To Prolong the Lifetime of Wireless Sensor Networks: The Min-max Fair Scheduling in a Multi-access Contra-Polymatroid

From an information-theoretic point of view, we investigate the min-max power scheduling problem in multi-access transmission. We prove that the min-max optimal vector in a contrapolymatroid is the base with the minimal distance to the equal allocation vector. Because we can realize any base of the contra-polymatroid by time sharing among the vertices, the problem searching for the min-max optimal vector is converted to a convex optimization problem solving the time sharing coefficients. Different from the traditional algorithms exploiting bottleneck link or waterfilling, the proposed method simplifies the computation of the min-max optimal vector and directly outputs the system parameters to realize the min-max fair scheduling. By adopting the proposed method and applying the acquired min-max optimal scheduling to multi-access transmission, the network lifetime of the wireless sensor network is prolonged.