A proof of Parisi's conjecture on the random assignment problem
2004 (English)In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 128, no 3, 419-440 p.Article in journal (Refereed) Published
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/k(2) 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.
IdentifiersURN: urn:nbn:se:kth:diva-23139ISI: 000188747900004OAI: oai:DiVA.org:kth-23139DiVA: diva2:341837
QC 201005252010-08-102010-08-10Bibliographically approved