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Random walks on the vertices of transportation polytopes with constant number of sources

Cryan, M., Dyer, M., Müller, H. and Stougie, L. (2008) Random walks on the vertices of transportation polytopes with constant number of sources. Random Structures and Algorithms, 33 (3). pp. 333-355. ISSN 1042-9832

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Abstract

We consider the problem of uniformly sampling a vertex of a transportation polytope with m sources and n destinations, where m is a constant. We analyze a natural random walk on the edge-vertex graph of the polytope. The analysis makes use of the multicommodity flow technique of Sinclair [Combin Probab Comput 1 (1992), 351-370] together with ideas developed by Morris and Sinclair [SIAM J Comput 34 (2004), 195-226] for the knapsack problem, and Cryan et al. [SIAM J Comput 36 (2006), 247-278] for contingency tables, to establish that the random walk approaches the uniform distribution in time nO(m2).

Item Type: Article
Keywords: transportation polytope • random walk • rapid mixing
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Mrs Yasmin Aziz
Date Deposited: 18 Nov 2008 12:11
Last Modified: 29 Sep 2010 14:22
Published Version: http://dx.doi.org/10.1002/rsa.2022
Status: Published
Publisher: John Wiley
Refereed: Yes
Identification Number: 10.1002/rsa.20222
URI: http://eprints.whiterose.ac.uk/id/eprint/4920

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