Improved approximation of the minimum cover time

Eden Chlamtac, Uriel Feige

Research output: Contribution to journalArticlepeer-review

Abstract

Feige and Rabinovich, in [Feige and Rabinovich, Rand. Struct. Algorithms 23(1) (2003) 1-22], gave a deterministic O(log4n) approximation for the time it takes a random walk to cover a given graph starting at a given vertex. This approximation algorithm was shown to work for arbitrary reversible Markov chains. We build on the results of [Feige and Rabinovich, Rand. Struct. Algorithms 23(1) (2003) 1-22], and show that the original algorithm gives a O(log2n) approximation as it is, and that it can be modified to give a O(logn(loglogn)2) approximation. Moreover, we show that given any c(n)-approximation algorithm for the maximum cover time (maximized over all initial vertices) of a reversible Markov chain, we can give a corresponding algorithm for the general cover time (of a random walk or reversible Markov chain) with approximation ratio O(c(n)logn).

Original languageEnglish
Pages (from-to)22-38
Number of pages17
JournalTheoretical Computer Science
Volume341
Issue number1-3
DOIs
StatePublished - 5 Sep 2005
Externally publishedYes

Keywords

  • Approximation algorithms
  • Cover time
  • Markov chains
  • Random walks

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