Phase transition in the assignment problem for random matrices
Computational Complexity
2007-05-23 v1 Statistical Mechanics
Abstract
We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.
Cite
@article{arxiv.cs/0511107,
title = {Phase transition in the assignment problem for random matrices},
author = {J. G. Esteve and F. Falceto},
journal= {arXiv preprint arXiv:cs/0511107},
year = {2007}
}
Comments
7 pages, 5 figures; accepted for publication in Europhys. Lett. http://www.edpsciences.org/journal/index.cfm?edpsname=epl