### 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 language | English |
---|---|

Pages (from-to) | 467-475 |

Number of pages | 9 |

Journal | Annual Symposium on Foundations of Computer Science - Proceedings |

Publication status | Published - Dec 1 2000 |

Event | 41st Annual Symposium on Foundations of Computer Science (FOCS 2000) - Redondo Beach, CA, USA Duration: Nov 12 2000 → Nov 14 2000 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science - Proceedings*, 467-475.