Strong Formulations for 2-Node-Connected Steiner Network Problems

Authors:
Markus Chimani;Maria Kandyba;Ivana Ljubić;Petra Mutzel
Affiliations:
Faculty of Computer Science, Dortmund University of Technology, Germany;Faculty of Computer Science, Dortmund University of Technology, Germany;Faculty of Business, Economics and Statistics, University of Vienna, Austria;Faculty of Computer Science, Dortmund University of Technology, Germany
Venue:
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Year:
2008

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Abstract

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 set are nodewise 2-connected. This problem class has received lively attention in the past, especially with regard to exact ILP formulations and their polyhedral properties.In this paper, we present a transformation of 2NCON into a related problem on directed graphs and use this to establish two novel ILP formulations, based on multi-commodity flow and on directed cuts, respectively. We prove the strength of our formulations over the known formulations, and compare our ILPs theoretically and experimentally. This paper thereby consitutes the first experimental study of exact 2NCON algorithms considering more than ~100 nodes, and shows that graphs with up to 4900 nodes can be solved to provable optimality.