### Abstract

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 language | English |
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Pages (from-to) | 9555-9567 |

Number of pages | 13 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 34 |

Issue number | 44 |

DOIs | |

Publication status | Published - 2001 Nov 9 |

Externally published | Yes |

### ASJC Scopus subject areas

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

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## Cite this

Sasamoto, T., Toyoizumi, T., & Nishimori, H. (2001). Statistical mechanics of an NP-complete problem: Subset sum.

*Journal of Physics A: Mathematical and General*,*34*(44), 9555-9567. https://doi.org/10.1088/0305-4470/34/44/314