTeXRIS

T. Sasamoto, T. Toyoizumi, H. Nishimori. 2001-06-18. Statistical Mechanics of an NP-complete Problem: Subset Sum. https://doi.org/10.1088/0305-4470%2F34%2F44%2F314

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