• 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}
}
• Published 18 December 2019
• Mathematics
• ArXiv

### Proofs of the Parisi and Coppersmith-Sorkin conjectures for the finite random assignment problem

44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
• 2003
Both Parisi's conjecture and Sorkin's conjecture are generalized to the average value of the smallest k-assignment when there are n jobs and m machines and are proved based on a common set of combinatorial and probabilistic arguments.

### Belief Propagation: An Asymptotically Optimal Algorithm for the Random Assignment Problem

• Computer Science
Math. Oper. Res.
• 2009
The objective method is used to analyze the performance of BP as the size of the underlying graph becomes large and establishes that the dynamic of BP on Knn converges in distribution as n → ∞ to an appropriately defined dynamic on the Poisson weighted infinite tree, and proves correlation decay for this limiting dynamic.

### A proof of Parisi’s conjecture on the random assignment problem

• Mathematics
• 2003
Abstract.An assignment problem is the optimization problem of finding, in an m by n matrix of nonnegative real numbers, k entries, no two in the same row or column, such that their sum is minimal.

### A Nearly Tight Sum-of-Squares Lower Bound for the Planted Clique Problem

• Mathematics, Computer Science
2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
• 2016
We prove that with high probability over the choice of a random graph G from the Erdös-Rényi distribution G(n,1/2), the nO(d)-time degree d Sum-of-Squares semidefinite programming relaxation for

### Belief propagation for optimal edge-cover in the random complete graph

• Computer Science, Mathematics
ArXiv
• 2012
The objective method of Aldous is applied to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs and shows that a belief propagation algorithm converges asymptotically to the optimal solution.

### Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method

• Mathematics
Random Struct. Algorithms
• 2006
This work extends the results to maximum weight matchings in G(n, c/n) and G r (n) using the recently developed local weak convergence method further reduced to a certain local optimality property exhibited by the models it considers.

### Sudden Emergence of a Giantk-Core in a Random Graph

• Mathematics
J. Comb. Theory, Ser. B
• 1996
These proofs are based on the probabilistic analysis of an edge deletion algorithm that always find ak-core if the graph has one, and demonstrate that, unlike the 2-core, when ak- core appears for the first time it is very likely to be giant, of size ?pk(?k)n.

### Linear phase transition in random linear constraint satisfaction problems

It is proved that the feasibility property experiences a linear phase transition, when n→∞ and m = cn for a constant c, and it is extended to maximum weight b-matchings also in G(n, cn).