TY - GEN

T1 - Random Walks on the Vertices of Transportation Polytopes with Constant Number of Sources

AU - Cryan, Mary

AU - Dyer, Martin

AU - Müller, Haiko

AU - Stougie, Leen

PY - 2003

Y1 - 2003

N2 - 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).

AB - 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).

M3 - Conference contribution

SN - 0-89871-538-5

T3 - SODA '03

SP - 330

EP - 339

BT - Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Society for Industrial and Applied Mathematics

CY - Philadelphia, PA, USA

ER -