A Generalized Cover Time for Random Walks on Graphs
نویسندگان
چکیده
Abstract. Given a random walk on a graph, the cover time is the rst time (number of steps) that every vertex has been hit (covered) by the walk. De ne the marking time for the walk as follows. When the walk reaches vertex vi, a coin is ipped and with probability pi the vertex is marked (or colored). We study the time that every vertex is marked. (When all the pi's are equal to 1, this gives the usual cover time problem.) General formulas are given for the marking time of a graph. Connections are made with the generalized coupon collector's problem. Asymptotics for small pi's are given. Techniques used include combinatorics of random walks, theory of determinants, analysis and probabilistic considerations.
منابع مشابه
Springer (original Version in Lncs) a Generalized Cover Time for Random Walks on Graphs
Given a random walk on a graph, the cover time is the rst time (number of steps) that every vertex has been hit (covered) by the walk. Deene the marking time for the walk as follows. When the walk reaches vertex vi, a coin is ipped and with probability pi the vertex is marked (or colored). We study the time that every vertex is marked. (When all the pi's are equal to 1, this gives the usual cov...
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