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We consider the real-world problem of extending a given infrastructure network in order to connect new customers. By representing the infrastructure by a single root node, this problem can be formulated as a 2-root-connected prize-collecting Steiner network problem in which certain customer nodes require two node-disjoint paths to the root, and other(More)
Given an undirected graph <i>G</i> &equals; (<i>V</i>,<i>E</i>) with edge weights and a positive integer number <i>k</i>, the <i>k</i>-cardinality tree problem consists of finding a subtree <i>T</i> of <i>G</i> with exactly <i>k</i> edges and the minimum possible weight. Many algorithms have been proposed to solve this NP-hard problem, resulting in mainly(More)
We consider {0,1,2}-Survivable Network Design problems with node-connectivity constraints. In the most prominent variant, we are given an edge-weighted graph and two customer sets R 1 and R 2 ; we ask for a minimum cost subgraph that connects all customers, and guarantees two-node-connectivity for the R 2 customers. We also consider an alternative of this(More)
We consider a survivable network design problem known as the 2-Node-Connected Steiner Network Problem (2NCON): we are given a weighted undirected graph with a node partition into two sets of customer nodes and one set of Steiner nodes. We ask for the minimum weight connected subgraph containing all customer nodes, in which the nodes of the second customer(More)
Connected facility location problems combine cost-efficient facility placement (including cheap client-to-facility-connection) with the requirement to connect the facilities among each other. Such network design problems arise, e.g., in telecommuni-cation applications where networks consist of a central core and local clients that have to be connected to(More)
We discuss a general approach to hybridize traditional construction heuristics for combinatorial optimization problems with numerical based evolutionary algorithms. Therefore, we show how to augment a construction heuristic with real-valued parameters, called control values. An evolutionary algorithm for numerical optimization uses this enhanced heuristic(More)
Connected facility location combines cost-efficient facility placement and the requirement to connect the facilities among each other. Such problems arise, e.g., in telecommunication applications where networks consist of a central core and local clients connected to it. Reliability of the core is a central issue, and we may hence require the core to be at(More)
We consider the real-world problem of extending a given infrastructure network in order to connect new customers. By representing the infrastructure by a single root node, this problem can be formulated as a 2-root-connected prize-collecting Steiner network problem in which certain customer nodes require two node-disjoint paths to the root, and other(More)