Stretch Factor in Wireless Sensor Networks with Directional Antennae

Abstract

Traditional study of wireless sensor networks has relied on the assumption that sensors transmit and receive using an omnidirectional antenna. There has been some recent study using a model where sensors transmit using a directional antenna. This study has focused on the problem of finding an optimal transmission range so that there exists an orientation of the antennae at each sensor which creates a strongly connected communication network. This is known as the Antenna Orientation Problem for Strong Connectivity. In this paper we examine a similar problem: we wish to optimize not only the transmission range, but also the hop-stretch factor of the communication network (in relation to the omnidirectional model). We refer to this as the Antenna Orientation Problem with Constant Stretch Factor. We present approximations to this problem for antennae with angles π/2 ≤ φ ≤ 2π.