Deterministic Approximation of the Cover Time

Uriel Feige, Yuri Rabinovich

Research output: Contribution to journalArticlepeer-review


The cover time is the expected time it takes a random walk to cover all vertices of a graph. Despite the fact that it can be approximated with arbitrary precision by a simple polynomial time Monte-Carlo algorithm which simulates the random walk, it is not known whether the cover time of a graph can be computed in deterministic polynomial time. In the present paper we establish a deterministic polynomial time algorithm that, for any graph and any starting vertex, approximates the cover time within polylogarithmic factors. More generally, our algorithm approximates the cover time for arbitrary reversible Markov chains. The new aspect of our algorithm is that the starting vertex of the random walk may be arbitrary and is given as part of the input, whereas previous deterministic approximation algorithms for the cover time assume that the walk starts at the worst possible vertex. In passing, we show that the starting vertex can make a difference of up to a multiplicative factor of Θ(n3/2/√log n) in the cover time of an n-vertex graph.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalRandom Structures and Algorithms
Issue number1
StatePublished - Aug 2003

ASJC Scopus subject areas

  • Software
  • General Mathematics
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics


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