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 |
|---|---|
| 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 |
|---|
Other
| Other | Proceedings of the International Conference on VLSI, VLSI'03 |
|---|---|
| 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
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 proceeding › Conference contribution
}
TY - GEN
T1 - Reducing the Hitting and the Cover Times of Random Walks on Finite Graphs by Local Topological Information
AU - Ikeda, Satoshi
AU - Kubo, Izumi
AU - Yamashita, Masafumi
PY - 2003/12/1
Y1 - 2003/12/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=1642378864&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:1642378864
SN - 1932415106
T3 - Proceedings of the International Conference on VLSI
SP - 203
EP - 207
BT - Proceedings of the International Conference on VLSI, VLSI 03
A2 - Arbania, H.R.
A2 - Yang, L.T.
ER -