Random multi-index matching problems
arXiv:cond-mat/0507180 · doi:10.1088/1742-5468/2005/09/P09006
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.
22 pages, 16 figures