Abstract
We study bottleneck constrained network upgrading problems. We are given an edge weighted graph G=(V,E) where node v ∈ V can be upgraded at a cost of c(v). This upgrade reduces the delay of each link emanating from v. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has a good performance. The performance is measured by the bottleneck weight of a constrained forest defined by a proper function [GW95]. These problems are a generalization of the node weighted constrained forest problems studied by Klein and Ravi [KR95].
The main result of the paper is a polynomial time approximation algorithm for this problem with performance guarantee of \(2 \ln (\sqrt{e}/2\cdot \vert K\vert)\), where K:={ v : f({v})=1 } is the set of terminals given by the proper function f. We also prove that the performance bound is tight up to small constant factors by providing a lower bound of ln ∣K∣. Our results are obtained by extending the elegant solution based decomposition technique of [KR95] for approximating node weighted constrained forest problems. The results presented here extend those in [KR95,KM + 97].
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© 1998 Springer-Verlag Berlin Heidelberg
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Krumke, S.O., Marathe, M.V., Noltemeier, H., Ravi, S.S., Wirth, H.C. (1998). Upgrading Bottleneck Constrained Forests. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_18
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DOI: https://doi.org/10.1007/10692760_18
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