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Random multi-index matching problems

O. C. Martin·M. Mezard·O. Rivoire
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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.

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O. C. Martin, M. Mezard, O. Rivoire. 2005-07-07. Random multi-index matching problems. https://doi.org/10.1088/1742-5468%2F2005%2F09%2Fp09006

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