7 Search Results for "Bentert, Matthias"


Document
Cluster Editing with Overlapping Communities

Authors: Emmanuel Arrighi, Matthias Bentert, Pål Grønås Drange, Blair D. Sullivan, and Petra Wolf

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
Cluster Editing, also known as correlation clustering, is a well-studied graph modification problem. In this problem, one is given a graph and allowed to perform up to k edge additions and deletions to transform it into a cluster graph, i.e., a graph consisting of a disjoint union of cliques. However, in real-world networks, clusters are often overlapping. For example, in social networks, a person might belong to several communities - e.g. those corresponding to work, school, or neighborhood. Another strong motivation comes from language networks where trying to cluster words with similar usage can be confounded by homonyms, that is, words with multiple meanings like "bat". The recently introduced operation of vertex splitting is one natural approach to incorporating such overlap into Cluster Editing. First used in the context of graph drawing, this operation allows a vertex v to be replaced by two vertices whose combined neighborhood is the neighborhood of v (and thus v can belong to more than one cluster). The problem of transforming a graph into a cluster graph using at most k edge additions, edge deletions, or vertex splits is called Cluster Editing with Vertex Splitting and is known to admit a polynomial kernel with respect to k and an O(9^{k²} + n + m)-time (parameterized) algorithm. However, it was not known whether the problem is NP-hard, a question which was originally asked by Abu-Khzam et al. [Combinatorial Optimization, 2018]. We answer this in the affirmative. We further give an improved algorithm running in O(2^{7klog k} + n + m) time.

Cite as

Emmanuel Arrighi, Matthias Bentert, Pål Grønås Drange, Blair D. Sullivan, and Petra Wolf. Cluster Editing with Overlapping Communities. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{arrighi_et_al:LIPIcs.IPEC.2023.2,
  author =	{Arrighi, Emmanuel and Bentert, Matthias and Drange, P\r{a}l Gr{\o}n\r{a}s and Sullivan, Blair D. and Wolf, Petra},
  title =	{{Cluster Editing with Overlapping Communities}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.2},
  URN =		{urn:nbn:de:0030-drops-194218},
  doi =		{10.4230/LIPIcs.IPEC.2023.2},
  annote =	{Keywords: graph modification, correlation clustering, vertex splitting, NP-hardness, parameterized algorithm}
}
Document
On the Complexity of Finding a Sparse Connected Spanning Subgraph in a Non-Uniform Failure Model

Authors: Matthias Bentert, Jannik Schestag, and Frank Sommer

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
We study a generalization of the classic Spanning Tree problem that allows for a non-uniform failure model. More precisely, edges are either safe or unsafe and we assume that failures only affect unsafe edges. In Unweighted Flexible Graph Connectivity we are given an undirected graph G = (V,E) in which the edge set E is partitioned into a set S of safe edges and a set U of unsafe edges and the task is to find a set T of at most k edges such that T - {u} is connected and spans V for any unsafe edge u ∈ T. Unweighted Flexible Graph Connectivity generalizes both Spanning Tree and Hamiltonian Cycle. We study Unweighted Flexible Graph Connectivity in terms of fixed-parameter tractability (FPT). We show an almost complete dichotomy on which parameters lead to fixed-parameter tractability and which lead to hardness. To this end, we obtain FPT-time algorithms with respect to the vertex deletion distance to cluster graphs and with respect to the treewidth. By exploiting the close relationship to Hamiltonian Cycle, we show that FPT-time algorithms for many smaller parameters are unlikely under standard parameterized complexity assumptions. Regarding problem-specific parameters, we observe that Unweighted Flexible Graph Connectivity admits an FPT-time algorithm when parameterized by the number of unsafe edges. Furthermore, we investigate a below-upper-bound parameter for the number of edges of a solution. We show that this parameter also leads to an FPT-time algorithm.

Cite as

Matthias Bentert, Jannik Schestag, and Frank Sommer. On the Complexity of Finding a Sparse Connected Spanning Subgraph in a Non-Uniform Failure Model. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bentert_et_al:LIPIcs.IPEC.2023.4,
  author =	{Bentert, Matthias and Schestag, Jannik and Sommer, Frank},
  title =	{{On the Complexity of Finding a Sparse Connected Spanning Subgraph in a Non-Uniform Failure Model}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.4},
  URN =		{urn:nbn:de:0030-drops-194232},
  doi =		{10.4230/LIPIcs.IPEC.2023.4},
  annote =	{Keywords: Flexible graph connectivity, NP-hard problem, parameterized complexity, below-guarantee parameterization, treewidth}
}
Document
Fully Polynomial-Time Algorithms Parameterized by Vertex Integrity Using Fast Matrix Multiplication

Authors: Matthias Bentert, Klaus Heeger, and Tomohiro Koana

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


Abstract
We study the computational complexity of several polynomial-time-solvable graph problems parameterized by vertex integrity, a measure of a graph’s vulnerability to vertex removal in terms of connectivity. Vertex integrity is the smallest number ι such that there is a set S of ι' ≤ ι vertices such that every connected component of G-S contains at most ι-ι' vertices. It is known that the vertex integrity lies between the well-studied parameters vertex cover number and tree-depth. Our work follows similar studies for vertex cover number [Alon and Yuster, ESA 2007] and tree-depth [Iwata, Ogasawara, and Ohsaka, STACS 2018]. Alon and Yuster designed algorithms for graphs with small vertex cover number using fast matrix multiplications. We demonstrate that fast matrix multiplication can also be effectively used when parameterizing by vertex integrity ι by developing efficient algorithms for problems including an O(ι^{ω-1}n)-time algorithm for Maximum Matching and an O(ι^{(ω-1)/2}n²) ⊆ O(ι^{0.687} n²)-time algorithm for All-Pairs Shortest Paths. These algorithms can be faster than previous algorithms parameterized by tree-depth, for which fast matrix multiplication is not known to be effective.

Cite as

Matthias Bentert, Klaus Heeger, and Tomohiro Koana. Fully Polynomial-Time Algorithms Parameterized by Vertex Integrity Using Fast Matrix Multiplication. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bentert_et_al:LIPIcs.ESA.2023.16,
  author =	{Bentert, Matthias and Heeger, Klaus and Koana, Tomohiro},
  title =	{{Fully Polynomial-Time Algorithms Parameterized by Vertex Integrity Using Fast Matrix Multiplication}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{16:1--16:16},
  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.2023.16},
  URN =		{urn:nbn:de:0030-drops-186692},
  doi =		{10.4230/LIPIcs.ESA.2023.16},
  annote =	{Keywords: FPT in P, Algebraic Algorithms, Adaptive Algorithms, Subgraph Detection, Matching, APSP}
}
Document
Track A: Algorithms, Complexity and Games
Using a Geometric Lens to Find k Disjoint Shortest Paths

Authors: Matthias Bentert, André Nichterlein, Malte Renken, and Philipp Zschoche

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
Given an undirected n-vertex graph and k pairs of terminal vertices (s_1,t_1), …, (s_k,t_k), the k-Disjoint Shortest Paths (k-DSP) problem asks whether there are k pairwise vertex-disjoint paths P_1, …, P_k such that P_i is a shortest s_i-t_i-path for each i ∈ [k]. Recently, Lochet [SODA '21] provided an algorithm that solves k-DSP in n^{O(k^{5^k})} time, answering a 20-year old question about the computational complexity of k-DSP for constant k. On the one hand, we present an improved O(kn^{16k ⋅ k! + k + 1})-time algorithm based on a novel geometric view on this problem. For the special case k = 2, we show that the running time can be further reduced to O(nm) by small modifications of the algorithm and a further refined analysis. On the other hand, we show that k-DSP is W[1]-hard with respect to k, showing that the dependency of the degree of the polynomial running time on the parameter k is presumably unavoidable.

Cite as

Matthias Bentert, André Nichterlein, Malte Renken, and Philipp Zschoche. Using a Geometric Lens to Find k Disjoint Shortest Paths. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bentert_et_al:LIPIcs.ICALP.2021.26,
  author =	{Bentert, Matthias and Nichterlein, Andr\'{e} and Renken, Malte and Zschoche, Philipp},
  title =	{{Using a Geometric Lens to Find k Disjoint Shortest Paths}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.26},
  URN =		{urn:nbn:de:0030-drops-140954},
  doi =		{10.4230/LIPIcs.ICALP.2021.26},
  annote =	{Keywords: graph algorithms, dynamic programming, W\lbrack1\rbrack-hardness, geometry}
}
Document
Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters

Authors: Matthias Bentert, Klaus Heeger, and Dušan Knop

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)


Abstract
In the presented paper, we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph G, two vertices s and t, and positive integers β and λ. The task is to find a set F of edges of size at most β such that every s-t-path of length at most λ in G contains some edge in F. Bazgan et al. [Networks, 2019] conjectured that Length-Bounded Cut admits a polynomial-time algorithm if the input graph G is a proper interval graph. We confirm this conjecture by providing a dynamic-programming based polynomial-time algorithm. Moreover, we strengthen the W[1]-hardness result of Dvořák and Knop [Algorithmica, 2018] for Length-Bounded Cut parameterized by pathwidth. Our reduction is shorter, and the target of the reduction has stronger structural properties. Consequently, we give W[1]-hardness for the combined parameter pathwidth and maximum degree of the input graph. Finally, we prove that Length-Bounded Cut is W[1]-hard for the feedback vertex number. Both our hardness results complement known XP algorithms.

Cite as

Matthias Bentert, Klaus Heeger, and Dušan Knop. Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bentert_et_al:LIPIcs.ISAAC.2020.36,
  author =	{Bentert, Matthias and Heeger, Klaus and Knop, Du\v{s}an},
  title =	{{Length-Bounded Cuts: Proper Interval Graphs and Structural Parameters}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.36},
  URN =		{urn:nbn:de:0030-drops-133800},
  doi =		{10.4230/LIPIcs.ISAAC.2020.36},
  annote =	{Keywords: Edge-disjoint paths, pathwidth, feedback vertex number}
}
Document
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-dev.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}
}
Document
Tree Containment With Soft Polytomies

Authors: Matthias Bentert, Josef Malík, and Mathias Weller

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)


Abstract
The Tree Containment problem has many important applications in the study of evolutionary history. Given a phylogenetic network N and a phylogenetic tree T whose leaves are labeled by a set of taxa, it asks if N and T are consistent. While the case of binary N and T has received considerable attention, the more practically relevant variant dealing with biological uncertainty has not. Such uncertainty manifests itself as high-degree vertices ("polytomies") that are "jokers" in the sense that they are compatible with any binary resolution of their children. Contrasting the binary case, we show that this problem, called Soft Tree Containment, is NP-hard, even if N is a binary, multi-labeled tree in which each taxon occurs at most thrice. On the other hand, we reduce the case that each label occurs at most twice to solving a 2-SAT instance of size O(|T|^3). This implies NP-hardness and polynomial-time solvability on reticulation-visible networks in which the maximum in-degree is bounded by three and two, respectively.

Cite as

Matthias Bentert, Josef Malík, and Mathias Weller. Tree Containment With Soft Polytomies. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{bentert_et_al:LIPIcs.SWAT.2018.9,
  author =	{Bentert, Matthias and Mal{\'\i}k, Josef and Weller, Mathias},
  title =	{{Tree Containment With Soft Polytomies}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.9},
  URN =		{urn:nbn:de:0030-drops-88353},
  doi =		{10.4230/LIPIcs.SWAT.2018.9},
  annote =	{Keywords: Phylogenetics, Reticulation-Visible Networks, Multifurcating Trees}
}
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