Cryan, M., Dyer, M., Müller, H. et al. (1 more author) (2008) Random walks on the vertices of transportation polytopes with constant number of sources. Random Structures and Algorithms, 33 (3). pp. 333-355. ISSN 1042-9832
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 nO(m2).
|Keywords:||transportation polytope • random walk • rapid mixing|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)|
|Depositing User:||Mrs Yasmin Aziz|
|Date Deposited:||18 Nov 2008 12:11|
|Last Modified:||18 Jun 2015 17:26|