Statistical mechanics of an NP-complete problem: Subset sum

Tomohiro Sasamoto, Taro Toyoizumi, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)9555-9567
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number44
Publication statusPublished - 2001 Nov 9
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)


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