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Erschienen in:
01.01.2016
1.61-approximation for min-power strong connectivity with two power levels
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 1/2016
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Abstract
Given a directed simple graph \(G=(V,E)\) and a cost function \(c:E \rightarrow R_+\), the power of a vertex \(u\) in a directed spanning subgraph \(H\) is given by \(p_H(u) = \max _{uv \in E(H)} c(uv)\), and corresponds to the energy consumption required for wireless node \(u\) to transmit to all nodes \(v\) with \(uv \in E(H)\). The power of \(H\) is given by \(p(H) = \sum _{u \in V} p_H(u)\). Power Assignment seeks to minimize \(p(H)\) while \(H\) satisfies some connectivity constraint. In this paper, we assume \(E\) is bidirected (for every directed edge \(e \in E\), the opposite edge exists and has the same cost), while \(H\) is required to be strongly connected. Moreover, we assume \(c:E \rightarrow \{A,B\}\), where \(0 \le A < B\). We improve the best known approximation ratio from 1.75 (Chen et al. IEEE GLOBECOM 2005) to \(\pi ^2/6 - 1/36 + \epsilon \le 1.61\) using an adaptation of the algorithm developed by Khuller et al. [SIAM J Comput 24(4):859–872 1995, Discr Appl Math 69(3):281–289 1996] for (unweighted) Minimum Strongly Connected Subgraph.