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Random assignment and shortest path problems
Abstract : We explore a similarity between the $n$ by $n$ random assignment problem and the random shortest path problem on the complete graph on $n+1$ vertices. This similarity is a consequence of the proof of the Parisi formula for the assignment problem given by C. Nair, B. Prabhakar and M. Sharma in 2003. We give direct proofs of the analogs for the shortest path problem of some results established by D. Aldous in connection with his $\zeta (2)$ limit theorem for the assignment problem.
Keywords :
minimum matching
random tree
Cited literature [14 references]
https://hal.inria.fr/hal-01184708
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Submitted on : Monday, August 17, 2015 - 2:24:54 PM
Last modification on : Thursday, May 11, 2017 - 1:02:51 AM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:10:07 PM
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 2:24:54 PM
Last modification on : Thursday, May 11, 2017 - 1:02:51 AM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:10:07 PM
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