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We study budget constrained network upgrading problems. We are given an undirected edge weighted graph ¦ ¨ § © w here node ! " can be upgraded at a cost of # $ © % &. 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 that the resulting network has a minimum spanning tree of weight no… (More)

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)

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)