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

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 nO(m2 ) .

• Type: Conference
• Year: 2003
• Where: SODA
• Authors: Mary Cryan, Martin E. Dyer, Haiko Müller, Leen Stougie
• Keywords: Algorithms, Natural Random Walk, Random Walk, SODA 2003, Transportation Polytope