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The authors consider the rate allocation problem for data aggregation in wireless sensor networks with two objectives: Maximizing the Minimum (Max - Min) lifetime of an aggregation cluster and achieving fairness among all data sources. The two objectives are generally correlated with each other and usually, they cannot be maximized simultaneously. They adopt a lexicographic method to solve this multi-objective programming problem. First, they recursively induce the Max - Min lifetime for the aggregation cluster. Under the given Max - Min lifetime, they then formulate the problem of maximizing fairness as a convex optimization problem, and derive the optimal rate allocation strategy by iterations.
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