Random walks on the vertices of transportation polytopes with constant number of sources (2003)
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| Venue: | Proc. 14th Ann. ACM-SIAM Symp. Disc. Alg. (Baltimore, MD) 330–339, ACM |
| Citations: | 12 - 3 self |
BibTeX
@INPROCEEDINGS{Cryan03randomwalks,
author = {Mary Cryan and Martin Dyer and Haiko Müller and Leen Stougie},
title = {Random walks on the vertices of transportation polytopes with constant number of sources},
booktitle = {Proc. 14th Ann. ACM-SIAM Symp. Disc. Alg. (Baltimore, MD) 330–339, ACM},
year = {2003},
pages = {330--339}
}
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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 multi-commodity flow technique of Sinclair [30] together with ideas developed by Morris and Sinclair [24, 25] for the knapsack problem, and Cryan et al. [3] for contingency tables, to establish that the random walk approaches the uniform distribution in time n O(m2). 1
