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A proof of Parisi’s conjecture on the random assignment problem
 PROBAB. THEORY RELAT. FIELDS
, 2003
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A Proof of a Conjecture of Buck, Chan and Robbins on the Expected Value of the Minimum Assignment, Random Structures and Algorithms
 RANDOM STRUCTURES AND ALGORITHMS
, 2005
"... We prove the main conjecture of the paper “On the expected value of the minimum ..."
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Cited by 12 (9 self)
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We prove the main conjecture of the paper “On the expected value of the minimum
A simple proof of the Parisi and COPPERSMITHSORKIN FORMULAS FOR THE RANDOM ASSIGNMENT PROBLEM
 LINKÖPING STUDIES IN MATHEMATICS, NO. 6
, 2005
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Exact formulas and limits for a class of random optimization problems
 LINKÖPING STUDIES IN MATHEMATICS
, 2005
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Towards the Resolution of CoppersmithSorkin Conjectures
 Proceedings of the 40th Annual Allerton Conference on Communication, Control and Computing
, 2002
"... A kmatching is a set of k elements of a matrix, no two of which belong to the same row or column. The minimum weight kmatching of an m × n matrix C is the kmatching whose entries have the smallest sum. Coppersmith and Sorkin conjectured that if C is generated by choosing each entry independently ..."
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A kmatching is a set of k elements of a matrix, no two of which belong to the same row or column. The minimum weight kmatching of an m × n matrix C is the kmatching whose entries have the smallest sum. Coppersmith and Sorkin conjectured that if C is generated by choosing each entry independently from the exponential distribution of rate 1, then the expected value of the weight of the minimum weight kmatching is given by an explicit formula, whose proof is largely unknown. In this paper we describe our efforts to prove the CoppersmithSorkin conjecture by identifying the terms in the explicit formula to be the mean values of certain random variables which are functions of the matrix elements. We further conjecture that the distributions of these random variables are pure exponentials. We have partial theoretical backing and some simulation evidence for these conjectures. In the process we also prove a general combinatorial lemma about matchings in matrices. 1
Random Assignment with Integer Costs
 Combin. Probab. Comput
, 2001
"... The random assignment problem is to minimize the cost of an assignment in a nn matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n 2 , and random permutations of 1, 2, . . . ..."
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The random assignment problem is to minimize the cost of an assignment in a nn matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n 2 , and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n 2 for the whole matrix. We find the limit of the expected cost for the n 2 cases, and prove bounds for the n cases. This is done by simple coupling arguments together with Aldous recent results for the continuous case. We also present a simulation study of these cases. 1
COMPLETING A k − 1 ASSIGNMENT
, 2004
"... Abstract. We consider the distribution of the value of the optimal kassignment in an m × nmatrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the ..."
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Abstract. We consider the distribution of the value of the optimal kassignment in an m × nmatrix, where the entries are independent exponential random variables with arbitrary rates. We give closed formulas for both the Laplace transform of this random variable and for its expected value under the condition that there is a zerocost k − 1assignment. 1.
Random Assignment with Integer Costs
"... The random assignment problem is to minimize the cost of an assignment in a n × n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2,..., m, for m = n or n 2, and random permutations of 1, 2,..., n fo ..."
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The random assignment problem is to minimize the cost of an assignment in a n × n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2,..., m, for m = n or n 2, and random permutations of 1, 2,..., n for each row, or of 1, 2,..., n 2 for the whole matrix. We find the limit of the expected cost for the “n 2 ” cases, and prove bounds for the “n ” cases. This is done by simple coupling arguments together with Aldous recent results for the continuous case. We also present a simulation study of these cases. 1.