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A proof of Parisi's conjecture on the random assignment problem
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2004 (English)Article in journal (Refereed) Published
Abstract [en]

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. Such an optimization problem is called a random assignment problem if the matrix entries are random variables. We give a formula for the expected value of the optimal k-assignment in a matrix where some of the entries are zero, and all other entries are independent exponentially distributed random variables with mean 1. Thereby we prove the formula 1 + 1/4 + 1/9 + ⋯ + 1/k2 conjectured by G. Parisi for the case k = m = n, and the generalized conjecture of D. Coppersmith and G. B. Sorkin for arbitrary k, m and n.

Place, publisher, year, edition, pages
2004. Vol. 128, no 3, 419-440 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-23595DOI: 10.1007/s00440-003-0308-9Local ID: 3085OAI: oai:DiVA.org:liu-23595DiVA: diva2:243910
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2011-01-12

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Linusson, SvanteWästlund, Johan

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