Cover time, the blanket time, and the Matthews bound

J. Kahn, J. H. Kim, L. Lovasz, V. H. Vu

Research output: Contribution to journalConference article

28 Citations (Scopus)

Abstract

We prove upper and lower bounds and give an approximation algorithm for the cover time of the random walk on a graph. We introduce a parameter M motivated by the well-known Matthews bounds on the cover time, C, and prove that M/2≤C = O(M(ln ln n)2). We give a deterministic polynomial time algorithm to approximate M within a factor of 2; this then approximates C within a factor of O((ln ln n)2), improving the previous bound O(ln n) due to Matthews. The blanket time B was introduced by Winkler and Zuckerman: it is the expectation of the first time when all vertices are visited within a constant factor of the number of times suggested by the stationary distribution. Obviously C≤B. Winkler and Zuckerman conjectured B = O(C) and proved B = O(C ln n). Our bounds above are also valid for the blanket time, and so it follows that B = O(C(ln ln n)2).

Original languageEnglish
Pages (from-to)467-475
Number of pages9
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
Publication statusPublished - Dec 1 2000
Event41st Annual Symposium on Foundations of Computer Science (FOCS 2000) - Redondo Beach, CA, USA
Duration: Nov 12 2000Nov 14 2000

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ASJC Scopus subject areas

  • Hardware and Architecture

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