Coverage characteristics of self-repelling random walks in mobile ad-hoc networks

Abstract

A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed for two dimensional lattices and these walks have been shown to exhibit a remarkable uniformity with which they visit nodes in a graph. In this paper, we extend this analysis to self-repelling random walks on mobile networks in which the underlying graph itself is temporally evolving. Using network simulations in ns-3, we characterize the number of times each node is visited from the start until all nodes have been visited at least once. We evaluate under different mobility models and on networks ranging from 100 to 1000 nodes. Our results show that until about 85% coverage, duplicate visits are very rare highlighting the efficiency with which a majority of nodes in the network can be visited. Even at 100% coverage, the exploration overhead (the ratio of number of steps to number of unique visited nodes) remains low and under 2. Our analysis shows that self-repelling random walks are effective, structure-free tools for data aggregation in mobile ad-hoc networks.