An Exact Algorithm for the Steiner Forest Problem

The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. The problem has famous linear programming based 2-approximations [Agrawal et al., 1995; Goemans and Williamson, 1995; Jain, 2001] whose bottleneck is the fact that the most natural formulation of the problem as an integer linear program (ILP) has an integrality gap of 2. We propose new cut-based ILP formulations for the problem along with exact branch-and-bound based algorithms. While our new formulations cannot improve the integrality gap, we can prove that one of them yields stronger linear programming bounds than the two previous strongest formulations: The directed cut formulation [Balakrishnan et al., 1989; Chopra and Rao, 1994] and the advanced flow-based formulation by Magnanti and Raghavan [Magnanti and Raghavan, 2005]. In an experimental evaluation, we show that the linear programming bounds of the new formulations are indeed strong on practical instances and that our new branch-and-bound algorithms outperform branch-and-bound algorithms based on the previous formulations. Our formulations can be seen as a cut-based analogon to [Magnanti and Raghavan, 2005], whose existence was an open problem

An Exact Algorithm for the Steiner Forest Problem

The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. The problem has famous linear programming based 2-approximations [Agrawal et al., 1995; Goemans and Williamson, 1995; Jain, 2001] whose bottleneck is the fact that the most natural formulation of the problem as an integer linear program (ILP) has an integrality gap of 2. We propose new cut-based ILP formulations for the problem along with exact branch-and-bound based algorithms. While our new formulations cannot improve the integrality gap, we can prove that one of them yields stronger linear programming bounds than the two previous strongest formulations: The directed cut formulation [Balakrishnan et al., 1989; Chopra and Rao, 1994] and the advanced flow-based formulation by Magnanti and Raghavan [Magnanti and Raghavan, 2005]. In an experimental evaluation, we show that the linear programming bounds of the new formulations are indeed strong on practical instances and that our new branch-and-bound algorithms outperform branch-and-bound algorithms based on the previous formulations. Our formulations can be seen as a cut-based analogon to [Magnanti and Raghavan, 2005], whose existence was an open problem

AIUCD2017 - Book of Abstracts

Questo volume raccoglie gli abstract degli interventi presentati alla conferenza AIUCD 2017. AIUCD 2017 si è svolta dal 26 al 28 Gennaio 2017 a Roma, ed è stata verrà organizzata dal Digilab, Università Sapienza in cooperazione con il network ITN DiXiT (Digital Scholarly Editions Initial Training Network). AIUCD 2017 ha ospitato anche la terza edizione dell’EADH Day, tenutosi il 25 Gennaio 2017. Gli abstract pubblicati in questo volume hanno ottenuto il parere favorevole da parte di valutatori esperti della materia, attraverso un processo di revisione anonima sotto la responsabilità del Comitato di Programma Internazionale di AIUCD 2017

AIUCD2017 - Book of Abstracts

Questo volume raccoglie gli abstract degli interventi presentati alla conferenza AIUCD 2017. AIUCD 2017 si è svolta dal 26 al 28 Gennaio 2017 a Roma, ed è stata verrà organizzata dal Digilab, Università Sapienza in cooperazione con il network ITN DiXiT (Digital Scholarly Editions Initial Training Network). AIUCD 2017 ha ospitato anche la terza edizione dell’EADH Day, tenutosi il 25 Gennaio 2017. Gli abstract pubblicati in questo volume hanno ottenuto il parere favorevole da parte di valutatori esperti della materia, attraverso un processo di revisione anonima sotto la responsabilità del Comitato di Programma Internazionale di AIUCD 2017