### 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 |

Publication status | Published - Oct 1998 |

### Fingerprint

### Keywords

- Commute time
- Random walk

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Graph Theory*,

*29*(2), 57-62.

**Random Walks and the Regeneration Time.** / Beveridge, Andrew; Lovász, L.

Research output: Contribution to journal › Article

*Journal of Graph Theory*, vol. 29, no. 2, pp. 57-62.

}

TY - JOUR

T1 - Random Walks and the Regeneration Time

AU - Beveridge, Andrew

AU - Lovász, L.

PY - 1998/10

Y1 - 1998/10

N2 - 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.

AB - 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.

KW - Commute time

KW - Random walk

UR - http://www.scopus.com/inward/record.url?scp=0346968482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346968482&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346968482

VL - 29

SP - 57

EP - 62

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 2

ER -