Checking for optimal solutions in some $NP$-complete problems
统计力学
2007-05-23 v1 无序系统与神经网络
摘要
For some weighted -complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we consider the weighted tripartite matching problem, a well known -complete problem. We write mean-field finite temperature equations for this model, and show that they become exact at zero temperature. As a consequence, given a possible solution, we propose an algorithm which allows to check in a polynomial time if the solution is indeed optimal. This algorithm is generalized to a class of variants of the multiple traveling salesmen problem.
引用
@article{arxiv.cond-mat/0503634,
title = {Checking for optimal solutions in some $NP$-complete problems},
author = {Henri Orland and Michel Bauer},
journal= {arXiv preprint arXiv:cond-mat/0503634},
year = {2007}
}