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).

Reducing the Hitting and the Cover Times of Random Walks on Finite Graphs by Local Topological Information. / Ikeda, Satoshi; Kubo, Izumi; Yamashita, Masafumi.

Proceedings of the International Conference on VLSI, VLSI 03. ed. / H.R. Arbania; L.T. Yang. 2003. p. 203-207 (Proceedings of the International Conference on VLSI).

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

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 HR Arbania & LT Yang (eds), Proceedings of the International Conference on VLSI, VLSI 03. Proceedings of the International Conference on VLSI, pp. 203-207, Proceedings of the International Conference on VLSI, VLSI'03, Las Vegas, NV, United States, 6/23/03.
Ikeda S, Kubo I, Yamashita M. Reducing the Hitting and the Cover Times of Random Walks on Finite Graphs by Local Topological Information. In Arbania HR, Yang LT, editors, Proceedings of the International Conference on VLSI, VLSI 03. 2003. p. 203-207. (Proceedings of the International Conference on VLSI).
Ikeda, Satoshi ; Kubo, Izumi ; Yamashita, Masafumi. / Reducing the Hitting and the Cover Times of Random Walks on Finite Graphs by Local Topological Information. Proceedings of the International Conference on VLSI, VLSI 03. editor / H.R. Arbania ; L.T. Yang. 2003. pp. 203-207 (Proceedings of the International Conference on VLSI).
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