The planted $k$-factor problem

Gabriele Sicuro; Lenka Zdeborová

doi:10.1088/1751-8121/abee9d

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arXiv · 2010.13700

The planted $k$-factor problem

Gabriele Sicuro·Lenka Zdeborová

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Abstract

We consider the problem of recovering an unknown $k$-factor, hidden in a weighted random graph. For $k=1$ this is the planted matching problem, while the $k=2$ case is closely related to the planted travelling salesman problem. The inference problem is solved by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted sub-graph. We argue that, in the large size limit, a phase transition can appear between a full and a partial recovery phase as function of the signal-to-noise ratio. We give a criterion for the location of the transition.

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

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Gabriele Sicuro, Lenka Zdeborová. 2020-10-26. The planted $k$-factor problem. https://doi.org/10.1088/1751-8121%2Fabee9d

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