Biased Random Walks in Uniform Wireless Networks

A recurrent problem when designing distributed applications is to search for a node with known property. File searching in peer-to-peer (P2P) applications, resource discovery in service-oriented architectures (SOAs), and path discovery in routing can all be cast as a search problem. Random walk-based search algorithms are often suggested for tackling the search problem, especially in very dynamic systems-like mobile wireless networks. The cost and the effectiveness of a random walk-based search algorithm are measured by the excepted number of transmissions required before hitting the target. Hence, to have a low hitting time is a critical goal. This paper studies the effect of biasing random walk toward the target on the hitting time. For a walk running over a network with uniform node distribution, a simple upper bound that connects the hitting time to the bias level is obtained. The key result is that even a modest bias level is able to reduce the hitting time significantly. This paper also proposes a search protocol for mobile wireless networks, whose results are interpreted in the light of the theoretical study. The proposed solution is for unstructured wireless mobile networks.