Solving group Steiner problems as Steiner problems

Solving group Steiner problems as Steiner problems

The generalized spanning tree or group Steiner problem (GSP) is a generalization of the Steiner problem in graphs (SPG): one requires a tree spanning (at least) one vertex of each subset, given in a family of vertex subsets, while minimizing the sum of the corresponding edge costs. Specialized solution procedures have been developed for this problem. In this paper we investigate the performance...

Solving Rectilinear Steiner Tree Problems

The rectilinear Steiner tree problem asks for a shortest tree connecting given points in the plane with rectilinear distance. The best theoretically analyzed algorithm for this problem with a fairly practical behaviour bases on dynamic programming and has a running time of O(n 2 2:62 n) (Ganley/Cohoon). The best implementation can solve random problems of size 35 (Salowe/Warme) within a day. In...

Solving large Steiner Triple Covering Problems

Computing the 1-width of the incidence matrix of a Steiner Triple System gives rise to small set covering instances that provide a computational challenge for integer programming techniques. One major source of difficulty for instances of this family is their highly symmetric structure, which impairs the performance of most branch-and-bound algorithms. The largest instance in the family that ha...

Approximating Fault-Tolerant Group-Steiner Problems

In this paper, we initiate the study of designing approximation algorithms for FaultTolerant Group-Steiner (FTGS) problems. The motivation is to protect the well-studied group-Steiner networks from edge or vertex failures. In Fault-Tolerant Group-Steiner problems, we are given a graph with edge(or vertex-) costs, a root vertex, and a collection of subsets of vertices called groups. The objectiv...

Steiner Tree Problems