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

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 V of sensors equipped with directional antennas with beam-width theta = pi/3, the objective is to determine an orientation of the antennas and a minimum transmission range r = O(1) 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 pi/3 directional antennas is also NP-hard where we have to determine an orientation of the antennas as well as a power assignment r to the nodes such that the resulting symmetric communication graph is connected, and (2) Sigma(u is an element of S)r(u)(beta) is minimized (beta is the distance-power gradient, 2 <= beta <= 6). We propose an O(n(2)) heuristic algorithm and demonstrate by simulation that our method is better than the Ice-cream method.