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Documents authored by Göke, Alexander

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APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.25
Hitting Weighted Even Cycles in Planar Graphs

Authors: Alexander Göke, Jochen Koenemann, Matthias Mnich, and Hao Sun

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
A classical branch of graph algorithms is graph transversals, where one seeks a minimum-weight subset of nodes in a node-weighted graph G which intersects all copies of subgraphs F from a fixed family F. Many such graph transversal problems have been shown to admit polynomial-time approximation schemes (PTAS) for planar input graphs G, using a variety of techniques like the shifting technique (Baker, J. ACM 1994), bidimensionality (Fomin et al., SODA 2011), or connectivity domination (Cohen-Addad et al., STOC 2016). These techniques do not seem to apply to graph transversals with parity constraints, which have recently received significant attention, but for which no PTASs are known. In the even-cycle transversal (ECT) problem, the goal is to find a minimum-weight hitting set for the set of even cycles in an undirected graph. For ECT, Fiorini et al. (IPCO 2010) showed that the integrality gap of the standard covering LP relaxation is Θ(log n), and that adding sparsity inequalities reduces the integrality gap to 10. Our main result is a primal-dual algorithm that yields a 47/7 ≈ 6.71-approximation for ECT on node-weighted planar graphs, and an integrality gap of the same value for the standard LP relaxation on node-weighted planar graphs.
Cite as

Alexander Göke, Jochen Koenemann, Matthias Mnich, and Hao Sun. Hitting Weighted Even Cycles in Planar Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{goke_et_al:LIPIcs.APPROX/RANDOM.2021.25,
  author =	{G\"{o}ke, Alexander and Koenemann, Jochen and Mnich, Matthias and Sun, Hao},
  title =	{{Hitting Weighted Even Cycles in Planar Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{25:1--25:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.25},
  URN =		{urn:nbn:de:0030-drops-147186},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.25},
  annote =	{Keywords: Even cycles, planar graphs, integrality gap}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.59
Hitting Long Directed Cycles Is Fixed-Parameter Tractable

Authors: Alexander Göke, Dániel Marx, and Matthias Mnich

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
In the Directed Long Cycle Hitting Set problem we are given a directed graph G, and the task is to find a set S of at most k vertices/arcs such that G-S has no cycle of length longer than ℓ. We show that the problem can be solved in time 2^O(ℓ^6 + ℓ k^3 log k + k^5 log k log ℓ) ⋅ n^O(1), that is, it is fixed-parameter tractable (FPT) parameterized by k and ℓ. This algorithm can be seen as a far-reaching generalization of the fixed-parameter tractability of Mixed Graph Feedback Vertex Set [Bonsma and Lokshtanov WADS 2011], which is already a common generalization of the fixed-parameter tractability of (undirected) Feedback Vertex Set and the Directed Feedback Vertex Set problems, two classic results in parameterized algorithms. The algorithm requires significant insights into the structure of graphs without directed cycles of length longer than ℓ and can be seen as an exact version of the approximation algorithm following from the Erdős-Pósa property for long cycles in directed graphs proved by Kreutzer and Kawarabayashi [STOC 2015].
Cite as

Alexander Göke, Dániel Marx, and Matthias Mnich. Hitting Long Directed Cycles Is Fixed-Parameter Tractable. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{goke_et_al:LIPIcs.ICALP.2020.59,
  author =	{G\"{o}ke, Alexander and Marx, D\'{a}niel and Mnich, Matthias},
  title =	{{Hitting Long Directed Cycles Is Fixed-Parameter Tractable}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{59:1--59:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.59},
  URN =		{urn:nbn:de:0030-drops-124664},
  doi =		{10.4230/LIPIcs.ICALP.2020.59},
  annote =	{Keywords: Directed graphs, directed feedback vertex set, circumference}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2019.17
Resolving Infeasibility of Linear Systems: A Parameterized Approach

Authors: Alexander Göke, Lydia Mirabel Mendoza Cadena, and Matthias Mnich

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
Deciding feasibility of large systems of linear equations and inequalities is one of the most fundamental algorithmic tasks. However, due to inaccuracies of the data or modeling errors, in practical applications one often faces linear systems that are infeasible. Extensive theoretical and practical methods have been proposed for post-infeasibility analysis of linear systems. This generally amounts to detecting a feasibility blocker of small size k, which is a set of equations and inequalities whose removal or perturbation from the large system of size m yields a feasible system. This motivates a parameterized approach towards post-infeasibility analysis, where we aim to find a feasibility blocker of size at most k in fixed-parameter time f(k)* m^{O(1)}. On the one hand, we establish parameterized intractability (W[1]-hardness) results even in very restricted settings. On the other hand, we develop fixed-parameter algorithms parameterized by the number of perturbed inequalities and the number of positive/negative right-hand sides. Our algorithms capture the case of Directed Feedback Arc Set, a fundamental parameterized problem whose fixed-parameter tractability was shown by Chen et al. (STOC 2008).
Cite as

Alexander Göke, Lydia Mirabel Mendoza Cadena, and Matthias Mnich. Resolving Infeasibility of Linear Systems: A Parameterized Approach. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{goke_et_al:LIPIcs.IPEC.2019.17,
  author =	{G\"{o}ke, Alexander and Mendoza Cadena, Lydia Mirabel and Mnich, Matthias},
  title =	{{Resolving Infeasibility of Linear Systems: A Parameterized Approach}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.17},
  URN =		{urn:nbn:de:0030-drops-114787},
  doi =		{10.4230/LIPIcs.IPEC.2019.17},
  annote =	{Keywords: Infeasible subsystems, linear programming, fixed-parameter algorithms}
}
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