Symmetric Connectivity in Wireless Sensor Networks with π/3 Directional Antennas

Abstract

Directional Wireless Sensor Networks (DWSNs) have been a very active research topic as they have a wide range of applications in both military and civilian areas. In this paper, we study the Antenna Orientation (AO) and Antenna Orientation and Power Assignment (AOPA) problems, two important issues in DWSNs. In the AO problem, given a set [Formula: see text] of sensors equipped with directional antennas with beam-width [Formula: see text], the objective is to determine an orientation of the antennas and a minimum transmission range [Formula: see text] such that the induced symmetric communication graph is connected. We prove that the AO problem is NP-hard. We then extend our proof technique and show that the AOPA problem for DWSNs equipped with [Formula: see text] directional antennas is also NP-hard where we have to determine an orientation of the antennas as well as a power assignment [Formula: see text] to the nodes such that the resulting symmetric communication graph is connected, and (2) [Formula: see text] is minimized ([Formula: see text] is the distance-power gradient, [Formula: see text]). We propose an [Formula: see text] heuristic algorithm and demonstrate by simulation that our method is better than the Ice-cream method.