Exact formulas and limits for a class of random optimization problems
2005 (English)Report (Other academic)
We obtain an exact formula for the expected value of the optimum for a certain class of random combinatorial optimization problems on bipartite graphs. By applying this formula, we compute the limit as n → ∞ of the expected value of the minimum 2-factor in the complete bipartite graph Kn,n with independent exp(1) edge costs. This limit, approximately 4.0831, is conjectured to be twice the value obtained non-rigorously by W. Krauth, M. M´ezard and G. Parisi for the minimum travelling salesman tour on the complete graph.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press , 2005. , 17 p.
Linköping Studies in Mathematics, ISSN 1652-4454 (online), 0348-2960 (print) ; 5
IdentifiersURN: urn:nbn:se:liu:diva-62949OAI: oai:DiVA.org:liu-62949DiVA: diva2:375250