Random multi-index matching problems
Disordered Systems and Neural Networks
2009-11-11 v1
Abstract
The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.
Keywords
Cite
@article{arxiv.cond-mat/0507180,
title = {Random multi-index matching problems},
author = {O. C. Martin and M. Mezard and O. Rivoire},
journal= {arXiv preprint arXiv:cond-mat/0507180},
year = {2009}
}
Comments
22 pages, 16 figures