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An instance of the (r, p)-centroid problem is given by an edge and node weighted graph. Two competitors, the leader and the follower, are allowed to place p or r facilities, respectively, into the graph. Users at the nodes connect to the closest facility. A solution of the (r, p)-centroid problem is a leader placement such that the maximum total weight of… (More)

w q x * A preliminary version of this paper appeared as KM 97. 93 We study budget constrained network upgrading problems. We are given an Ž. undirected edge-weighted graph G s V, E , where nodë g V can be upgraded Ž. at a cost of c ¨. This upgrade reduces the weight of each edge incident on¨. The goal is to find a minimum cost set of nodes to be upgraded so… (More)

Inspired by the fact that many combinatorial optimization problems arising in practice are NP-hard, the design of efficient approximation algorithms has been a major research topic for the last years. Since we can not expect to solve any NP-hard problem in polynomial time, it is meaningful to compromise optimality of a solution and settle for a "… (More)