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Constructive bounds and exact expectations for the random assignment problem

Coppersmith , Don and Sorkin, Gregory B. (1999) Constructive bounds and exact expectations for the random assignment problem. Random Structures and Algorithms, 15 (2). pp. 113-144. ISSN 1042-9832

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Abstract

The random assignment problem is to choose a minimum-cost perfect matching in a complete n×n bipartite graph, whose edge weights are chosen randomly from some distribution such as the exponential distribution with mean 1. In this case it is known that the expectation does not grow unboundedly with n, but approaches some limiting value c* between 1.51 and 2. The limit is conjectured to be π2/6, while a recent conjecture is that for finite n, the expected cost is ∑ 1/i2. This paper contains two principal results. First, by defining and analyzing a constructive algorithm, we show that the limiting expectation is c*<1.94. Second, we extend the finite-n conjecture to partial assignments on complete m×n bipartite graphs and prove it in some limited cases.

Item Type: Article
Official URL: http://eu.wiley.com/WileyCDA/WileyTitle/productCd-...
Additional Information: ©1999 John Wiley & Sons, Inc.
Library of Congress subject classification: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 13 Apr 2011 14:30
URL: http://eprints.lse.ac.uk/35511/

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