### Abstract

A random walk on a graph is a process in which a particle on a vertex repeatedly moves to its adjacent vertex according to transition probability, which is given in advance. The behavior of random walks depend on its transition probability, and the ''speed'' of random walks also can be measured from several viewpoints. Among the several measures, the hitting time and the cover time are two popular ones and often used for evaluation. In this paper, we consider the speed of random walks from the viewpoint of topological information of graphs and its use. For example, it is known that a simple random walk, in which a particle moves to its adjacent vertex uniformly at random, visits all the vertices in O(n ^{3}) expected steps (which is the cover time), while a random walk utilizing all the topological information on a graph can visit all the vertices in O(n ^{2}) expected steps, where n is the number of vertices. In this paper, we briefly survey work focusing on the relationship between the speed of random walks on a graph and its usage of topological information.

Original language | English |
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Title of host publication | Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011 |

Pages | 360-363 |

Number of pages | 4 |

DOIs | |

Publication status | Published - Dec 1 2011 |

Event | 2nd International Conference on Networking and Computing, ICNC 2011 - Osaka, Japan Duration: Nov 30 2011 → Dec 2 2011 |

### Publication series

Name | Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011 |
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### Other

Other | 2nd International Conference on Networking and Computing, ICNC 2011 |
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Country | Japan |

City | Osaka |

Period | 11/30/11 → 12/2/11 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Computer Science Applications

### Cite this

*Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011*(pp. 360-363). [6131864] (Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011). https://doi.org/10.1109/ICNC.2011.70

**Fast random walks on finite graphs and graph topological information.** / Ono, Hirotaka.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011.*, 6131864, Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011, pp. 360-363, 2nd International Conference on Networking and Computing, ICNC 2011, Osaka, Japan, 11/30/11. https://doi.org/10.1109/ICNC.2011.70

}

TY - GEN

T1 - Fast random walks on finite graphs and graph topological information

AU - Ono, Hirotaka

PY - 2011/12/1

Y1 - 2011/12/1

N2 - A random walk on a graph is a process in which a particle on a vertex repeatedly moves to its adjacent vertex according to transition probability, which is given in advance. The behavior of random walks depend on its transition probability, and the ''speed'' of random walks also can be measured from several viewpoints. Among the several measures, the hitting time and the cover time are two popular ones and often used for evaluation. In this paper, we consider the speed of random walks from the viewpoint of topological information of graphs and its use. For example, it is known that a simple random walk, in which a particle moves to its adjacent vertex uniformly at random, visits all the vertices in O(n 3) expected steps (which is the cover time), while a random walk utilizing all the topological information on a graph can visit all the vertices in O(n 2) expected steps, where n is the number of vertices. In this paper, we briefly survey work focusing on the relationship between the speed of random walks on a graph and its usage of topological information.

AB - A random walk on a graph is a process in which a particle on a vertex repeatedly moves to its adjacent vertex according to transition probability, which is given in advance. The behavior of random walks depend on its transition probability, and the ''speed'' of random walks also can be measured from several viewpoints. Among the several measures, the hitting time and the cover time are two popular ones and often used for evaluation. In this paper, we consider the speed of random walks from the viewpoint of topological information of graphs and its use. For example, it is known that a simple random walk, in which a particle moves to its adjacent vertex uniformly at random, visits all the vertices in O(n 3) expected steps (which is the cover time), while a random walk utilizing all the topological information on a graph can visit all the vertices in O(n 2) expected steps, where n is the number of vertices. In this paper, we briefly survey work focusing on the relationship between the speed of random walks on a graph and its usage of topological information.

UR - http://www.scopus.com/inward/record.url?scp=84856851377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856851377&partnerID=8YFLogxK

U2 - 10.1109/ICNC.2011.70

DO - 10.1109/ICNC.2011.70

M3 - Conference contribution

AN - SCOPUS:84856851377

SN - 9780769545691

T3 - Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011

SP - 360

EP - 363

BT - Proceedings - 2011 2nd International Conference on Networking and Computing, ICNC 2011

ER -