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

Yoshiaki Nonaka, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトルStochastic Algorithms
ホスト出版物のサブタイトルFoundations and Applications - 5th International Symposium, SAGA 2009, Proceedings
ページ104-116
ページ数13
DOI
出版ステータス出版済み - 2009
イベント5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009 - Sapporo, 日本
継続期間: 10 26 200910 28 2009

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5792 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他5th Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009
Country日本
CitySapporo
Period10/26/0910/28/09

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

フィンガープリント 「How to design a linear cover time random walk on a finite graph」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル