Reducing the Hitting and the Cover Times of Random Walks on Finite Graphs by Local Topological Information

Satoshi Ikeda, Izumi Kubo, Masafumi Yamashita

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

2 Citations (Scopus)

Abstract

For any undirected connected graph G = (V, E) with order n, let P (β) = (puv(β))u,v∈V be a transition matrix defined by puv(β) = exp[-βU(u,v)]/∑w∈N(u)exp[-βU(u,w)] for u ∈ V, v ∈ N(u), where β is a real number, N(u) is the set of vertices adjacent to a vertex u, deg(u) = |N(u)|, and U(·, ·) is a potential function defined as U(u, v) = U(v) = log deg(v) for v ∈ N(u), u ∈ V. In this paper, we show that for any undirected graph with order n, the cover time and the mean hitting time for P(1/2) are bounded by O(n2 log n) and O(n2), respectively. Since the mean hitting time of a path graph of order n, for any transition matrix, is ω(n2), P(1/2) is best possible with respect to the mean hitting time.

Original languageEnglish
Title of host publicationProceedings of the International Conference on VLSI, VLSI 03
EditorsH.R. Arbania, L.T. Yang
Pages203-207
Number of pages5
Publication statusPublished - Dec 1 2003
EventProceedings of the International Conference on VLSI, VLSI'03 - Las Vegas, NV, United States
Duration: Jun 23 2003Jun 26 2003

Publication series

NameProceedings of the International Conference on VLSI

Other

OtherProceedings of the International Conference on VLSI, VLSI'03
CountryUnited States
CityLas Vegas, NV
Period6/23/036/26/03

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Electrical and Electronic Engineering

Cite this

Ikeda, S., Kubo, I., & Yamashita, M. (2003). Reducing the Hitting and the Cover Times of Random Walks on Finite Graphs by Local Topological Information. In H. R. Arbania, & L. T. Yang (Eds.), Proceedings of the International Conference on VLSI, VLSI 03 (pp. 203-207). (Proceedings of the International Conference on VLSI).