On the Complexity of Sub-Tree Scheduling for Wireless Sensor Networks with Partial Coverage
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Given an undirected graph G whose edge weights change over s time slots, the sub-tree scheduling for wireless sensor networks with partial coverage asks to partition the vertices of G in s non-empty trees such that the total weight of the trees is minimized. In this note we show that the problem is NP-hard in both the cases where s (i) is part of the input and (ii) is a fixed instance parameter. In both our proofs we reduce from the cardinality Steiner tree problem. We additionally give polynomial-time algorithms for structured inputs of the problem.
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