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 language | English |
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| Title of host publication | Proceedings of the International Conference on VLSI, VLSI 03 |
| Editors | H.R. Arbania, L.T. Yang |
| Pages | 203-207 |
| Number of pages | 5 |
| Publication status | Published - Dec 1 2003 |
| Event | Proceedings of the International Conference on VLSI, VLSI'03 - Las Vegas, NV, United States Duration: Jun 23 2003 → Jun 26 2003 |
Publication series
| Name | Proceedings of the International Conference on VLSI |
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Other
| Other | Proceedings of the International Conference on VLSI, VLSI'03 |
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| Country | United States |
| City | Las Vegas, NV |
| Period | 6/23/03 → 6/26/03 |
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).