Coverage Problem for Sensors Embedded in Temperature Sensitive Environments

The coverage and connectivity problem in sensor networks has received significant attention of the research community in the recent years. In this paper, we study this problem for sensors deployed in temperature sensitive environments. This paper is motivated by the issues encountered during deployment of bio-sensors in a human/animal body. Radio transmitters during operation dissipate energy and raise the temperature of its surroundings. A temperature sensitive environment like the human body can tolerate such increase in temperature only up to a certain threshold value, beyond which serious injury may occur. To avoid such injuries, the sensor placement must be carried out in a way that ensures the surrounding temperature to remain within the threshold. Using a thermal model for heat distribution from multiple heat sources (radio transmitters), we observed that if the sensor nodes are placed sufficiently apart from each other, then the temperature of the surrounding area does not exceed the threshold. This minimum separation distance constraint gives rise to a new version of the sensor coverage problem that has not been studied earlier. We prove that both the optimization version and the feasibility version of the new problem are NP-complete. We further show that an epsiv-approximation algorithm for the problem cannot exist unless P = NP. We provide two heuristic solutions for the problem and evaluate the efficacy of these solutions by comparing their performances against the optimal solution. The simulation results show that our heuristic solutions almost always find near optimal solution in a fraction of the time needed to find the optimal solution. Finally, an algorithm for forming a connected sensor network with minimum transmission power in such a scenario is provided.