6 Search Results for "K�nig, Felix G."

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.36
Coloring and Recognizing Mixed Interval Graphs

Authors: Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
A mixed interval graph is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are defined by the geometry of intervals. In a proper coloring of a mixed interval graph G, an interval u receives a lower (different) color than an interval v if G contains arc (u,v) (edge {u,v}). Coloring of mixed graphs has applications, for example, in scheduling with precedence constraints; see a survey by Sotskov [Mathematics, 2020]. For coloring general mixed interval graphs, we present a min {ω(G), λ(G)+1}-approximation algorithm, where ω(G) is the size of a largest clique and λ(G) is the length of a longest directed path in G. For the subclass of bidirectional interval graphs (introduced recently for an application in graph drawing), we show that optimal coloring is NP-hard. This was known for general mixed interval graphs. We introduce a new natural class of mixed interval graphs, which we call containment interval graphs. In such a graph, there is an arc (u,v) if interval u contains interval v, and there is an edge {u,v} if u and v overlap. We show that these graphs can be recognized in polynomial time, that coloring them with the minimum number of colors is NP-hard, and that there is a 2-approximation algorithm for coloring.
Cite as

Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Felix Klesen, Paweł Rzążewski, Alexander Wolff, and Johannes Zink. Coloring and Recognizing Mixed Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{gutowski_et_al:LIPIcs.ISAAC.2023.36,
  author =	{Gutowski, Grzegorz and Junosza-Szaniawski, Konstanty and Klesen, Felix and Rz\k{a}\.{z}ewski, Pawe{\l} and Wolff, Alexander and Zink, Johannes},
  title =	{{Coloring and Recognizing Mixed Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.36},
  URN =		{urn:nbn:de:0030-drops-193388},
  doi =		{10.4230/LIPIcs.ISAAC.2023.36},
  annote =	{Keywords: Interval Graphs, Mixed Graphs, Graph Coloring}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.71
Coloring Tournaments with Few Colors: Algorithms and Complexity

Authors: Felix Klingelhoefer and Alantha Newman

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
A k-coloring of a tournament is a partition of its vertices into k acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a 2-colorable tournament with few colors. This problem does not seem to have been addressed before, although it is a special case of coloring a 2-colorable 3-uniform hypergraph with few colors, which is a well-studied problem with super-constant lower bounds. We present an efficient decomposition lemma for tournaments and show that it can be used to design polynomial-time algorithms to color various classes of tournaments with few colors, including an algorithm to color a 2-colorable tournament with ten colors. For the classes of tournaments considered, we complement our upper bounds with strengthened lower bounds, painting a comprehensive picture of the algorithmic and complexity aspects of coloring tournaments.
Cite as

Felix Klingelhoefer and Alantha Newman. Coloring Tournaments with Few Colors: Algorithms and Complexity. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 71:1-71:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{klingelhoefer_et_al:LIPIcs.ESA.2023.71,
  author =	{Klingelhoefer, Felix and Newman, Alantha},
  title =	{{Coloring Tournaments with Few Colors: Algorithms and Complexity}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{71:1--71:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.71},
  URN =		{urn:nbn:de:0030-drops-187247},
  doi =		{10.4230/LIPIcs.ESA.2023.71},
  annote =	{Keywords: Tournaments, Graph Coloring, Algorithms, Complexity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.123
Twin-Width and Types

Authors: Jakub Gajarský, Michał Pilipczuk, Wojciech Przybyszewski, and Szymon Toruńczyk

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study problems connected to first-order logic in graphs of bounded twin-width. Inspired by the approach of Bonnet et al. [FOCS 2020], we introduce a robust methodology of local types and describe their behavior in contraction sequences - the decomposition notion underlying twin-width. We showcase the applicability of the methodology by proving the following two algorithmic results. In both statements, we fix a first-order formula φ(x_1,…,x_k) and a constant d, and we assume that on input we are given a graph G together with a contraction sequence of width at most d. - One can in time 𝒪(n) construct a data structure that can answer the following queries in time 𝒪(log log n): given w_1,…,w_k, decide whether φ(w_1,…,w_k) holds in G. - After 𝒪(n)-time preprocessing, one can enumerate all tuples w₁,…,w_k that satisfy φ(x_1,…,x_k) in G with 𝒪(1) delay. In the first case, the query time can be reduced to 𝒪(1/ε) at the expense of increasing the construction time to 𝒪(n^{1+ε}), for any fixed ε > 0. Finally, we also apply our tools to prove the following statement, which shows optimal bounds on the VC density of set systems that are first-order definable in graphs of bounded twin-width. - Let G be a graph of twin-width d, A be a subset of vertices of G, and φ(x_1,…,x_k,y_1,…,y_l) be a first-order formula. Then the number of different subsets of A^k definable by φ using l-tuples of vertices from G as parameters, is bounded by O(|A|^l).
Cite as

Jakub Gajarský, Michał Pilipczuk, Wojciech Przybyszewski, and Szymon Toruńczyk. Twin-Width and Types. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 123:1-123:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2022.123,
  author =	{Gajarsk\'{y}, Jakub and Pilipczuk, Micha{\l} and Przybyszewski, Wojciech and Toru\'{n}czyk, Szymon},
  title =	{{Twin-Width and Types}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{123:1--123:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.123},
  URN =		{urn:nbn:de:0030-drops-164640},
  doi =		{10.4230/LIPIcs.ICALP.2022.123},
  annote =	{Keywords: twin-width, FO logic, model checking, query answering, enumeration}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2022.5
Fault-Tolerant Edge-Disjoint s-t Paths - Beyond Uniform Faults

Authors: David Adjiashvili, Felix Hommelsheim, Moritz Mühlenthaler, and Oliver Schaudt

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
The Edge-disjoint s-t Paths Problem (s-t EDP) is a classical network design problem whose goal is to connect for some k ≥ 1 two given vertices of a graph under the condition that any k-1 edges of the graph may fail. We extend the simple uniform failure model of the s-t EDP as follows: the edge set of the graph is partitioned into vulnerable, and safe edges, and a set of at most k vulnerable edges may fail, while safe edges do not fail. In particular we study the Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest s-t Path problem in this non-uniform failure model as well as the Fault-Tolerant Flow (FTF) problem, the counterpart of s-t EDP. We present complexity results alongside exact and approximation algorithms for both problems. We emphasize the vast increase in complexity of the problems compared to s-t EDP.
Cite as

David Adjiashvili, Felix Hommelsheim, Moritz Mühlenthaler, and Oliver Schaudt. Fault-Tolerant Edge-Disjoint s-t Paths - Beyond Uniform Faults. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{adjiashvili_et_al:LIPIcs.SWAT.2022.5,
  author =	{Adjiashvili, David and Hommelsheim, Felix and M\"{u}hlenthaler, Moritz and Schaudt, Oliver},
  title =	{{Fault-Tolerant Edge-Disjoint s-t Paths - Beyond Uniform Faults}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.5},
  URN =		{urn:nbn:de:0030-drops-161659},
  doi =		{10.4230/LIPIcs.SWAT.2022.5},
  annote =	{Keywords: graph algorithms, network design, fault tolerance, approximation algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2012.58
Multi-Dimensional Commodity Covering for Tariff Selection in Transportation

Authors: Felix G. König, Jannik Matuschke, and Alexander Richter

Published in: OASIcs, Volume 25, 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2012)

Abstract
In this paper, we study a multi-dimensional commodity covering problem, which we encountered as a subproblem in optimizing large scale transportation networks in logistics. The problem asks for a selection of containers for transporting a given set of commodities, each commodity having different extensions of properties such as weight or volume. Each container can be selected multiple times and is specified by a fixed charge and capacities in the relevant properties. The task is to find a cost minimal collection of containers and a feasible assignment of the demand to all selected containers. From theoretical point of view, by exploring similarities to the well known SetCover problem, we derive NP-hardness and see that the non-approximability result known for set cover also carries over to our problem. For practical applications we need very fast heuristics to be integrated into a meta-heuristic framework that - depending on the context - either provide feasible near optimal solutions or only estimate the cost value of an optimal solution. We develop and analyze a flexible family of greedy algorithms that meet these challenges. In order to find best-performing configurations for different requirements of the meta-heuristic framework, we provide an extensive computational study on random and real world instance sets obtained from our project partner 4flow AG. We outline a trade-off between running times and solution quality and conclude that the proposed methods achieve the accuracy and efficiency necessary for serving as a key ingredient in more complex meta-heuristics enabling the optimization of large-scale networks.
Cite as

Felix G. König, Jannik Matuschke, and Alexander Richter. Multi-Dimensional Commodity Covering for Tariff Selection in Transportation. In 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 25, pp. 58-70, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

Copy BibTex To Clipboard

@InProceedings{konig_et_al:OASIcs.ATMOS.2012.58,
  author =	{K\"{o}nig, Felix G. and Matuschke, Jannik and Richter, Alexander},
  title =	{{Multi-Dimensional Commodity Covering for Tariff Selection in Transportation}},
  booktitle =	{12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{58--70},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-45-3},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{25},
  editor =	{Delling, Daniel and Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2012.58},
  URN =		{urn:nbn:de:0030-drops-37034},
  doi =		{10.4230/OASIcs.ATMOS.2012.58},
  annote =	{Keywords: Covering, Heuristics, Transportation, Tariff Selection}
}
Document
DOI: 10.4230/DagSemProc.09261.26
Sequencing and Scheduling in Coil Coating with Shuttles

Authors: Wiebke Höhn, Felix G. König, Marco E. Lübbecke, and Rolf H. Möhring

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

Abstract
Applying combinatorial optimization in real life yields cost savings delighting the industry. Beyond that, at the core of some applications also lies a pretty (sub)problem rejoicing the mathematician. In our application coils of sheet metal are coated with k layers out of hundreds of colors. Coils are stapled together to run through k coaters, and non-productive time occurs e.g. when the color in a coater needs to be changed. Some coaters have two parallel tanks, enabling either parallel colors or cleaning of one tank during production. We present our sequencing and scheduling scheme in use at the plant today, lower bounds proving solution quality, and problems in the edge-wise union of interval graphs as a pretty mathematical subproblem.
Cite as

Wiebke Höhn, Felix G. König, Marco E. Lübbecke, and Rolf H. Möhring. Sequencing and Scheduling in Coil Coating with Shuttles. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{hohn_et_al:DagSemProc.09261.26,
  author =	{H\"{o}hn, Wiebke and K\"{o}nig, Felix G. and L\"{u}bbecke, Marco E. and M\"{o}hring, Rolf H.},
  title =	{{Sequencing and Scheduling in Coil Coating with Shuttles}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--29},
  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-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.26},
  URN =		{urn:nbn:de:0030-drops-21654},
  doi =		{10.4230/DagSemProc.09261.26},
  annote =	{Keywords: Sequencing, scheduling, coil coating, mutli-interval graphs, heuristics, branch and price}
}
  • Refine by Author
  • 2 König, Felix G.
  • 1 Adjiashvili, David
  • 1 Gajarský, Jakub
  • 1 Gutowski, Grzegorz
  • 1 Hommelsheim, Felix
  • Show More...

  • Refine by Classification
  • 2 Mathematics of computing → Approximation algorithms
  • 1 Mathematics of computing → Graph theory
  • 1 Theory of computation → Finite Model Theory
  • 1 Theory of computation → Network flows
  • 1 Theory of computation → Routing and network design problems

  • Refine by Keyword
  • 2 Graph Coloring
  • 1 Algorithms
  • 1 Complexity
  • 1 Covering
  • 1 FO logic
  • Show More...

  • Refine by Type
  • 6 document

  • Refine by Publication Year
  • 2 2022
  • 2 2023
  • 1 2009
  • 1 2012

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact