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
Original language | English |
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Pages (from-to) | 333-335 |
Journal | Random Structures and Algorithms |
Volume | 33 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2008 |