Determining Sensor Locations in Wireless Sensor Networks

Network lifetime plays an important role in the design of wireless sensor networks. This paper studies the problem of prolonging the wireless sensor network's lifetime, through introducing additional sensors at proper locations to achieve the goal of minimizing the length of the longest edge in the network. The problem is in fact the bottleneck Steiner tree problem, trying to find a Steiner tree minimizing the length of the longest edges for the given n terminals in the Euclidean plane by introducing at most k Steiner points. A restricted bottleneck Steiner tree problem is studied in this paper, which requires that only degree ≥3 Steiner points are not allowed to be adjacent in the optimal solution. We show that the restricted problem is MAX-SNP hard and cannot be approximated within performance ratio 2 in polynomial time unless P = NP; we first propose a polynomial time 3-approximation algorithm and then improve the ratio to 2+ε for any given ε>0, by presenting a polynomial time randomized approximation algorithm, which is almost optimal to the restricted problem.