Recovery thresholds in the sparse planted matching problem

Guilhem Semerjian; Gabriele Sicuro; Lenka Zdeborová

doi:10.1103/physreve.102.022304

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arXiv · 2005.11274

Recovery thresholds in the sparse planted matching problem

Guilhem Semerjian·Gabriele Sicuro·Lenka Zdeborová

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Abstract

We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted matching. A recent work has demonstrated the existence of a phase transition, in the large size limit, between a full and a partial recovery phase for a specific form of the weights distribution on fully connected graphs. We generalize and extend this result in two directions: we obtain a criterion for the location of the phase transition for generic weights distributions and possibly sparse graphs, exploiting a technical connection with branching random walk processes, as well as a quantitatively more precise description of the critical regime around the phase transition.

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cond-mat.dis-nn cs.DM math.PR

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Guilhem Semerjian, Gabriele Sicuro, Lenka Zdeborová. 2020-05-22. Recovery thresholds in the sparse planted matching problem. https://doi.org/10.1103/physreve.102.022304

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