## AbstractWe study the computational complexity of relay placement in energy-constrained wireless sensor networks. The goal is to optimise balanced data gathering, where the utility function is a weighted sum of the minimum and average amount of data collected from each sensor node. We define a number of classes of simplified relay placement problems, including a planar problem with a simple cost model for radio communication. We prove that all of these problem classes are NP-hard, and that in some cases even finding approximative solutions is NP-hard.
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