### Abstract

We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time-the expected time required to visit every node in a graph at least once-and we show that for a large collection of interesting graphs, running many random walks in parallel jdelds a speed-up in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speed-up is sometimes possible, but that some natural graphs allow only a logarithmic speed-up. A problem related to ours (in which the walks start from some probabilistic distribution on vertices) was previously studied in the context of space efficient algorithms for undirected fit-connectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds.

Original language | English (US) |
---|---|

Title of host publication | SPAA'08 - Proceedings of the 20th Annual Symposium on Parallelism in Algorithms and Architectures |

Publisher | Association for Computing Machinery |

Pages | 119-128 |

Number of pages | 10 |

ISBN (Print) | 9781595939739 |

DOIs | |

State | Published - Jan 1 2008 |

Externally published | Yes |

Event | 20th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'08 - Munich, Germany Duration: Jun 14 2008 → Jun 16 2008 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
---|

### Other

Other | 20th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA'08 |
---|---|

Country | Germany |

City | Munich |

Period | 6/14/08 → 6/16/08 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Hardware and Architecture
- Software

### Keywords

- Cover time
- Distributed algorithms
- Graph search
- Random walks
- Speed-up

## Fingerprint Dive into the research topics of 'Many random walks are faster than one'. Together they form a unique fingerprint.

## Cite this

*SPAA'08 - Proceedings of the 20th Annual Symposium on Parallelism in Algorithms and Architectures*(pp. 119-128). (Annual ACM Symposium on Parallelism in Algorithms and Architectures). Association for Computing Machinery. https://doi.org/10.1145/1378533.1378557