Random multi-index matching problems

Details Random multi-index matching problems Random multi-index matching problems

2005-07-07

arxiv.org/abs/cond-mat/0507180v1

J. Stat. Mech. (2005) P09006

Physics

Condensed Matter

Disordered Systems and Neural Networks

22 pages, 16 figures

Scientific paper

10.1088/1742-5468/2005/09/P09006

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.

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