Expansion of random 0/1 polytopes

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2022-07-08 DOI:10.1002/rsa.21184

Brett Leroux, Luis Rademacher

引用次数: 1

Abstract

A 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.

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随机0/1多面体的展开

Milena Mihail和Umesh Vazirani的猜想(Proc. 24 Annu)。美国电脑。理论第一版。， ACM, Victoria, BC, 1992, pp. 26-38 .)指出，每个多面体的图的边展开至少是一个。边缘展开的任何下界都给出了多面体图上随机游走混合时间的上界。这种随机游走很重要，因为它们可以用来从一组组合对象中均匀随机地生成一个元素。Mihail和Vazirani猜想的一种较弱的形式是，一个多面体的图的边展开式大于某多项式函数的1 /。这个猜想的弱版本将满足所有应用。我们的主要结果是，随机多面体的图的边展开至少是高概率的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.