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

Y1 - 2003

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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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.

T2 - Proceedings of the International Conference on VLSI, VLSI'03

Y2 - 23 June 2003 through 26 June 2003

ER -