44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
DOI: 10.1109/sfcs.2003.1238191
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Proofs of the Parisi and Coppersmith-Sorkin conjectures for the finite random assignment problem

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Cited by 19 publications
(22 citation statements)
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References 20 publications
(28 reference statements)
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“…However, calculation of explicit constants in dimensions d Ն 2 seems beyond the reach of analytic techniques. For the mean-field bipartite MM problem, impressive recent work (26,27) has proven an exact formula giving the expectation of the finite-n minimum total matching length, though such exact methods seem unlikely to be widely feasible.…”
Section: Discussionmentioning
confidence: 99%
“…However, calculation of explicit constants in dimensions d Ն 2 seems beyond the reach of analytic techniques. For the mean-field bipartite MM problem, impressive recent work (26,27) has proven an exact formula giving the expectation of the finite-n minimum total matching length, though such exact methods seem unlikely to be widely feasible.…”
Section: Discussionmentioning
confidence: 99%
“…Let C n denote the cost of the minimum perfect matching in the n by n complete bipartite graph. The problem of establishing a good upper bound on var (C n ) for large n has been considered by several researchers [9], [32], [42]. The first proof that var (C n )!0 was obtained by M. Talagrand [42] with the method described in §9.…”
Section: The Variance Of Bipartite Matchingmentioning
confidence: 99%
“…So, if we replace e by f in T 1 we will, by (11), save at least 0.1/n. If we repeat this for all bad edges, then we will have a tree containing all of the Monday purchased edges and it will, in expectation, be at least 0.1 E[b] /n cheaper.…”
Section: Beyond the Threshold Heuristicmentioning
confidence: 99%
“…Another natural question might be to consider a 2-stage version of the random assignment problem. See Aldous [1,2], Linusson and Wästlund [10], and Nair, Prabhakar and Sharma [11] for recent work on the standard one-stage analysis. In principal, one could try to carry out a similar 2-stage probabilistic analysis for any combinatorial optimization problem.…”
Section: Open Questionsmentioning
confidence: 99%