### Abstract

Consider a graph G and a random walk on it. We want to stop the random walk at certain times (using an optimal stopping rule) to obtain independent samples from a given distribution ρ on the nodes. For an undirected graph, the expected time between consecutive samples is maximized by a distribution equally divided between two nodes, and so the worst expected time is 1/4 of the maximum commute time between two nodes. In the directed case, the expected time for this distribution is within a factor of 2 of the maximum.

Original language | English |
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Pages (from-to) | 57-62 |

Number of pages | 6 |

Journal | Journal of Graph Theory |

Volume | 29 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 1998 |

### Keywords

- Commute time
- Random walk

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Beveridge, A., & Lovász, L. (1998). Random Walks and the Regeneration Time.

*Journal of Graph Theory*,*29*(2), 57-62. https://doi.org/10.1002/(SICI)1097-0118(199810)29:2<57::AID-JGT1>3.0.CO;2-B