Asymptotics in the random assignment problem
نویسندگان
چکیده
منابع مشابه
Asymptotics in the random assignment problem
In the deterministic assignment problem, there are n jobs, n machines and a n x n non-negative matrix (t j,,,) representing the cost of performing job j on machine m. An assignment is a permutation ~ of {1, ..., n}, indicating that job j is assigned to machine ~(j). The optimal assignment has cost min~tj ,~(j) , j the minimum taken over permutations re. For the random assignment problem we defi...
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Parisi’s famous (proven) conjecture states that the expected cost of an optimal assignment in a complete bipartite graph on n + n nodes with i. i. d. exponential edge costs with mean 1 is ∑n i=1 1/i , which converges to an asymptotic limit of π/6 as n tends to infinity. We consider a generalization of this question to complete “partitioned” bipartite hypergraphs G2,n that contain edges of size ...
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The random assignment (or bipartite matching) problem asks about An = minπ ∑ n i=1 c(i, π(i)), where (c(i, j)) is a n × n matrix with i.i.d. entries, say with exponential(1) distribution, and the minimum is over permutations π. Mézard and Parisi (1987) used the replica method from statistical physics to argue non-rigorously that EAn → ζ(2) = π /6. Aldous (1992) identified the limit in terms of ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 1992
ISSN: 0178-8051,1432-2064
DOI: 10.1007/bf01192719