Abstract
Power optimization is a central issue in wireless network design. Given a (possibly directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider several fundamental undirected network design problems under the power minimization criteria. Given a graph with edge costs and degree requirements {r(v):v ∈ V}, the Minimum-Power Edge-Multi-Cover () problem is to find a minimum-power subgraph of so that the degree of every node v is at least r(v). We give an O(logn)-approximation algorithms for , improving the previous ratio O(log4 n) of [11]. This is used to derive an O(logn + α)-approximation algorithm for the undirected Minimum-Power k -Connected Subgraph () problem, where is the best known ratio for the min-cost variant of the problem (currently, for n ≥ 2k 2 and otherwise). Surprisingly, it shows that the min-power and the min-cost versions of the k -Connected Subgraph problem are equivalent with respect to approximation, unless the min-cost variant admits an o(logn)-approximation, which seems to be out of reach at the moment. We also improve the best known approximation ratios for small requirements. Specifically, we give a 3/2-approximation algorithm for with r(v) ∈ {0,1}, improving over the 2-approximation by [11], and a \(3\frac{2}{3}\)-approximation for the minimum-power 2-Connected and 2-Edge-Connected Subgraph problems, improving the 4-approximation by [4]. Finally, we give a 4 r max -approximation algorithm for the undirected Minimum-Power Steiner Network () problem: find a minimum-power subgraph that contains r(u,v) pairwise edge-disjoint paths for every pair u,v of nodes.
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Kortsarz, G., Mirrokni, V.S., Nutov, Z., Tsanko, E. (2008). Approximating Minimum-Power Degree and Connectivity Problems. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_37
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DOI: https://doi.org/10.1007/978-3-540-78773-0_37
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