STRONG CONNECTIVITY IN SENSOR NETWORKS WITH GIVEN NUMBER OF DIRECTIONAL ANTENNAE OF BOUNDED ANGLE

Abstract

Traditional approaches to connectivity in sensor networks are based on the omnidirectional antenna model which relies on the assumption that the sensors send and receive in all directions. Current technologies make possible the utilization of sensors with directional antenna capabilities whereby the sensors send and/or receive along a sector of a predefined angle (or beam-width). Although several researchers in the scientific literature have investigated the impact of directional antennae on network throughput, energy consumption, as well as security very little is known concerning the effect of directional antennae on its connectivity. In this paper, we introduce for the first time a new sensor model with each sensor being able to transmit in any one of k directions, for some fixed k, and explore the algorithmic limits and potential of such a directional antenna model. More specifically, given a set of n sensors in the plane, we consider the problem of establishing a strongly connected ad hoc network from these sensors using directional antennae. In particular, we prove that given such set of sensors, each equipped with k, 1 ≤ k ≤ 5, directional antennae with any angle of transmission, these antennae can be oriented in such a way that the resulting communication structure is a strongly connected digraph spanning all n sensors. Moreover, the transmission range of the antennae is at most [Formula: see text] times the optimal range (a range necessary to establish a connected network on the same set of sensors using omnidirectional antennae). The algorithm which constructs this orientation runs in O(n) time provided a minimum spanning tree on the set of sensors is given. We show that our solution can be used to give a tradeoff on the range and angle when each sensor has one antenna. Further, we also prove that for two antennae it is NP-hard to decide whether such an orientation exists if both the transmission angle and range are small for each antennae.