Typical behavior of the linear programming method for combinatorial optimization problems: From a statistical-mechanical perspective
Disordered Systems and Neural Networks
2014-03-31 v1 Statistical Mechanics
Information Theory
math.IT
Abstract
Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a lattice-gas model on the Erd\"os-R\'enyi random graphs is analyzed by a replica method. It is found that the LP optimal solution is typically equal to that of the IP below the critical average degree c*=e in the thermodynamic limit. The critical threshold for LP=IP is beyond a mathematical result, c=1, and coincides with the replica-symmetry-breaking threshold of the IP.
Cite
@article{arxiv.1309.6925,
title = {Typical behavior of the linear programming method for combinatorial optimization problems: From a statistical-mechanical perspective},
author = {Satoshi Takabe and Koji Hukushima},
journal= {arXiv preprint arXiv:1309.6925},
year = {2014}
}
Comments
5 pages, 3 figures