Random walk with jumps in large-scale random geometric graphs

Abstract

The information dissemination problem in large-scale networking environments like wireless sensor networks and ad hoc networks is studied here considering random geometric graphs and random walk based approaches. A new type of random walk based agent is proposed in this paper and an analytical expression with respect to coverage (i.e., the proportion of the network nodes visited by the random walk agent) as a function of the number of the agent movements is derived. It is observed that the cover time of many of already existing random walk based variants is large in random geometric graphs of low degree (as it is commonly the case is wireless environments). As this inefficiency is attributed (as discussed in the paper) to the inability of existing random walk based solutions to move away from already likely covered areas, a mechanism for directional movement (i.e., jumping) of the random walk based agent is proposed and studied, that allows the agent to jump to different network areas, most likely not covered yet. The proposed mechanism (Jumping Random Walk) is studied analytically and via simulations and the parameters (of the network topology and the mechanism) under which the proposed scheme outperforms existing random walk based variations are determined.