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The multi-index matching problem generalizes the well known matching problem by going from pairs to d -uplets. We use the cavity method from statistical physics to analyse its properties when the costs of the d -uplets are random. At low temperatures we find for d ≥ 3 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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A 2005 study studied this question.
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