• Corpus ID: 209414792

The Planted Matching Problem: Phase Transitions and Exact Results

@article{Moharrami2019ThePM,
  title={The Planted Matching Problem: Phase Transitions and Exact Results},
  author={Mehrdad Moharrami and Cristopher Moore and Jiaming Xu},
  journal={ArXiv},
  year={2019},
  volume={abs/1912.08880}
}
We study the problem of recovering a planted matching in randomly weighted complete bipartite graphs $K_{n,n}$. For some unknown perfect matching $M^*$, the weight of an edge is drawn from one distribution $P$ if $e \in M^*$ and another distribution $Q$ if $e \notin M^*$. Our goal is to infer $M^*$, exactly or approximately, from the edge weights. In this paper we take $P=\exp(\lambda)$ and $Q=\exp(1/n)$, in which case the maximum-likelihood estimator of $M^*$ is the minimum-weight matching $M_… 

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