Abstract
Given a (directed or undirected) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present improved approximation algorithms and inapproximability results for some classic network design problems under the power minimization criteria. In particular, we give a logarithmic approximation algorithm for the problem of finding a minpower subgraph that contains k internally-disjoint paths from a given node s to every other node, and show that several other problems are unlikely to admit a polylogarithmic approximation.
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