Upgrading bottleneck constrained forests Original Research Article

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 (Goemans and Williamson, SIAM J. Comput. 24 (1995) 296–317). These problems are a generalization of the node weighted constrained forest problems studied by Klein and Ravi (J. Algorithms 19 (1995) 104–115). The main result of the paper is a polynomial-time approximation algorithm for this problem with performance guarantee of 2 ln(e/2·|K|), 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 (Klein and Ravi, J. Algorithms 19 (1995) 104–115) for approximating node weighted constrained forest problems. These results obtained extend those in (Klein and Ravi, J. Algorithms 19 (1995) 104–115, Krumke et al., Lecture Notes in Comput. Sci., Vol. 1197, 1996, pp. 293–307).