On the Phase Transition Analysis of k/Q-coverage Problem in Wireless Sensor Networks

Phase transition is an important area of research in studying empirical hardness of NP-complete problems. We explore the possibility of phase transition phenomena in k/Q-coverage problem of wireless sensor networks wherein there exists some parameter for which the problem exhibits a sharp transition as the value of the parameters increase. We identify sensing range as one such parameter that triggers phase transition. The phase-transition region is identified. The problem can be solved easily (believed to be in polynomial time) if the parameters are outside this critical region. This work would be an addition to the existing models whose phase transition has already been studied. It would give an idea on the choice of parameters to be adopted for making k/Q-coverage problem solvable in real applications.