TY - JOUR

T1 - Statistical mechanics of an NP-complete problem

T2 - Subset sum

AU - Sasamoto, Tomohiro

AU - Toyoizumi, Taro

AU - Nishimori, Hidetoshi

N1 - Copyright:
Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2001/11/9

Y1 - 2001/11/9

N2 - We study the 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.

AB - We study the 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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U2 - 10.1088/0305-4470/34/44/314

DO - 10.1088/0305-4470/34/44/314

M3 - Article

AN - SCOPUS:0035834624

VL - 34

SP - 9555

EP - 9567

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 44

ER -