Random walks on the vertices of transportation polytopes with constant number of sources
Mary Cryan, Martin Dyer, Haiko Müller, Leen Stougie · Random Structures and Algorithms · 2008
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 n . © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008