Low hitting time random walks in wireless networks

Random walks can be conveniently exploited for implementing probabilistic algorithms to solve many searching problems arised by distributed applications, for example, service discovery, p2p file sharing, etc. In this paper we consider random walks executed on uniform wireless networks and study how to reduce the expected number of walk steps required to reach a target, namely the hitting time. The latter is the main search performance metric of a random walk based algorithm, since it determines the average response to a search as well as its cost; thus, the actual convenience of using random walks compared to other solutions depends on achieving a low hitting time. We show how in uniform wireless networks, the natural implementation of a random walk which selects the next node to visit at random among all neighbors is not a good choice, since it has a strong negative effect on the hitting time. This paper studies such a negative effect analytically and proposes two neighbor selection rules aiming at reducing the hitting time. A simulation study confirms the benefits of the proposed solutions. Copyright (c) 2008 John Wiley & Sons, Ltd.