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Documents authored by Pfetsch, Marc E.

Document
DOI: 10.4230/LIPIcs.SEA.2025.24
A New Relaxation for Tree-Based Problems and Minimum Power-Cost Spanning Trees

Authors: Luzie Marianczuk, Ernst Althaus, Stefan Irnich, and Marc E. Pfetsch

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
In this paper, we investigate lower bounds of tree-based optimization problems in order to obtain effective exact algorithms, such as branch-and-bound algorithms. Our new approach inherits the development of dynamic programming algorithms for constrained shortest path problems, as they occur as subproblems in Lagrangian relaxation algorithms and column generation-based algorithms for variants of the Vehicle Routing Problem. In the q-route relaxation, paths must satisfy a capacity constraint while the elementarity constraint is relaxed, that is, paths may contain cycles. An analogue of q-routes for tree optimization problems are q-arbs, a structure that relaxes elementarity for arborescences. We introduce a generalized formulation of q-arbs for a broad class of tree-based problems, and apply the neighborhood restrictions of so-called ng-routes to them to obtain tighter bounds. We apply the new dynamic programming approach to the Minimum Power-Cost Spanning Tree Problem and show empirically that the resulting bounds are often better than traditional LP-based lower bounds of (mixed) integer programming models.
Cite as

Luzie Marianczuk, Ernst Althaus, Stefan Irnich, and Marc E. Pfetsch. A New Relaxation for Tree-Based Problems and Minimum Power-Cost Spanning Trees. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{marianczuk_et_al:LIPIcs.SEA.2025.24,
  author =	{Marianczuk, Luzie and Althaus, Ernst and Irnich, Stefan and Pfetsch, Marc E.},
  title =	{{A New Relaxation for Tree-Based Problems and Minimum Power-Cost Spanning Trees}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.24},
  URN =		{urn:nbn:de:0030-drops-232620},
  doi =		{10.4230/LIPIcs.SEA.2025.24},
  annote =	{Keywords: lower bounds, symmetric connectivity, power range assignment, dynamic programming, optimal substructure}
}
Document
DOI: 10.4230/DagSemProc.09261.15
Line Planning and Connectivity

Authors: Ralf Borndörfer, Marika Neumann, and Marc E. Pfetsch

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract
The line planning problem in public transport deals with the construction of a system of lines that is both attractive for the passengers and of low costs for the operator. In general, the computed line system should be connected, i.e., for each two stations there have to be a path that is covered by the lines. This subproblem is a generalization of the well-known Steiner tree problem; we call it the Steiner connectivity Problem. We discuss complexity of this problem, generalize the so-called Steiner partition inequalities and give a transformation to the directed Steiner tree problem. We show that directed models provide tight formulations for the Steiner connectivity problem, similar as for the Steiner tree problem.
Cite as

Ralf Borndörfer, Marika Neumann, and Marc E. Pfetsch. Line Planning and Connectivity. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{borndorfer_et_al:DagSemProc.09261.15,
  author =	{Bornd\"{o}rfer, Ralf and Neumann, Marika and Pfetsch, Marc E.},
  title =	{{Line Planning and Connectivity}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.15},
  URN =		{urn:nbn:de:0030-drops-21661},
  doi =		{10.4230/DagSemProc.09261.15},
  annote =	{Keywords: Steiner tree, generalization, paths}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2008.1583
Line Planning on Paths and Tree Networks with Applications to the Quito Trolebús System

Authors: Luis M. Torres, Ramiro Torres, Ralf Borndörfer, and Marc E. Pfetsch

Published in: OASIcs, Volume 9, 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08) (2008)

Abstract
Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebús system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebús System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
Cite as

Luis M. Torres, Ramiro Torres, Ralf Borndörfer, and Marc E. Pfetsch. Line Planning on Paths and Tree Networks with Applications to the Quito Trolebús System. In 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08). Open Access Series in Informatics (OASIcs), Volume 9, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{torres_et_al:OASIcs.ATMOS.2008.1583,
  author =	{Torres, Luis M. and Torres, Ramiro and Bornd\"{o}rfer, Ralf and Pfetsch, Marc E.},
  title =	{{Line Planning on Paths and Tree Networks with Applications to the Quito Troleb\'{u}s System}},
  booktitle =	{8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08)},
  pages =	{1--13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-07-1},
  ISSN =	{2190-6807},
  year =	{2008},
  volume =	{9},
  editor =	{Fischetti, Matteo and Widmayer, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2008.1583},
  URN =		{urn:nbn:de:0030-drops-15838},
  doi =		{10.4230/OASIcs.ATMOS.2008.1583},
  annote =	{Keywords: Line planning, computational complexity, public transport, combinatorial optimization}
}
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