The complexity of symmetric connectivity in directional wireless sensor networks

Abstract

In this paper, we investigate the Antenna Orientation (AO) and Antenna Orientation and Power Assignment (AOPA) problems concerning symmetric connectivity in Directional Wireless Sensor Networks (DWSNs) where each sensor node is equipped with $$ 2 \le k \le 5$$ directional antennas having beam-width $$\theta \ge 0$$. The AO problem for DWSNs is closely related with the well-known Euclidean Degree-Bounded Minimum Bottleneck Spanning Tree (EBMBST) problem where different cases for the degree bound have been studied. While current works on DWSNs focus on solving each case of k ($$=2,3,4$$) separately, we propose a uniform approach for the AO problem that yields constant-factor approximation algorithms for the AO as well as the EBMBST problem where the degree bound is between 2 and 4. Our method achieves the same constant factors. For the AOPA problem, to the best of our knowledge, our paper provides the first results concerning this problem. We show that the problem is NP-hard when $$2 \le k \le 4$$. We also establish the first constant-factor approximation algorithms for the problem. Finally, we perform some simulations to understand the practical performance of our algorithms.