Affiliation:
1. Department of Mathematics University of California, Davis Davis California 95616 USA
Abstract
AbstractA conjecture of Milena Mihail and Umesh Vazirani (Proc. 24th Annu. ACM Symp. Theory Comput., ACM, Victoria, BC, 1992, pp. 26–38.) states that the edge expansion of the graph of every polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a polytope in is greater than one over some polynomial function of . This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of a random polytope in is at least with high probability.
Funder
National Science Foundation of Sri Lanka
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software
Reference22 articles.
1. Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid
2. On 0-1 Polytopes with Many Facets
3. Random half-integral polytopes
4. An approximate isoperimetric inequality for r$$ \mathrm{r} $$‐sets;Christofides D.;Electron. J. Comb.,2013
5. Bolyai Society Mathematical Studies;Fan R.,1996