Optimal Memory - aware Sensor Network

Gossiping is an important problem in Radio Networks that has been well studied, leading to many important results. However, due to the strong resource limitations of sensor nodes, previous solutions are frequently not feasible in Sensor Networks. In this paper, we study the gossiping problem in the restrictive context of Sensor Networks. By exploiting the geometry of sensor node distributions, we present a reduced, optimal running time of Θ(D + ∆) for a distributed algorithm that completes gossiping with high probability in a Sensor Network of unknown topology and adversarial start-up, where D is the diameter and ∆ the maximum degree of the network. Given that an algorithm for gossiping also solves the broadcast problem, this result shows that the classic broadcast lower bound of Kushilevitz and Mansour does not hold if nodes are allowed to do preprocessing, given that the topology used in that paper is feasible for Sensor Networks. The proposed algorithm requires that a linear number of messages can be stored and transmitted in one time unit. When only a constant number of messages can be stored, an optimal distributed algorithm that solves the problem in linear time is also given. keywords: radio networks, sensor networks, gossiping, distributed algorithms, broadcast, convergecast.