Strong Connectivity of Sensor Networks with Double Antennae

Abstract

Inspired by the well-known Dipole and Yagi antennae we introduce and study a new theoretical model of directional antennae that we call double antennae. Given a set P of n sensors in the plane equipped with double antennae of angle φ and with dipole-like and Yagi-like antenna propagation patterns, we study the connectivity and stretch factor problems, namely finding the minimum range such that double antennae of that range can be oriented so as to guarantee strong connectivity or stretch factor of the resulting network. We introduce the new concepts of (2,φ)-connectivity and φ-angular range r _φ (P) and use it to characterize the optimality of our algorithms. We prove that r _φ (P) is a lower bound on the range required for strong connectivity and show how to compute r _φ (P) in time polynomial in n. We give algorithms for orienting the antennae so as to attain strong connectivity using optimal range when φ ≥ 2 π/3, and algorithms approximating the range for φ ≥ π/2. For φ < π/3, we show that the problem is NP-complete to approximate within a factor $\sqrt{3}$. For φ ≥ π/2, we give an algorithm to orient the antennae so that the resulting network has a stretch factor of at most 4 compared to the underlying unit disk graph.