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From an information-theoretic point of view, we investigate the min-max powerscheduling problem in multi-access transmission. We prove that the min-maxoptimal vector in a contrapolymatroid is the base with the minimal distance tothe equal allocation vector. Because we can realize any base of thecontra-polymatroid by time sharing among the vertices, the problem searchingfor the min-max optimal vector is converted to a convex optimization problemsolving the time sharing coefficients. Different from the traditionalalgorithms exploiting bottleneck link or waterfilling, the proposed methodsimplifies the computation of the min-max optimal vector and directly outputsthe system parameters to realize the min-max fair scheduling. By adopting theproposed method and applying the acquired min-max optimal scheduling tomulti-access transmission, the network lifetime of the wireless sensor networkis prolonged.

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