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Asymptotics in the random assignment problem
 PROBABILITY THEORY
, 1992
"... We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on ..."
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We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve
A generalization of the random assignment problem
"... Abstract. We give a conjecture for the expected value of the optimal kassignment in an m × nmatrix, where the entries are all exp(1)distributed random variables or zeros. We prove this conjecture in the case there is a zerocost k − 1assignment. Assuming our conjecture, we determine some limits, ..."
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Cited by 11 (8 self)
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Abstract. We give a conjecture for the expected value of the optimal kassignment in an m × nmatrix, where the entries are all exp(1)distributed random variables or zeros. We prove this conjecture in the case there is a zerocost k − 1assignment. Assuming our conjecture, we determine some limits
Towards the distribution of the smallest matching in the Random Assignment Problem
"... We consider the problem of minimizing cost among onetoone assignments of n jobs onto n machines. The random assignment problem refers to the case when the cost associated with performing jobs on machines are random variables. Aldous established the expected value of the smallest cost, An, in the l ..."
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We consider the problem of minimizing cost among onetoone assignments of n jobs onto n machines. The random assignment problem refers to the case when the cost associated with performing jobs on machines are random variables. Aldous established the expected value of the smallest cost, An
Constructive Bounds and Exact Expectations for the Random Assignment Problem
, 1998
"... The random assignment problem is to choose a minimumcost perfect matching in a complete n x n bipartite graph, whose edge weights are chosen randomly from some distribution such as the exponential distribution with mean 1. In this case it is known that the expectation does not grow unboundedly with ..."
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Cited by 54 (6 self)
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The random assignment problem is to choose a minimumcost perfect matching in a complete n x n bipartite graph, whose edge weights are chosen randomly from some distribution such as the exponential distribution with mean 1. In this case it is known that the expectation does not grow unboundedly
Exact Expectations and Distributions or the Random Assignment Problem
, 1999
"... A generalization of the random assignment problem asks the expected cost of the minimumcost matching of cardinality k in a complete bipartire graph Kmr*, with independent random edge weights. With weights drawn from the exponential(l) distribution, the answer has been conjectured 1 to be ]1,5_ ..."
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Cited by 20 (0 self)
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A generalization of the random assignment problem asks the expected cost of the minimumcost matching of cardinality k in a complete bipartire graph Kmr*, with independent random edge weights. With weights drawn from the exponential(l) distribution, the answer has been conjectured 1 to be ]1
The ζ(2) Limit in the Random Assignment Problem
, 2000
"... The random assignment (or bipartite matching) problem asks about An = min P n i=1 c(i; (i)), where (c(i; j)) is a n \Theta n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations . M'ezard and Parisi (1987) used the replica method from sta ..."
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Cited by 56 (1 self)
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The random assignment (or bipartite matching) problem asks about An = min P n i=1 c(i; (i)), where (c(i; j)) is a n \Theta n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations . M'ezard and Parisi (1987) used the replica method from
Optimality of belief propagation for random assignment problem
 SYMPOSIUM ON DISCRETE ALGORITHMS
, 2009
"... The assignment problem concerns finding the minimumcost perfect matching in a complete weighted n × n bipartite graph. Any algorithm for this classical question clearly requires Ω(n 2) time, and the best known one (Edmonds and Karp, 1972) finds solution in O(n³). For decades, it has remained unknow ..."
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Cited by 9 (0 self)
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unknown whether optimal computation time is closer to n 3 or n 2. We provide answer to this question for random instance of assignment problem. Specifically, we establish that Belief Propagation finds solution in O(n²) time when edgeweights are i.i.d. with light tailed distribution.
Proofs of the Parisi and CoppersmithSorkin conjectures for the finite random assignment problem
, 2003
"... Suppose that there are jobs and machines and it costs to execute job on machine. The assignment problem concerns the determination of a onetoone assignment of jobs onto machines so as to minimize the cost of executing all the jobs. The average case analysis of the classical random assignment prob ..."
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Cited by 20 (1 self)
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Suppose that there are jobs and machines and it costs to execute job on machine. The assignment problem concerns the determination of a onetoone assignment of jobs onto machines so as to minimize the cost of executing all the jobs. The average case analysis of the classical random assignment
Belief propagation: an asymptotically optimal algorithm for the random assignment problem
"... The random assignment problem concerns finding the minimum cost assignment or matching in a complete bipartite graph with edge weights being i.i.d. with some distribution, say exponential(1) distribution. In a remarkable result by Aldous (2001), it was shown that the average cost of such an assignme ..."
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Cited by 11 (1 self)
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The random assignment problem concerns finding the minimum cost assignment or matching in a complete bipartite graph with edge weights being i.i.d. with some distribution, say exponential(1) distribution. In a remarkable result by Aldous (2001), it was shown that the average cost
Results 1  10
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