An extension of Matthews' bound to multiplex random walks

Yusuke Hosaka, Yukiko Yamauchi, Shuji Kijima, Hirotaka Ono, Masafumi Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Random walk is a powerful tool for searching a network, especially for a very large network such as the Internet. The cover time is an important measure of a random walk on a finite graph, and has been studied well. For the purpose of searching a network, it is quite natural to think that multiple crawlers might cover a network faster than a single crawler. Alon et al. (2011) showed that a multiple random walk by k crawlers covers a network k times faster than a single random walk in certain graphs such as complete graphs, random graphs, etc., while the speeding up ratio is limited only to log k times in other graphs such as cycles and paths. This paper investigates a multiplex random walk by k tokens, in which k tokens randomly walks on a graph independently according to an individual transition probability. For the cover time of a multiplex random walk, we present new inequalities similar to celebrated Matthews' inequalities for a single random walk, that provide upper and lower bounds of the cover time by its hitting times. We also show that the bounds are tight in certain graphs, namely complete graphs, bipartite complete graphs, and random graphs.

Original languageEnglish
Title of host publicationProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012
Pages872-877
Number of pages6
DOIs
Publication statusPublished - Oct 18 2012
Event2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012 - Shanghai, China
Duration: May 21 2012May 25 2012

Publication series

NameProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012

Other

Other2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012
CountryChina
CityShanghai
Period5/21/125/25/12

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Internet

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Hosaka, Y., Yamauchi, Y., Kijima, S., Ono, H., & Yamashita, M. (2012). An extension of Matthews' bound to multiplex random walks. In Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012 (pp. 872-877). [6270730] (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012). https://doi.org/10.1109/IPDPSW.2012.107

An extension of Matthews' bound to multiplex random walks. / Hosaka, Yusuke; Yamauchi, Yukiko; Kijima, Shuji; Ono, Hirotaka; Yamashita, Masafumi.

Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012. 2012. p. 872-877 6270730 (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hosaka, Y, Yamauchi, Y, Kijima, S, Ono, H & Yamashita, M 2012, An extension of Matthews' bound to multiplex random walks. in Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012., 6270730, Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012, pp. 872-877, 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012, Shanghai, China, 5/21/12. https://doi.org/10.1109/IPDPSW.2012.107
Hosaka Y, Yamauchi Y, Kijima S, Ono H, Yamashita M. An extension of Matthews' bound to multiplex random walks. In Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012. 2012. p. 872-877. 6270730. (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012). https://doi.org/10.1109/IPDPSW.2012.107
Hosaka, Yusuke ; Yamauchi, Yukiko ; Kijima, Shuji ; Ono, Hirotaka ; Yamashita, Masafumi. / An extension of Matthews' bound to multiplex random walks. Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012. 2012. pp. 872-877 (Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012).
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