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Documents authored by Kellerhals, Leon

Document
DOI: 10.4230/LIPIcs.IPEC.2022.19
Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees

Authors: Leon Kellerhals, Tomohiro Koana, and Pascal Kunz

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
Vertex Cover parameterized by the solution size k is the quintessential fixed-parameter tractable problem. FPT algorithms are most interesting when the parameter is small. Several lower bounds on k are well-known, such as the maximum size of a matching. This has led to a line of research on parameterizations of Vertex Cover by the difference of the solution size k and a lower bound. The most prominent cases for such lower bounds for which the problem is FPT are the matching number or the optimal fractional LP solution. We investigate parameterizations by the difference between k and other graph parameters including the feedback vertex number, the degeneracy, cluster deletion number, and treewidth with the goal of finding the border of fixed-parameter tractability for said difference parameterizations. We also consider similar parameterizations of the Feedback Vertex Set problem.
Cite as

Leon Kellerhals, Tomohiro Koana, and Pascal Kunz. Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kellerhals_et_al:LIPIcs.IPEC.2022.19,
  author =	{Kellerhals, Leon and Koana, Tomohiro and Kunz, Pascal},
  title =	{{Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.19},
  URN =		{urn:nbn:de:0030-drops-173758},
  doi =		{10.4230/LIPIcs.IPEC.2022.19},
  annote =	{Keywords: parameterized complexity, vertex cover, feedback vertex set, above guarantee parameterization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.26
The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing

Authors: Leon Kellerhals, Tomohiro Koana, André Nichterlein, and Philipp Zschoche

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
The Parameterized Algorithms and Computational Experiments challenge (PACE) 2021 was devoted to engineer algorithms solving the NP-hard Cluster Editing problem, also known as Correlation Clustering: Given an undirected graph the task is to compute a minimum number of edges to insert or remove in a way that the resulting graph is a cluster graph, that is, a graph in which each connected component is a clique. Altogether 67 participants from 21 teams, 11 countries, and 3 continents submitted their implementations to the competition. In this report, we describe the setup of the challenge, the selection of benchmark instances, and the ranking of the participating teams. We also briefly discuss the approaches used in the submitted solvers.
Cite as

Leon Kellerhals, Tomohiro Koana, André Nichterlein, and Philipp Zschoche. The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kellerhals_et_al:LIPIcs.IPEC.2021.26,
  author =	{Kellerhals, Leon and Koana, Tomohiro and Nichterlein, Andr\'{e} and Zschoche, Philipp},
  title =	{{The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.26},
  URN =		{urn:nbn:de:0030-drops-154096},
  doi =		{10.4230/LIPIcs.IPEC.2021.26},
  annote =	{Keywords: Correlation Clustering, Cluster Editing, Algorithm Engineering, FPT, Kernelization, Heuristics}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.55
Parameterized Algorithms for Diverse Multistage Problems

Authors: Leon Kellerhals, Malte Renken, and Philipp Zschoche

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
The world is rarely static - many problems need not only be solved once but repeatedly, under changing conditions. This setting is addressed by the multistage view on computational problems. We study the diverse multistage variant, where consecutive solutions of large variety are preferable to similar ones, e.g. for reasons of fairness or wear minimization. While some aspects of this model have been tackled before, we introduce a framework allowing us to prove that a number of diverse multistage problems are fixed-parameter tractable by diversity, namely Perfect Matching, s-t Path, Matroid Independent Set, and Plurality Voting. This is achieved by first solving special, colored variants of these problems, which might also be of independent interest.
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Leon Kellerhals, Malte Renken, and Philipp Zschoche. Parameterized Algorithms for Diverse Multistage Problems. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kellerhals_et_al:LIPIcs.ESA.2021.55,
  author =	{Kellerhals, Leon and Renken, Malte and Zschoche, Philipp},
  title =	{{Parameterized Algorithms for Diverse Multistage Problems}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{55:1--55:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.55},
  URN =		{urn:nbn:de:0030-drops-146360},
  doi =		{10.4230/LIPIcs.ESA.2021.55},
  annote =	{Keywords: Temporal graphs, dissimilar solutions, fixed-parameter tractability, perfect matchings, s-t paths, committee election, spanning forests, matroids}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2020.20
Parameterized Complexity of Geodetic Set

Authors: Leon Kellerhals and Tomohiro Koana

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
A vertex set S of a graph G is geodetic if every vertex of G lies on a shortest path between two vertices in S. Given a graph G and k ∈ ℕ, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size at most k. Complementing various works on Geodetic Set restricted to special graph classes, we initiate a parameterized complexity study of Geodetic Set and show, on the negative side, that Geodetic Set is W[1]-hard when parameterized by feedback vertex number, path-width, and solution size, combined. On the positive side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph.
Cite as

Leon Kellerhals and Tomohiro Koana. Parameterized Complexity of Geodetic Set. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kellerhals_et_al:LIPIcs.IPEC.2020.20,
  author =	{Kellerhals, Leon and Koana, Tomohiro},
  title =	{{Parameterized Complexity of Geodetic Set}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.20},
  URN =		{urn:nbn:de:0030-drops-133237},
  doi =		{10.4230/LIPIcs.IPEC.2020.20},
  annote =	{Keywords: NP-hard graph problems, Shortest paths, Tree-likeness, Parameter hierarchy, Data reduction, Integer linear programming}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.36
An Adaptive Version of Brandes' Algorithm for Betweenness Centrality

Authors: Matthias Bentert, Alexander Dittmann, Leon Kellerhals, André Nichterlein, and Rolf Niedermeier

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Betweenness centrality - measuring how many shortest paths pass through a vertex - is one of the most important network analysis concepts for assessing the relative importance of a vertex. The well-known algorithm of Brandes [2001] computes, on an n-vertex and m-edge graph, the betweenness centrality of all vertices in O(nm) worst-case time. In follow-up work, significant empirical speedups were achieved by preprocessing degree-one vertices and by graph partitioning based on cut vertices. We further contribute an algorithmic treatment of degree-two vertices, which turns out to be much richer in mathematical structure than the case of degree-one vertices. Based on these three algorithmic ingredients, we provide a strengthened worst-case running time analysis for betweenness centrality algorithms. More specifically, we prove an adaptive running time bound O(kn), where k < m is the size of a minimum feedback edge set of the input graph.
Cite as

Matthias Bentert, Alexander Dittmann, Leon Kellerhals, André Nichterlein, and Rolf Niedermeier. An Adaptive Version of Brandes' Algorithm for Betweenness Centrality. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bentert_et_al:LIPIcs.ISAAC.2018.36,
  author =	{Bentert, Matthias and Dittmann, Alexander and Kellerhals, Leon and Nichterlein, Andr\'{e} and Niedermeier, Rolf},
  title =	{{An Adaptive Version of Brandes' Algorithm for Betweenness Centrality}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{36:1--36:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.36},
  URN =		{urn:nbn:de:0030-drops-99846},
  doi =		{10.4230/LIPIcs.ISAAC.2018.36},
  annote =	{Keywords: network science, social network analysis, centrality measures, shortest paths, tree-like graphs, efficient pre- and postprocessing, FPT in P}
}
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