## 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 language | English |
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Pages (from-to) | 22-38 |

Number of pages | 17 |

Journal | Theoretical Computer Science |

Volume | 341 |

Issue number | 1-3 |

DOIs | |

State | Published - 5 Sep 2005 |

Externally published | Yes |

## Keywords

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