How to design a linear cover time random walk on a finite graph

Yoshiaki Nonaka, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita

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

1 Citation (Scopus)

Abstract

Arandom walk on a finite graph G = (V,E) is random token circulation on vertices of G. A token on a vertex in V moves to one of its adjacent vertices according to a transition probability matrix P. It is known that both of the hitting time and the cover time of the standard random walk are bounded by O(|V |3), in which the token randomly moves to an adjacent vertex with the uniform probability. This estimation is tight in a sense, that is, there exist graphs for which the hitting time and cover times of the standard random walk are Ω(|V |3). Thus the following questions naturally arise: is it possible to speed up a random walk, that is, to design a transition probability for G that achieves a faster cover time? Or, how large (or small) is the lower bound on the cover time of random walks on G? In this paper, we investigate how we can/cannot design a faster random walk in terms of the cover time. We give necessary conditions for a graph G to have a linear cover time random walk, i,e., the cover time of the random walk on G is O(|V |). We also present a class of graphs that have a linear cover time. As a byproduct, we obtain the lower bound Ω(|V

Original languageEnglish
Title of host publicationStochastic Algorithms
Subtitle of host publicationFoundations and Applications - 5th International Symposium, SAGA 2009, Proceedings
Pages104-116
Number of pages13
DOIs
Publication statusPublished - Dec 1 2009
Event5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009 - Sapporo, Japan
Duration: Oct 26 2009Oct 28 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5792 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009
CountryJapan
CitySapporo
Period10/26/0910/28/09

Fingerprint

Cover Time
Finite Graph
Linear Time
Random walk
Hitting Time
Byproducts
Adjacent
Graph in graph theory
Lower bound
Transition Probability Matrix
Design
Vertex of a graph
Transition Probability
Walk
Speedup
Necessary Conditions

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Nonaka, Y., Ono, H., Sadakane, K., & Yamashita, M. (2009). How to design a linear cover time random walk on a finite graph. In Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings (pp. 104-116). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5792 LNCS). https://doi.org/10.1007/978-3-642-04944-6_9

How to design a linear cover time random walk on a finite graph. / Nonaka, Yoshiaki; Ono, Hirotaka; Sadakane, Kunihiko; Yamashita, Masafumi.

Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. 2009. p. 104-116 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5792 LNCS).

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

Nonaka, Y, Ono, H, Sadakane, K & Yamashita, M 2009, How to design a linear cover time random walk on a finite graph. in Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5792 LNCS, pp. 104-116, 5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009, Sapporo, Japan, 10/26/09. https://doi.org/10.1007/978-3-642-04944-6_9
Nonaka Y, Ono H, Sadakane K, Yamashita M. How to design a linear cover time random walk on a finite graph. In Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. 2009. p. 104-116. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-04944-6_9
Nonaka, Yoshiaki ; Ono, Hirotaka ; Sadakane, Kunihiko ; Yamashita, Masafumi. / How to design a linear cover time random walk on a finite graph. Stochastic Algorithms: Foundations and Applications - 5th International Symposium, SAGA 2009, Proceedings. 2009. pp. 104-116 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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