2 Search Results for "Brunsch, Tobias"

Document
DOI: 10.4230/LIPIcs.ESA.2025.105
Parameterized Algorithms for Computing Pareto Sets

Authors: Joshua Marc Könen, Heiko Röglin, and Tarek Stuck

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The problem of computing the set of Pareto-optimal solutions has been studied for a variety of multiobjective optimization problems. For many such problems, algorithms are known that compute the Pareto set in (weak) output-polynomial time. These algorithms are often based on dynamic programming and by weak output-polynomial time, we mean that the running time depends polynomially on the size of the Pareto set but also on the sizes of the Pareto sets of the subproblems that occur in the dynamic program. For some problems, like the multiobjective minimum spanning tree problem, such algorithms are not known to exist and for other problems, like multiobjective versions of many NP-hard problems, such algorithms cannot exist, unless 𝒫 = 𝒩𝒫. Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first derive an algorithm to compute the Pareto set for the multicriteria s-t cut problem and show how this result can be applied to a polygon aggregation problem arising in cartography that has recently been introduced by Rottmann et al. (GIScience 2021). We also show how to apply these techniques to also compute the Pareto set of the multiobjective minimum spanning tree problem and for the multiobjective TSP. The running time of our algorithms is O(f(w)⋅poly(n,p_{max})), where f is some function in the treewidth w, n is the input size, and p_{max} is an upper bound on the size of the Pareto sets of the subproblems that occur in the dynamic program. Finally, we present an experimental evaluation of computing Pareto sets on real-world instances of polygon aggregation problems. For this matter we devised a task-specific data structure that allows for efficient storage and modification of large sets of Pareto-optimal solutions. Throughout the implementation process, we incorporated several improved strategies and heuristics that significantly reduced both runtime and memory usage, enabling us to solve instances with treewidth of up to 22 within reasonable amount of time. Moreover, we conducted a preprocessing study to compare different tree decompositions in terms of their estimated overall runtime.
Cite as

Joshua Marc Könen, Heiko Röglin, and Tarek Stuck. Parameterized Algorithms for Computing Pareto Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 105:1-105:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{konen_et_al:LIPIcs.ESA.2025.105,
  author =	{K\"{o}nen, Joshua Marc and R\"{o}glin, Heiko and Stuck, Tarek},
  title =	{{Parameterized Algorithms for Computing Pareto Sets}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{105:1--105:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.105},
  URN =		{urn:nbn:de:0030-drops-245749},
  doi =		{10.4230/LIPIcs.ESA.2025.105},
  annote =	{Keywords: parameterized algorithms, treewidth, multicriteria optimization problems, multicriteria MST, multicriteria TSP, polygon aggregation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.171
Solving Totally Unimodular LPs with the Shadow Vertex Algorithm

Authors: Tobias Brunsch, Anna Großwendt, and Heiko Röglin

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
We show that the shadow vertex simplex algorithm can be used to solve linear programs in strongly polynomial time with respect to the number n of variables, the number m of constraints, and 1/\delta, where \delta is a parameter that measures the flatness of the vertices of the polyhedron. This extends our recent result that the shadow vertex algorithm finds paths of polynomial length (w.r.t. n, m, and 1/delta) between two given vertices of a polyhedron [4]. Our result also complements a recent result due to Eisenbrand and Vempala [6] who have shown that a certain version of the random edge pivot rule solves linear programs with a running time that is strongly polynomial in the number of variables n and 1/\delta, but independent of the number m of constraints. Even though the running time of our algorithm depends on m, it is significantly faster for the important special case of totally unimodular linear programs, for which 1/delta\le n and which have only O(n^2) constraints.
Cite as

Tobias Brunsch, Anna Großwendt, and Heiko Röglin. Solving Totally Unimodular LPs with the Shadow Vertex Algorithm. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 171-183, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{brunsch_et_al:LIPIcs.STACS.2015.171,
  author =	{Brunsch, Tobias and Gro{\ss}wendt, Anna and R\"{o}glin, Heiko},
  title =	{{Solving Totally Unimodular LPs with the Shadow Vertex Algorithm}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{171--183},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.171},
  URN =		{urn:nbn:de:0030-drops-49125},
  doi =		{10.4230/LIPIcs.STACS.2015.171},
  annote =	{Keywords: linear optimization, simplex algorithm, shadow vertex method}
}
  • Refine by Type
  • 2 Document/PDF
  • 1 Document/HTML

  • Refine by Publication Year
  • 1 2025
  • 1 2015

  • Refine by Author
  • 2 Röglin, Heiko
  • 1 Brunsch, Tobias
  • 1 Großwendt, Anna
  • 1 Könen, Joshua Marc
  • 1 Stuck, Tarek

  • Refine by Series/Journal
  • 2 LIPIcs

  • Refine by Classification
  • 1 Theory of computation → Design and analysis of algorithms
  • 1 Theory of computation → Graph algorithms analysis
  • 1 Theory of computation → Parameterized complexity and exact algorithms

  • Refine by Keyword
  • 1 linear optimization
  • 1 multicriteria MST
  • 1 multicriteria TSP
  • 1 multicriteria optimization problems
  • 1 parameterized algorithms
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact