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

Yoshiaki Nonaka, Hirotaka Ono, Shuji Kijima, Masafumi Yamashita

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

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationTheory of Computing 2011 - Proceedings of the 17th Computing
Subtitle of host publicationThe Australasian Theory Symposium, CATS 2011
Pages63-68
Number of pages6
Publication statusPublished - Dec 1 2011
EventTheory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011 - Perth, WA, Australia
Duration: Jan 17 2011Jan 20 2011

Publication series

NameConferences in Research and Practice in Information Technology Series
Volume119
ISSN (Print)1445-1336

Other

OtherTheory of Computing 2011 - 17th Computing: The Australasian Theory Symposium, CATS 2011
CountryAustralia
CityPerth, WA
Period1/17/111/20/11

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Information Systems
  • Software

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