Cover time, the blanket time, and the Matthews bound

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

27 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
Title of host publicationAnnual Symposium on Foundations of Computer Science - Proceedings
PublisherIEEE
Pages467-475
Number of pages9
Publication statusPublished - 2000
Event41st Annual Symposium on Foundations of Computer Science (FOCS 2000) - Redondo Beach, CA, USA
Duration: Nov 12 2000Nov 14 2000

Other

Other41st Annual Symposium on Foundations of Computer Science (FOCS 2000)
CityRedondo Beach, CA, USA
Period11/12/0011/14/00

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Approximation algorithms
Polynomials

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Kahn, J., Kim, J. H., Lovász, L., & Vu, V. H. (2000). Cover time, the blanket time, and the Matthews bound. In Annual Symposium on Foundations of Computer Science - Proceedings (pp. 467-475). IEEE.

Cover time, the blanket time, and the Matthews bound. / Kahn, J.; Kim, J. H.; Lovász, L.; Vu, V. H.

Annual Symposium on Foundations of Computer Science - Proceedings. IEEE, 2000. p. 467-475.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kahn, J, Kim, JH, Lovász, L & Vu, VH 2000, Cover time, the blanket time, and the Matthews bound. in Annual Symposium on Foundations of Computer Science - Proceedings. IEEE, pp. 467-475, 41st Annual Symposium on Foundations of Computer Science (FOCS 2000), Redondo Beach, CA, USA, 11/12/00.
Kahn J, Kim JH, Lovász L, Vu VH. Cover time, the blanket time, and the Matthews bound. In Annual Symposium on Foundations of Computer Science - Proceedings. IEEE. 2000. p. 467-475
Kahn, J. ; Kim, J. H. ; Lovász, L. ; Vu, V. H. / Cover time, the blanket time, and the Matthews bound. Annual Symposium on Foundations of Computer Science - Proceedings. IEEE, 2000. pp. 467-475
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