We study the power assignment problem in radio networks, where each radio station can transmit in one of two possible power levels, corresponding to two ranges – short and long. We show that this problem is NP-hard, and present a polynomial-time assignment algorithm, such that the number of transmitters that are assigned long range by the algorithm is at most (11/6) times the number of transmitters that are assigned long range by an optimal algorithm.
Paz Carmi, Matthew J. Katz