Strong minimum energy topology in wireless sensor networks: NP-completeness and heuristics

Wireless sensor networks have recently attracted lots of research effort due to the wide range of applications. These networks must operate for months or years. However, the sensors are powered by battery, which may not be able to be recharged after they are deployed. Thus, energy-aware network management is extremely important. In this paper, we study the following problem: Given a set of sensors in the plane, assign transmit power to each sensor such that the induced topology containing only bidirectional links is strongly connected. This problem is significant in both theory and application. We prove its NP-completeness and propose two heuristics: power assignment based on minimum spanning tree (denoted by MST) and incremental power. We also show that the MST heuristic has a performance ratio of 2. Simulation study indicates that the performance of these two heuristics does not differ very much, but; on average, the incremental power heuristic is always better than MST.