Springer (original Version in Lncs) a Generalized Cover Time for Random Walks on Graphs
نویسندگان
چکیده
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 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
A Generalized Cover Time for Random Walks on Graphs
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...
متن کاملSimple Random Walks on Radio Networks (Simple Random Walks on Hyper-Graphs)
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless networks (and other networks), graphs are actually not the correct model of the communication; instead hyper-graphs better capture the communication over a wireless...
متن کاملExpander Properties and the Cover Time of Random Intersection Graphs
We investigate important combinatorial and algorithmic properties of Gn,m,p random intersection graphs. In particular, we prove that with high probability (a) random intersection graphs are expanders, (b) random walks on such graphs are “rapidly mixing” (in particular they mix in logarithmic time) and (c) the cover time of random walks on such graphs is optimal (i.e. it is Θ(n log n)). All resu...
متن کاملPageRank and random walks on graphs
We examine the relationship between PageRank and several invariants occurring in the study of random walks and electrical networks. We consider a generalized version of hitting time and effective resistance with an additional parameter which controls the ‘speed’ of diffusion. We will establish their connection with PageRank . Through these connections, a combinatorial interpretation of PageRank...
متن کاملRandom Walks on Graphs: A Survey
Various aspects of the theory of random walks on graphs are surveyed. In particular, estimates on the important parameters of access time, commute time, cover time and mixing time are discussed. Connections with the eigenvalues of graphs and with electrical networks, and the use of these connections in the study of random walks is described. We also sketch recent algorithmic applications of ran...
متن کامل