Checking for optimal solutions in some $NP$-complete problems
| dc.creator | Orland, Henri | |
| dc.creator | Bauer, Michel | |
| dc.date | 2005-03-27 | |
| dc.date.accessioned | 2026-07-25T23:25:59Z | |
| dc.description | For some weighted $NP$-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 $NP$-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. | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0503634 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0503634 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/98398 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Checking for optimal solutions in some $NP$-complete problems | |
| dc.type | text |