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

Authors:
Mary Cryan;Martin Dyer;Haiko Müller;Leen Stougie
Affiliations:
University of Leeds, Leeds, England;University of Leeds, Leeds, England;University of Leeds, Leeds, England;Eindhoven University of Technology, the Netherlands and CWI Amsterdam, the Netherlands
Venue:
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2003

Citing 8
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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 analyse a natural random walk on the edge-vertex graph of the polytope. The analysis makes use of the multicommodity flow technique of Sinclair [20] together with ideas developed by Morris and Sinclair [15, 16] for the knapsack problem, and Cryan et al. [2] for contingency tables, to establish that the random walk approaches the uniform distribution in time nO(m2).