The equivalent subgraph and directed cut polyhedra on series-parallel graphs
SIAM Journal on Discrete Mathematics
The prize collecting Steiner tree problem: theory and practice
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Strong lower bounds for the prize collecting Steiner problem in graphs
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Strong Formulations for 2-Node-Connected Steiner Network Problems
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
HM '08 Proceedings of the 5th International Workshop on Hybrid Metaheuristics
Approximation and Online Algorithms
Obtaining optimal k-cardinality trees fast
Journal of Experimental Algorithmics (JEA)
Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach
INFORMS Journal on Computing
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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 customers only a simple path. Herein, we present a novel ILP approach to solve this problem to optimality based on directed cuts. This formulation becomes possible by exploiting a certain orientability of the given graph. To our knowledge, this is the first time that such an argument is used for a problem with node-disjointness constraints. We prove that this formulation is stronger than the well-known undirected cut approach. Our experiments show its efficiency over the other formulations presented for this problem, i.e., the undirected cut approach and a formulation based on multi-commodity flow.