, Volume 105, Issue 2, pp 427449
First online:
An Algorithmic Framework for the Exact Solution of the PrizeCollecting Steiner Tree Problem
 Ivana LjubićAffiliated withVienna University of Technology Email author
 , René WeiskircherAffiliated withVienna University of Technology
 , Ulrich PferschyAffiliated withUniversity of Graz
 , Gunnar W. KlauAffiliated withVienna University of Technology
 , Petra MutzelAffiliated withVienna University of Technology
 , Matteo FischettiAffiliated withDEI, University of Padova
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The PrizeCollecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network connecting them have to be chosen in the most profitable way.
Our main contribution is the formulation and implementation of a branchandcut algorithm based on a directed graph model where we combine several stateoftheart methods previously used for the Steiner tree problem. Our method outperforms the previously published results on the standard benchmark set of problems.
We can solve all benchmark instances from the literature to optimality, including some of them for which the optimum was not known. Compared to a recent algorithm by Lucena and Resende, our new method is faster by more than two orders of magnitude. We also introduce a new class of more challenging instances and present computational results for them. Finally, for a set of largescale realworld instances arising in the design of fiber optic networks, we also obtain optimal solution values.
Keywords
BranchandCut Steiner Arborescence Prize Collecting Network Design Title
 An Algorithmic Framework for the Exact Solution of the PrizeCollecting Steiner Tree Problem
 Journal

Mathematical Programming
Volume 105, Issue 23 , pp 427449
 Cover Date
 200602
 DOI
 10.1007/s101070050660x
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 BranchandCut
 Steiner Arborescence
 Prize Collecting
 Network Design
 Industry Sectors
 Authors

 Ivana Ljubić ^{(1)}
 René Weiskircher ^{(1)}
 Ulrich Pferschy ^{(2)}
 Gunnar W. Klau ^{(1)}
 Petra Mutzel ^{(1)}
 Matteo Fischetti ^{(3)}
 Author Affiliations

 1. Vienna University of Technology, Favoritenstr. 911, 1040, Vienna, Austria
 2. University of Graz, Universitätsstr. 15, 8010, Graz, Austria
 3. DEI, University of Padova, via Gradenigo 6/a, 35131, Padova, Italy