33 Search Results for "Komusiewicz, Christian"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2024.28
Maximizing Phylogenetic Diversity Under Ecological Constraints: A Parameterized Complexity Study

Authors: Christian Komusiewicz and Jannik Schestag

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)

Abstract
In the NP-hard Optimizing Phylogenetic Diversity with Dependencies(PDD) problem, the input consists of a phylogenetic tree 𝒯 over a set of taxa X, a food-web that describes the prey-predator relationships in X, and integers k and D. The task is to find a set S of k species that is viable in the food-web such that the subtree of 𝒯 obtained by retaining only the vertices of S has total edge weight at least D. Herein, viable means that for every predator taxon of S, the set S contains at least one prey taxon. We provide the first systematic analysis of PDD and its special case with star trees, s-PDD, from a parameterized complexity perspective. For solution-size related parameters, we show that PDD is fixed-parameter tractable (FPT) with respect to D and with respect to k plus the height of the phylogenetic tree. Moreover, we consider structural parameterizations of the food-web. For example, we show an FPT-algorithm for the parameter that measures the vertex deletion distance to graphs where every connected component is a complete graph. Finally, we show that s-PDD admits an FPT-algorithm for the treewidth of the food-web. This disproves, unless P = NP, a conjecture of Faller et al. [Annals of Combinatorics, 2011] who conjectured that s-PDD is NP-hard even when the food-web is a tree.
Cite as

Christian Komusiewicz and Jannik Schestag. Maximizing Phylogenetic Diversity Under Ecological Constraints: A Parameterized Complexity Study. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{komusiewicz_et_al:LIPIcs.FSTTCS.2024.28,
  author =	{Komusiewicz, Christian and Schestag, Jannik},
  title =	{{Maximizing Phylogenetic Diversity Under Ecological Constraints: A Parameterized Complexity Study}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.28},
  URN =		{urn:nbn:de:0030-drops-222175},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.28},
  annote =	{Keywords: phylogenetic diversity, food-webs, structural parameterization, color-coding, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2024.16
Modularity Clustering Parameterized by Max Leaf Number

Authors: Jaroslav Garvardt and Christian Komusiewicz

Published in: LIPIcs, Volume 321, 19th International Symposium on Parameterized and Exact Computation (IPEC 2024)

Abstract
The modularity score is one of the most important measures for assessing the quality of clusterings of undirected graphs. In the notoriously difficult Modularity problem, one is given an undirected graph G and the task is to find a clustering with maximum modularity. We show that Modularity is fixed-parameter tractable with respect to the max leaf number of G. This improves on a previous result by Meeks and Skerman [Algorithmica '20] who showed an XP-algorithm for this parameter. In addition, we strengthen previous hardness results for Modularity by showing W[1]-hardness for the parameter vertex deletion distance to disjoint union of stars.
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Jaroslav Garvardt and Christian Komusiewicz. Modularity Clustering Parameterized by Max Leaf Number. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{garvardt_et_al:LIPIcs.IPEC.2024.16,
  author =	{Garvardt, Jaroslav and Komusiewicz, Christian},
  title =	{{Modularity Clustering Parameterized by Max Leaf Number}},
  booktitle =	{19th International Symposium on Parameterized and Exact Computation (IPEC 2024)},
  pages =	{16:1--16:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-353-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{321},
  editor =	{Bonnet, \'{E}douard and Rz\k{a}\.{z}ewski, Pawe{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2024.16},
  URN =		{urn:nbn:de:0030-drops-222426},
  doi =		{10.4230/LIPIcs.IPEC.2024.16},
  annote =	{Keywords: Graph clustering, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2024.32
When Can Cluster Deletion with Bounded Weights Be Solved Efficiently?

Authors: Jaroslav Garvardt, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 322, 35th International Symposium on Algorithms and Computation (ISAAC 2024)

Abstract
In the NP-hard Weighted Cluster Deletion problem, the input is an undirected graph G = (V,E) and an edge-weight function ω: E → ℕ, and the task is to partition the vertex set V into cliques so that the total weight of edges in the cliques is maximized. Recently, it has been shown that Weighted Cluster Deletion is NP-hard on some graph classes where Cluster Deletion, the special case where every edge has unit weight, can be solved in polynomial time. We study the influence of the value t of the largest edge weight assigned by ω on the problem complexity for such graph classes. Our main results are that Weighted Cluster Deletion is fixed-parameter tractable with respect to t on graph classes whose graphs consist of well-separated clusters that are connected by a sparse periphery. Concrete examples for such classes are split graphs and graphs that are close to cluster graphs. We complement our results by strengthening previous hardness results for Weighted Cluster Deletion. For example, we show that Weighted Cluster Deletion is NP-hard on restricted subclasses of cographs even when every edge has weight 1 or 2.
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Jaroslav Garvardt, Christian Komusiewicz, and Nils Morawietz. When Can Cluster Deletion with Bounded Weights Be Solved Efficiently?. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{garvardt_et_al:LIPIcs.ISAAC.2024.32,
  author =	{Garvardt, Jaroslav and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{When Can Cluster Deletion with Bounded Weights Be Solved Efficiently?}},
  booktitle =	{35th International Symposium on Algorithms and Computation (ISAAC 2024)},
  pages =	{32:1--32:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-354-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{322},
  editor =	{Mestre, Juli\'{a}n and Wirth, Anthony},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.32},
  URN =		{urn:nbn:de:0030-drops-221592},
  doi =		{10.4230/LIPIcs.ISAAC.2024.32},
  annote =	{Keywords: Graph clustering, split graphs, cographs, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.102
SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints

Authors: Henning Martin Woydt, Christian Komusiewicz, and Frank Sommer

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
In the Cardinality-Constrained Maximization (Minimization) problem the input is a universe 𝒰, a function f: 2^{{𝒰}} → ℝ, and an integer k, and the task is to find a set S ⊆ 𝒰 with |S| ≤ k that maximizes (minimizes) f(S). Many well-studied problems such as Facility Location, Partial Dominating Set, Group Closeness Centrality and Euclidean k-Medoid Clustering are special cases of Cardinality-Constrained Maximization (Minimization). All the above-mentioned problems have the diminishing return property, that is, the improvement of adding an element e ∈ 𝒰 to a set S is at least as large as adding e to any superset of S. This property is called submodularity for maximization problems and supermodularity for minimization problems. In this work we develop a new exact branch-and-cut algorithm SubModST for the generic Submodular Cardinality-Constrained Maximization and Supermodular Cardinality-Constrained Minimization. We develop several speed-ups for SubModST and we show their effectiveness on six example problems. We show that SubModST outperforms the state-of-the-art solvers developed by Csókás and Vinkó [J. Glob. Optim. '24] and Uematsu et al. [J. Oper. Res. Soc. Japan '20] for Submodular Cardinality-Constrained Maximization by orders of magnitudes.
Cite as

Henning Martin Woydt, Christian Komusiewicz, and Frank Sommer. SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 102:1-102:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{woydt_et_al:LIPIcs.ESA.2024.102,
  author =	{Woydt, Henning Martin and Komusiewicz, Christian and Sommer, Frank},
  title =	{{SubModST: A Fast Generic Solver for Submodular Maximization with Size Constraints}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{102:1--102:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.102},
  URN =		{urn:nbn:de:0030-drops-211730},
  doi =		{10.4230/LIPIcs.ESA.2024.102},
  annote =	{Keywords: Branch-and-Cut, Lazy Evaluations, Facility Location, Group Closeness Centrality, Partial Dominating Set}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.60
On the Complexity of Community-Aware Network Sparsification

Authors: Emanuel Herrendorf, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
In the NP-hard Π-Network Sparsification problem, we are given an edge-weighted graph G, a collection 𝒞 of c subsets of V(G), called communities, and two numbers 𝓁 and b, and the question is whether there exists a spanning subgraph G' of G with at most 𝓁 edges of total weight at most b such that G'[C] fulfills Π for each community C ∈ 𝒞. We study the fine-grained and parameterized complexity of two special cases of this problem: Connectivity NWS where Π is the connectivity property and Stars NWS, where Π is the property of having a spanning star. First, we provide a tight 2^Ω(n²+c)-time running time lower bound based on the ETH for both problems, where n is the number of vertices in G even if all communities have size at most 4, G is a clique, and every edge has unit weight. For the connectivity property, the unit weight case with G being a clique is the well-studied problem of computing a hypergraph support with a minimum number of edges. We then study the complexity of both problems parameterized by the feedback edge number t of the solution graph G'. For Stars NWS, we present an XP-algorithm for t answering an open question by Korach and Stern [Discret. Appl. Math. '08] who asked for the existence of polynomial-time algorithms for t = 0. In contrast, we show for Connectivity NWS that known polynomial-time algorithms for t = 0 [Korach and Stern, Math. Program. '03; Klemz et al., SWAT '14] cannot be extended to larger values of t by showing NP-hardness for t = 1.
Cite as

Emanuel Herrendorf, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. On the Complexity of Community-Aware Network Sparsification. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{herrendorf_et_al:LIPIcs.MFCS.2024.60,
  author =	{Herrendorf, Emanuel and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{On the Complexity of Community-Aware Network Sparsification}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{60:1--60:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.60},
  URN =		{urn:nbn:de:0030-drops-206169},
  doi =		{10.4230/LIPIcs.MFCS.2024.60},
  annote =	{Keywords: parameterized complexity, hypergraph support, above guarantee parameterization, exponential-time-hypothesis}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.54
On the Complexity of Computing Time Series Medians Under the Move-Split-Merge Metric

Authors: Jana Holznigenkemper, Christian Komusiewicz, Nils Morawietz, and Bernhard Seeger

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
We initiate a study of the complexity of MSM-Median, the problem of computing a median of a set of k real-valued time series under the move-split-merge distance. This distance measure is based on three operations: moves, which may shift a data point in a time series; splits, which replace one data point in a time series by two consecutive data points of the same value; and merges, which replace two consecutive data points of equal value by a single data point of the same value. The cost of a move operation is the difference of the data point value before and after the operation, the cost of split and merge operations is defined via a given constant c. Our main results are as follows. First, we show that MSM-Median is NP-hard and W[1]-hard with respect to k for time series with at most three distinct values. Under the Exponential Time Hypothesis (ETH) our reduction implies that a previous dynamic programming algorithm with running time |I|^𝒪(k) [Holznigenkemper et al., Data Min. Knowl. Discov. '23] is essentially optimal. Here, |I| denotes the total input size. Second, we show that MSM-Median can be solved in 2^𝒪(d/c)⋅|I|^𝒪(1) time where d is the total distance of the median to the input time series.
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Jana Holznigenkemper, Christian Komusiewicz, Nils Morawietz, and Bernhard Seeger. On the Complexity of Computing Time Series Medians Under the Move-Split-Merge Metric. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 54:1-54:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{holznigenkemper_et_al:LIPIcs.MFCS.2023.54,
  author =	{Holznigenkemper, Jana and Komusiewicz, Christian and Morawietz, Nils and Seeger, Bernhard},
  title =	{{On the Complexity of Computing Time Series Medians Under the Move-Split-Merge Metric}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{54:1--54:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.54},
  URN =		{urn:nbn:de:0030-drops-185889},
  doi =		{10.4230/LIPIcs.MFCS.2023.54},
  annote =	{Keywords: Parameterized Complexity, Median String, Time Series, ETH}
}
Document
DOI: 10.4230/LIPIcs.SEA.2023.14
A Graph-Theoretic Formulation of Exploratory Blockmodeling

Authors: Alexander Bille, Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 265, 21st International Symposium on Experimental Algorithms (SEA 2023)

Abstract
We present a new simple graph-theoretic formulation of the exploratory blockmodeling problem on undirected and unweighted one-mode networks. Our formulation takes as input the network G and the maximum number t of blocks for the solution model. The task is to find a minimum-size set of edge insertions and deletions that transform the input graph G into a graph G' with at most t neighborhood classes. Herein, a neighborhood class is a maximal set of vertices with the same neighborhood. The neighborhood classes of G' directly give the blocks and block interactions of the computed blockmodel. We analyze the classic and parameterized complexity of the exploratory blockmodeling problem, provide a branch-and-bound algorithm, an ILP formulation and several heuristics. Finally, we compare our exact algorithms to previous ILP-based approaches and show that the new algorithms are faster for t ≥ 4.
Cite as

Alexander Bille, Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. A Graph-Theoretic Formulation of Exploratory Blockmodeling. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bille_et_al:LIPIcs.SEA.2023.14,
  author =	{Bille, Alexander and Gr\"{u}ttemeier, Niels and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Graph-Theoretic Formulation of Exploratory Blockmodeling}},
  booktitle =	{21st International Symposium on Experimental Algorithms (SEA 2023)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-279-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{265},
  editor =	{Georgiadis, Loukas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.14},
  URN =		{urn:nbn:de:0030-drops-183648},
  doi =		{10.4230/LIPIcs.SEA.2023.14},
  annote =	{Keywords: Clustering, Exact Algorithms, ILP-Formulation, Branch-and-Bound, Social Networks}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.18
On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem

Authors: Christian Komusiewicz, Simone Linz, Nils Morawietz, and Jannik Schestag

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
Maximum Parsimony is the problem of computing a most parsimonious phylogenetic tree for a taxa set X from character data for X. A common strategy to attack this notoriously hard problem is to perform a local search over the phylogenetic tree space. Here, one is given a phylogenetic tree T and wants to find a more parsimonious tree in the neighborhood of T. We study the complexity of this problem when the neighborhood contains all trees within distance k for several classic distance functions. For the nearest neighbor interchange (NNI), subtree prune and regraft (SPR), tree bisection and reconnection (TBR), and edge contraction and refinement (ECR) distances, we show that, under the exponential time hypothesis, there are no algorithms with running time |I|^o(k) where |I| is the total input size. Hence, brute-force algorithms with running time |X|^𝒪(k) ⋅ |I| are essentially optimal. In contrast to the above distances, we observe that for the sECR-distance, where the contracted edges are constrained to form a subtree, a better solution within distance k can be found in k^𝒪(k) ⋅ |I|^𝒪(1) time.
Cite as

Christian Komusiewicz, Simone Linz, Nils Morawietz, and Jannik Schestag. On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{komusiewicz_et_al:LIPIcs.CPM.2023.18,
  author =	{Komusiewicz, Christian and Linz, Simone and Morawietz, Nils and Schestag, Jannik},
  title =	{{On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.18},
  URN =		{urn:nbn:de:0030-drops-179729},
  doi =		{10.4230/LIPIcs.CPM.2023.18},
  annote =	{Keywords: phylogenetic trees, parameterized complexity, tree distances, NNI, TBR}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.20
Parameterized Local Search for Vertex Cover: When Only the Search Radius Is Crucial

Authors: Christian Komusiewicz and Nils Morawietz

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

Abstract
A k-swap W for a vertex cover S of a graph G is a vertex set of size at most k such that S' = (S ⧵ W) ∪ (W ⧵ S), the symmetric difference of S and W, is a vertex cover of G. If |S'| < |S|, then W is improving. In LS-Vertex Cover, one is given a vertex cover S of a graph G and wants to know if there is an improving k-swap for S in G. In applications of LS-Vertex Cover, k is a very small parameter that can be set by a user to determine the trade-off between running time and solution quality. Consequently, k can be considered to be a constant. Motivated by this and the fact that LS-Vertex Cover is W[1]-hard with respect to k, we aim for algorithms with running time 𝓁^f(k) ⋅ n^𝒪(1) where 𝓁 is a structural graph parameter upper-bounded by n. We say that such a running time grows mildly with respect to 𝓁 and strongly with respect to k. We obtain algorithms with such a running time for 𝓁 being the h-index of G, the treewidth of G, or the modular-width of G. In addition, we consider a novel parameter, the maximum degree over all quotient graphs in a modular decomposition of G. Moreover, we adapt these algorithms to the more general problem where each vertex is assigned a weight and where we want to find a d-improving k-swap, that is, a k-swap which decreases the weight of the vertex cover by at least d.
Cite as

Christian Komusiewicz and Nils Morawietz. Parameterized Local Search for Vertex Cover: When Only the Search Radius Is Crucial. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{komusiewicz_et_al:LIPIcs.IPEC.2022.20,
  author =	{Komusiewicz, Christian and Morawietz, Nils},
  title =	{{Parameterized Local Search for Vertex Cover: When Only the Search Radius Is Crucial}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{20:1--20:18},
  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.2022.20},
  URN =		{urn:nbn:de:0030-drops-173764},
  doi =		{10.4230/LIPIcs.IPEC.2022.20},
  annote =	{Keywords: Local Search, Structural parameterization, Fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.66
Finding 3-Swap-Optimal Independent Sets and Dominating Sets Is Hard

Authors: Christian Komusiewicz and Nils Morawietz

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
For PLS-complete local search problems, there is presumably no polynomial-time algorithm which finds a locally optimal solution, even though determining whether a solution is locally optimal and replacing it by a better one if this is not the case can be done in polynomial time. We study local search for Weighted Independent Set and Weighted Dominating Set with the 3-swap neighborhood. The 3-swap neighborhood of a vertex set S in G is the set of vertex sets which can be obtained from S by exchanging at most three vertices. We prove the following dichotomy: On the negative side, the problem of finding a 3-swap-optimal independent set or dominating set is PLS-complete. On the positive side, locally optimal independent sets or dominating sets can be found in polynomial time when allowing all 3-swaps except a) the swaps that remove two vertices from the current solution and add one vertex to the solution or b) the swaps that remove one vertex from the current solution and add two vertices to the solution.
Cite as

Christian Komusiewicz and Nils Morawietz. Finding 3-Swap-Optimal Independent Sets and Dominating Sets Is Hard. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{komusiewicz_et_al:LIPIcs.MFCS.2022.66,
  author =	{Komusiewicz, Christian and Morawietz, Nils},
  title =	{{Finding 3-Swap-Optimal Independent Sets and Dominating Sets Is Hard}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.66},
  URN =		{urn:nbn:de:0030-drops-168644},
  doi =		{10.4230/LIPIcs.MFCS.2022.66},
  annote =	{Keywords: Local Search, Graph problems, 3-swap neighborhood, PLS-completeness}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.42
Covering Many (Or Few) Edges with k Vertices in Sparse Graphs

Authors: Tomohiro Koana, Christian Komusiewicz, André Nichterlein, and Frank Sommer

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We study the following two fixed-cardinality optimization problems (a maximization and a minimization variant). For a fixed α between zero and one we are given a graph and two numbers k ∈ ℕ and t ∈ ℚ. The task is to find a vertex subset S of exactly k vertices that has value at least (resp. at most for minimization) t. Here, the value of a vertex set computes as α times the number of edges with exactly one endpoint in S plus 1-α times the number of edges with both endpoints in S. These two problems generalize many prominent graph problems, such as Densest k-Subgraph, Sparsest k-Subgraph, Partial Vertex Cover, and Max (k,n-k)-Cut. In this work, we complete the picture of their parameterized complexity on several types of sparse graphs that are described by structural parameters. In particular, we provide kernelization algorithms and kernel lower bounds for these problems. A somewhat surprising consequence of our kernelizations is that Partial Vertex Cover and Max (k,n-k)-Cut not only behave in the same way but that the kernels for both problems can be obtained by the same algorithms.
Cite as

Tomohiro Koana, Christian Komusiewicz, André Nichterlein, and Frank Sommer. Covering Many (Or Few) Edges with k Vertices in Sparse Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{koana_et_al:LIPIcs.STACS.2022.42,
  author =	{Koana, Tomohiro and Komusiewicz, Christian and Nichterlein, Andr\'{e} and Sommer, Frank},
  title =	{{Covering Many (Or Few) Edges with k Vertices in Sparse Graphs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.42},
  URN =		{urn:nbn:de:0030-drops-158525},
  doi =		{10.4230/LIPIcs.STACS.2022.42},
  annote =	{Keywords: Parameterized Complexity, Kernelization, Partial Vertex Cover, Densest k-Subgraph, Max (k,n-k)-Cut, Degeneracy}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.35
Essentially Tight Kernels For (Weakly) Closed Graphs

Authors: Tomohiro Koana, Christian Komusiewicz, and Frank Sommer

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We study kernelization of classic hard graph problems when the input graphs fulfill triadic closure properties. More precisely, we consider the recently introduced parameters closure number c and weak closure number γ [Fox et al., SICOMP 2020] in addition to the standard parameter solution size k. The weak closure number γ of a graph is upper-bounded by the minimum of its closure number c and its degeneracy d. For Capacitated Vertex Cover, Connected Vertex Cover, and Induced Matching we obtain the first kernels of size k^𝒪(γ), k^𝒪(γ), and (γk)^𝒪(γ), respectively. This extends previous results on the kernelization of these problems on degenerate graphs. These kernels are essentially tight as these problems are unlikely to admit kernels of size k^o(γ) by previous results on their kernelization complexity in degenerate graphs [Cygan et al., ACM TALG 2017]. For Capacitated Vertex Cover, we show that even a kernel of size k^o(c) is unlikely. In contrast, for Connected Vertex Cover, we obtain a problem kernel with 𝒪(ck²) vertices. Moreover, we prove that searching for an induced subgraph of order at least k belonging to a hereditary graph class 𝒢 admits a kernel of size k^𝒪(γ) when 𝒢 contains all complete and all edgeless graphs. Finally, we provide lower bounds for the kernelization of Independent Set on graphs with constant closure number c and kernels for Dominating Set on weakly closed split graphs and weakly closed bipartite graphs.
Cite as

Tomohiro Koana, Christian Komusiewicz, and Frank Sommer. Essentially Tight Kernels For (Weakly) Closed Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{koana_et_al:LIPIcs.ISAAC.2021.35,
  author =	{Koana, Tomohiro and Komusiewicz, Christian and Sommer, Frank},
  title =	{{Essentially Tight Kernels For (Weakly) Closed Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.35},
  URN =		{urn:nbn:de:0030-drops-154681},
  doi =		{10.4230/LIPIcs.ISAAC.2021.35},
  annote =	{Keywords: Fixed-parameter tractability, kernelization, c-closure, weak \gamma-closure, Independent Set, Induced Matching, Connected Vertex Cover, Ramsey numbers, Dominating Set}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.28
PACE Solver Description: ADE-Solver

Authors: Alexander Bille, Dominik Brandenstein, and Emanuel Herrendorf

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

Abstract
This document describes our exact solver "ADE" for the unweighted cluster editing problem submitted to the PACE 2021 competition. The solver’s core consists of an FPT-algorithm using a branch and bound strategy in conjunction with several data reduction rules.
Cite as

Alexander Bille, Dominik Brandenstein, and Emanuel Herrendorf. PACE Solver Description: ADE-Solver. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 28:1-28:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bille_et_al:LIPIcs.IPEC.2021.28,
  author =	{Bille, Alexander and Brandenstein, Dominik and Herrendorf, Emanuel},
  title =	{{PACE Solver Description: ADE-Solver}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{28:1--28:4},
  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.2021.28},
  URN =		{urn:nbn:de:0030-drops-154112},
  doi =		{10.4230/LIPIcs.IPEC.2021.28},
  annote =	{Keywords: Unweighted Cluster Editing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.37
Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration

Authors: Petr A. Golovach, Christian Komusiewicz, Dieter Kratsch, and Van Bang Le

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
An enumeration kernel as defined by Creignou et al. [Theory Comput. Syst. 2017] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions.
Cite as

Petr A. Golovach, Christian Komusiewicz, Dieter Kratsch, and Van Bang Le. Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{golovach_et_al:LIPIcs.STACS.2021.37,
  author =	{Golovach, Petr A. and Komusiewicz, Christian and Kratsch, Dieter and Le, Van Bang},
  title =	{{Refined Notions of Parameterized Enumeration Kernels with Applications to Matching Cut Enumeration}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.37},
  URN =		{urn:nbn:de:0030-drops-136823},
  doi =		{10.4230/LIPIcs.STACS.2021.37},
  annote =	{Keywords: enumeration problems, polynomial delay, output-sensitive algorithms, kernelization, structural parameterizations, matching cuts}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.47
Binary Matrix Completion Under Diameter Constraints

Authors: Tomohiro Koana, Vincent Froese, and Rolf Niedermeier

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that the resulting matrix has a specified maximum diameter (that is, upper-bounding the maximum Hamming distance between any two rows of the completed matrix) as well as a specified minimum Hamming distance between any two of the matrix rows. This scenario is closely related to consensus string problems as well as to recently studied clustering problems on incomplete data. We obtain an almost complete picture concerning the complexity landscape (P vs NP) regarding the diameter constraints and regarding the number of missing entries per row of the incomplete matrix. We develop polynomial-time algorithms for maximum diameter three, which are based on Deza’s theorem [Discret. Math. 1973, J. Comb. Theory, Ser. B 1974] from extremal set theory. In this way, we also provide one of the rare links between sunflower techniques and stringology. On the negative side, we prove NP-hardness for diameter at least four. For the number of missing entries per row, we show polynomial-time solvability when there is only one missing entry and NP-hardness when there can be at least two missing entries. In general, our algorithms heavily rely on Deza’s theorem and the correspondingly identified sunflower structures pave the way towards solutions based on computing graph factors and solving 2-SAT instances.
Cite as

Tomohiro Koana, Vincent Froese, and Rolf Niedermeier. Binary Matrix Completion Under Diameter Constraints. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{koana_et_al:LIPIcs.STACS.2021.47,
  author =	{Koana, Tomohiro and Froese, Vincent and Niedermeier, Rolf},
  title =	{{Binary Matrix Completion Under Diameter Constraints}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.47},
  URN =		{urn:nbn:de:0030-drops-136925},
  doi =		{10.4230/LIPIcs.STACS.2021.47},
  annote =	{Keywords: sunflowers, binary matrices, Hamming distance, stringology, consensus problems, complexity dichotomy, combinatorial algorithms, graph factors, 2-Sat, Hamming radius}
}
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