How slow, or fast, are standard random walks? - Analysis of hitting and cover times on trees

Yoshiaki Nonaka, Hirotaka Ono, Shuji Kijima, Masafumi Yamashita

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

2 被引用数 (Scopus)

抄録

Random walk is a powerful tool, not only for modeling, but also for practical use such as the Internet crawlers. Standard random walks on graphs have been well studied; It is well-known that both hitting time and cover time of a standard random walk are bounded by O(n 3) for any graph with n vertices, besides the bound is tight for some graphs. Ikeda et al. (2003) provided "β-random walk," which realizes O(n 2) hitting time and O(n 2 log n) cover times for any graph, thus it archives, in a sense, "n-times improvement" compared to the standard random walk. This paper is concerned with optimizations of hitting and cover times, by drawing a comparison between the standard random walk and the fastest random walk. We show for any tree that the hitting time of the standard random walk is at most O(√n)-times longer than one of the fastest random walk. Similarly, the cover time of the standard random walk is at most O(√n log n)-times longer than the fastest one, for any tree. We also show that our bound for the hitting time is tight by giving examples, while we only give a lower bound Ω(√n= log n) for the cover time.

本文言語英語
ホスト出版物のタイトルTheory of Computing 2011 - Proceedings of the 17th Computing
ホスト出版物のサブタイトルThe Australasian Theory Symposium, CATS 2011
ページ63-68
ページ数6
出版ステータス出版済み - 12 1 2011
イベントTheory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011 - Perth, WA, オーストラリア
継続期間: 1 17 20111 20 2011

出版物シリーズ

名前Conferences in Research and Practice in Information Technology Series
119
ISSN(印刷版)1445-1336

その他

その他Theory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011
国/地域オーストラリア
CityPerth, WA
Period1/17/111/20/11

All Science Journal Classification (ASJC) codes

  • コンピュータ ネットワークおよび通信
  • コンピュータ サイエンスの応用
  • ハードウェアとアーキテクチャ
  • 情報システム
  • ソフトウェア

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