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 | log |V |) of the cover time of any random walk on trees.

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 - 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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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