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Documents authored by 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.
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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.
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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.
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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.
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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.
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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
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.ISAAC.2020.20
Computing Dense and Sparse Subgraphs of Weakly Closed Graphs

Authors: Tomohiro Koana, Christian Komusiewicz, and Frank Sommer

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

Abstract
A graph G is weakly γ-closed if every induced subgraph of G contains one vertex v such that for each non-neighbor u of v it holds that |N(u)∩ N(v)| < γ. The weak closure γ(G) of a graph, recently introduced by Fox et al. [SIAM J. Comp. 2020], is the smallest number such that G is weakly γ-closed. This graph parameter is never larger than the degeneracy (plus one) and can be significantly smaller. Extending the work of Fox et al. [SIAM J. Comp. 2020] on clique enumeration, we show that several problems related to finding dense subgraphs, such as the enumeration of bicliques and s-plexes, are fixed-parameter tractable with respect to γ(G). Moreover, we show that the problem of determining whether a weakly γ-closed graph G has a subgraph on at least k vertices that belongs to a graph class 𝒢 which is closed under taking subgraphs admits a kernel with at most γ k² vertices. Finally, we provide fixed-parameter algorithms for Independent Dominating Set and Dominating Clique when parameterized by γ+k where k is the solution size.
Cite as

Tomohiro Koana, Christian Komusiewicz, and Frank Sommer. Computing Dense and Sparse Subgraphs of Weakly Closed Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{koana_et_al:LIPIcs.ISAAC.2020.20,
  author =	{Koana, Tomohiro and Komusiewicz, Christian and Sommer, Frank},
  title =	{{Computing Dense and Sparse Subgraphs of Weakly Closed Graphs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{20:1--20:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.20},
  URN =		{urn:nbn:de:0030-drops-133646},
  doi =		{10.4230/LIPIcs.ISAAC.2020.20},
  annote =	{Keywords: Fixed-parameter tractability, c-closure, degeneracy, clique relaxations, bicliques, dominating set}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.30
Colored Cut Games

Authors: Nils Morawietz, Niels Grüttemeier, Christian Komusiewicz, and Frank Sommer

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
In a graph G = (V,E) with an edge coloring 𝓁:E → C and two distinguished vertices s and t, a colored (s,t)-cut is a set C̃ ⊆ C such that deleting all edges with some color c ∈ C̃ from G disconnects s and t. Motivated by applications in the design of robust networks, we introduce a family of problems called colored cut games. In these games, an attacker and a defender choose colors to delete and to protect, respectively, in an alternating fashion. It is the goal of the attacker to achieve a colored (s,t)-cut and the goal of the defender to prevent this. First, we show that for an unbounded number of alternations, colored cut games are PSPACE-complete. We then show that, even on subcubic graphs, colored cut games with a constant number i of alternations are complete for classes in the polynomial hierarchy whose level depends on i. To complete the dichotomy, we show that all colored cut games are polynomial-time solvable on graphs with degree at most two. Finally, we show that all colored cut games admit a polynomial kernel for the parameter k+κ_r where k denotes the total attacker budget and, for any constant r, κ_r is the number of vertex deletions that are necessary to transform G into a graph where the longest path has length at most r. In the case of r = 1, κ₁ is the vertex cover number vc of the input graph and we obtain a kernel with 𝒪(vc²k²) edges. Moreover, we introduce an algorithm solving the most basic colored cut game, Colored (s,t)-Cut, in 2^{vc + k}n^{𝒪(1)} time.
Cite as

Nils Morawietz, Niels Grüttemeier, Christian Komusiewicz, and Frank Sommer. Colored Cut Games. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{morawietz_et_al:LIPIcs.FSTTCS.2020.30,
  author =	{Morawietz, Nils and Gr\"{u}ttemeier, Niels and Komusiewicz, Christian and Sommer, Frank},
  title =	{{Colored Cut Games}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.30},
  URN =		{urn:nbn:de:0030-drops-132719},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.30},
  annote =	{Keywords: Labeled Cut, Labeled Path, Network Robustness, Kernelization, PSPACE, Polynomial Hierarchy}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.65
Exploiting c-Closure in Kernelization Algorithms for Graph Problems

Authors: Tomohiro Koana, Christian Komusiewicz, and Frank Sommer

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
A graph is c-closed if every pair of vertices with at least c common neighbors is adjacent. The c-closure of a graph G is the smallest number c such that G is c-closed. Fox et al. [SIAM J. Comput. '20] defined c-closure and investigated it in the context of clique enumeration. We show that c-closure can be applied in kernelization algorithms for several classic graph problems. We show that Dominating Set admits a kernel of size k^𝒪(c), that Induced Matching admits a kernel with 𝒪(c⁷ k⁸) vertices, and that Irredundant Set admits a kernel with 𝒪(c^{5/2} k³) vertices. Our kernelization exploits the fact that c-closed graphs have polynomially-bounded Ramsey numbers, as we show.
Cite as

Tomohiro Koana, Christian Komusiewicz, and Frank Sommer. Exploiting c-Closure in Kernelization Algorithms for Graph Problems. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 65:1-65:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{koana_et_al:LIPIcs.ESA.2020.65,
  author =	{Koana, Tomohiro and Komusiewicz, Christian and Sommer, Frank},
  title =	{{Exploiting c-Closure in Kernelization Algorithms for Graph Problems}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{65:1--65:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.65},
  URN =		{urn:nbn:de:0030-drops-129316},
  doi =		{10.4230/LIPIcs.ESA.2020.65},
  annote =	{Keywords: Fixed-parameter tractability, kernelization, c-closure, Dominating Set, Induced Matching, Irredundant Set, Ramsey numbers}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.26
Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs

Authors: Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Given an undirected graph G and integers c and k, the Maximum Edge-Colorable Subgraph problem asks whether we can delete at most k edges in G to obtain a graph that has a proper edge coloring with at most c colors. We show that Maximum Edge-Colorable Subgraph admits, for every fixed c, a linear-size problem kernel when parameterized by the edge deletion distance of G to a graph with maximum degree c-1. This parameterization measures the distance to instances that, due to Vizing’s famous theorem, are trivial yes-instances. For c≤ 4, we also provide a linear-size kernel for the same parameterization for Multi Strong Triadic Closure, a related edge coloring problem with applications in social network analysis. We provide further results for Maximum Edge-Colorable Subgraph parameterized by the vertex deletion distance to graphs where every component has order at most c and for the list-colored versions of both problems.
Cite as

Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gruttemeier_et_al:LIPIcs.SWAT.2020.26,
  author =	{Gr\"{u}ttemeier, Niels and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.26},
  URN =		{urn:nbn:de:0030-drops-122731},
  doi =		{10.4230/LIPIcs.SWAT.2020.26},
  annote =	{Keywords: Graph coloring, social networks, parameterized complexity, kernelization}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.17
String Factorizations Under Various Collision Constraints

Authors: Niels Grüttemeier, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
In the NP-hard Equality-Free String Factorization problem, we are given a string S and ask whether S can be partitioned into k factors that are pairwise distinct. We describe a randomized algorithm for Equality-Free String Factorization with running time 2^k⋅ k^{𝒪(1)}+𝒪(n) improving over previous algorithms with running time k^{𝒪(k)}+𝒪(n) [Schmid, TCS 2016; Mincu and Popa, Proc. SOFSEM 2020]. Our algorithm works for the generalization of Equality-Free String Factorization where equality can be replaced by an arbitrary polynomial-time computable equivalence relation on strings. We also consider two factorization problems to which this algorithm does not apply, namely Prefix-Free String Factorization where we ask for a factorization of size k such that no factor is a prefix of another factor and Substring-Free String Factorization where we ask for a factorization of size k such that no factor is a substring of another factor. We show that these two problems are NP-hard as well. Then, we show that Prefix-Free String Factorization with the prefix-free relation is fixed-parameter tractable with respect to k by providing a polynomial problem kernel. Finally, we show a generic ILP formulation for R-Free String Factorization where R is an arbitrary relation on strings. This formulation improves over a previous one for Equality-Free String Factorization in terms of the number of variables.
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Niels Grüttemeier, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. String Factorizations Under Various Collision Constraints. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gruttemeier_et_al:LIPIcs.CPM.2020.17,
  author =	{Gr\"{u}ttemeier, Niels and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{String Factorizations Under Various Collision Constraints}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.17},
  URN =		{urn:nbn:de:0030-drops-121428},
  doi =		{10.4230/LIPIcs.CPM.2020.17},
  annote =	{Keywords: NP-hard problem, fixed-parameter algorithms, collision-aware string partitioning}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2018.19
Matching Cut: Kernelization, Single-Exponential Time FPT, and Exact Exponential Algorithms

Authors: Christian Komusiewicz, Dieter Kratsch, and Van Bang Le

Published in: LIPIcs, Volume 115, 13th International Symposium on Parameterized and Exact Computation (IPEC 2018)

Abstract
In a graph, a matching cut is an edge cut that is a matching. Matching Cut, which is known to be NP-complete, is the problem of deciding whether or not a given graph G has a matching cut. In this paper we show that Matching Cut admits a quadratic-vertex kernel for the parameter distance to cluster and a linear-vertex kernel for the parameter distance to clique. We further provide an O^*(2^{dc(G)}) time and an O^*(2^{dc^-}(G)}) time FPT algorithm for Matching Cut, where dc(G) and dc^-(G) are the distance to cluster and distance to co-cluster, respectively. We also improve the running time of the best known branching algorithm to solve Matching Cut from O^*(1.4143^n) to O^*(1.3803^n). Moreover, we point out that, unless NP subseteq coNP/poly, Matching Cut does not admit a polynomial kernel when parameterized by treewidth.
Cite as

Christian Komusiewicz, Dieter Kratsch, and Van Bang Le. Matching Cut: Kernelization, Single-Exponential Time FPT, and Exact Exponential Algorithms. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 19:1-19:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{komusiewicz_et_al:LIPIcs.IPEC.2018.19,
  author =	{Komusiewicz, Christian and Kratsch, Dieter and Le, Van Bang},
  title =	{{Matching Cut: Kernelization, Single-Exponential Time FPT, and Exact Exponential Algorithms}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{19:1--19:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-084-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{115},
  editor =	{Paul, Christophe and Pilipczuk, Michal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2018.19},
  URN =		{urn:nbn:de:0030-drops-102207},
  doi =		{10.4230/LIPIcs.IPEC.2018.19},
  annote =	{Keywords: matching cut, decomposable graph, graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.51
Solving Partition Problems Almost Always Requires Pushing Many Vertices Around

Authors: Iyad Kanj, Christian Komusiewicz, Manuel Sorge, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
A fundamental graph problem is to recognize whether the vertex set of a graph G can be bipartitioned into sets A and B such that G[A] and G[B] satisfy properties Pi_A and Pi_B, respectively. This so-called (Pi_A,Pi_B)-Recognition problem generalizes amongst others the recognition of 3-colorable, bipartite, split, and monopolar graphs. A powerful algorithmic technique that can be used to obtain fixed-parameter algorithms for many cases of (Pi_A,Pi_B)-Recognition, as well as several other problems, is the pushing process. For bipartition problems, the process starts with an "almost correct" bipartition (A',B'), and pushes appropriate vertices from A' to B' and vice versa to eventually arrive at a correct bipartition. In this paper, we study whether (Pi_A,Pi_B)-Recognition problems for which the pushing process yields fixed-parameter algorithms also admit polynomial problem kernels. In our study, we focus on the first level above triviality, where Pi_A is the set of P_3-free graphs (disjoint unions of cliques, or cluster graphs), the parameter is the number of clusters in the cluster graph G[A], and Pi_B is characterized by a set H of connected forbidden induced subgraphs. We prove that, under the assumption that NP not subseteq coNP/poly, (Pi_A,Pi_B)-Recognition admits a polynomial kernel if and only if H contains a graph of order at most 2. In both the kernelization and the lower bound results, we make crucial use of the pushing process.
Cite as

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, and Erik Jan van Leeuwen. Solving Partition Problems Almost Always Requires Pushing Many Vertices Around. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kanj_et_al:LIPIcs.ESA.2018.51,
  author =	{Kanj, Iyad and Komusiewicz, Christian and Sorge, Manuel and van Leeuwen, Erik Jan},
  title =	{{Solving Partition Problems Almost Always Requires Pushing Many Vertices Around}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah 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.2018.51},
  URN =		{urn:nbn:de:0030-drops-95140},
  doi =		{10.4230/LIPIcs.ESA.2018.51},
  annote =	{Keywords: Fixed-parameter algorithms, Kernelization, Vertex-partition problems, Reduction rules, Cross-composition}
}
Document
DOI: 10.4230/LIPIcs.CPM.2018.17
On the Maximum Colorful Arborescence Problem and Color Hierarchy Graph Structure

Authors: Guillaume Fertin, Julien Fradin, and Christian Komusiewicz

Published in: LIPIcs, Volume 105, 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

Abstract
Let G=(V,A) be a vertex-colored arc-weighted directed acyclic graph (DAG) rooted in some vertex r. The color hierarchy graph H(G) of G is defined as follows: the vertex set of H(G) is the color set C of G, and H(G) has an arc from c to c' if G has an arc from a vertex of color c to a vertex of color c'. We study the Maximum Colorful Arborescence (MCA) problem, which takes as input a DAG G such that H(G) is also a DAG, and aims at finding in G a maximum-weight arborescence rooted in r in which no color appears more than once. The MCA problem models the de novo inference of unknown metabolites by mass spectrometry experiments. Although the problem has been introduced ten years ago (under a different name), it was only recently pointed out that a crucial additional property in the problem definition was missing: by essence, H(G) must be a DAG. In this paper, we further investigate MCA under this new light and provide new algorithmic results for this problem, with a focus on fixed-parameter tractability (FPT) issues for different structural parameters of H(G). In particular, we develop an O^*(3^{{x_H}})-time algorithm for solving MCA, where {x_{H}} is the number of vertices of indegree at least two in H(G), thereby improving the O^*(3^{|C|})-time algorithm of Böcker et al. [Proc. ECCB '08]. We also prove that MCA is W[2]-hard with respect to the treewidth t_H of the underlying undirected graph of H(G), and further show that it is FPT with respect to t_H + l_{C}, where l_{C} := |V| - |C|.
Cite as

Guillaume Fertin, Julien Fradin, and Christian Komusiewicz. On the Maximum Colorful Arborescence Problem and Color Hierarchy Graph Structure. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{fertin_et_al:LIPIcs.CPM.2018.17,
  author =	{Fertin, Guillaume and Fradin, Julien and Komusiewicz, Christian},
  title =	{{On the Maximum Colorful Arborescence Problem and Color Hierarchy Graph Structure}},
  booktitle =	{29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-074-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{105},
  editor =	{Navarro, Gonzalo and Sankoff, David and Zhu, Binhai},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.17},
  URN =		{urn:nbn:de:0030-drops-86939},
  doi =		{10.4230/LIPIcs.CPM.2018.17},
  annote =	{Keywords: Subgraph problem, computational complexity, algorithms, fixed-parameter tractability, kernelization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2017.30
The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration

Authors: Holger Dell, Christian Komusiewicz, Nimrod Talmon, and Mathias Weller

Published in: LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Abstract
In this article, the Program Committee of the Second Parameterized Algorithms and Computational Experiments challenge (PACE 2017) reports on the second iteration of the PACE challenge. Track A featured the Treewidth problem and Track B the Minimum Fill-In problem. Over 44 participants on 17 teams from 11 countries submitted their implementations to the competition.
Cite as

Holger Dell, Christian Komusiewicz, Nimrod Talmon, and Mathias Weller. The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dell_et_al:LIPIcs.IPEC.2017.30,
  author =	{Dell, Holger and Komusiewicz, Christian and Talmon, Nimrod and Weller, Mathias},
  title =	{{The PACE 2017 Parameterized Algorithms and Computational Experiments Challenge: The Second Iteration}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{30:1--30:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Lokshtanov, Daniel and Nishimura, Naomi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.30},
  URN =		{urn:nbn:de:0030-drops-85582},
  doi =		{10.4230/LIPIcs.IPEC.2017.30},
  annote =	{Keywords: treewidth, minimum fill-in, contest, implementation challenge, FPT}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.11
Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping

Authors: Christian Komusiewicz, Mateus de Oliveira Oliveira, and Meirav Zehavi

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

Abstract
In the Maximum-Duo Preservation String Mapping (Max-Duo PSM) problem, the input consists of two related strings A and B of length n and a nonnegative integer k. The objective is to determine whether there exists a mapping m from the set of positions of A to the set of positions of B that maps only to positions with the same character and preserves at least k duos, which are pairs of adjacent positions. We develop a randomized algorithm that solves Max-Duo PSM in time 4^k * n^{O(1)}, and a deterministic algorithm that solves this problem in time 6.855^k * n^{O(1)}. The previous best known (deterministic) algorithm for this problem has running time (8e)^{2k+o(k)} * n^{O(1)} [Beretta et al., Theor. Comput. Sci. 2016]. We also show that Max-Duo PSM admits a problem kernel of size O(k^3), improving upon the previous best known problem kernel of size O(k^6).
Cite as

Christian Komusiewicz, Mateus de Oliveira Oliveira, and Meirav Zehavi. Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{komusiewicz_et_al:LIPIcs.CPM.2017.11,
  author =	{Komusiewicz, Christian and de Oliveira Oliveira, Mateus and Zehavi, Meirav},
  title =	{{Revisiting the Parameterized Complexity of Maximum-Duo Preservation String Mapping}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.11},
  URN =		{urn:nbn:de:0030-drops-73436},
  doi =		{10.4230/LIPIcs.CPM.2017.11},
  annote =	{Keywords: comparative genomics, parameterized complexity, kernelization}
}
Document
DOI: 10.4230/LIPIcs.CPM.2017.27
Beyond Adjacency Maximization: Scaffold Filling for New String Distances

Authors: Laurent Bulteau, Guillaume Fertin, and Christian Komusiewicz

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

Abstract
In Genomic Scaffold Filling, one aims at polishing in silico a draft genome, called scaffold. The scaffold is given in the form of an ordered set of gene sequences, called contigs. This is done by confronting the scaffold to an already complete reference genome from a close species. More precisely, given a scaffold S, a reference genome G and a score function f() between two genomes, the aim is to complete S by adding the missing genes from G so that the obtained complete genome S* optimizes f(S*, G). In this paper, we extend a model of Jiang et al. [CPM 2016] (i) by allowing the insertions of strings instead of single characters (i.e., some groups of genes may be forced to be inserted together) and (ii) by considering two alternative score functions: the first generalizes the notion of common adjacencies by maximizing the number of common k-mers between S* and G (k-Mer Scaffold Filling), the second aims at minimizing the number of breakpoints between S* and G (Min-Breakpoint Scaffold Filling). We study these problems from the parameterized complexity point of view, providing fixed-parameter (FPT) algorithms for both problems. In particular, we show that k-Mer Scaffold Filling is FPT wrt. parameter l, the number of additional k-mers realized by the completion of S—this answers an open question of Jiang et al. [CPM 2016]. We also show that Min-Breakpoint Scaffold Filling is FPT wrt. a parameter combining the number of missing genes, the number of gene repetitions and the target distance.
Cite as

Laurent Bulteau, Guillaume Fertin, and Christian Komusiewicz. Beyond Adjacency Maximization: Scaffold Filling for New String Distances. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bulteau_et_al:LIPIcs.CPM.2017.27,
  author =	{Bulteau, Laurent and Fertin, Guillaume and Komusiewicz, Christian},
  title =	{{Beyond Adjacency Maximization: Scaffold Filling for New String Distances}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.27},
  URN =		{urn:nbn:de:0030-drops-73364},
  doi =		{10.4230/LIPIcs.CPM.2017.27},
  annote =	{Keywords: computational biology, strings, FPT algorithms, kernelization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.30
The First Parameterized Algorithms and Computational Experiments Challenge

Authors: Holger Dell, Thore Husfeldt, Bart M. P. Jansen, Petteri Kaski, Christian Komusiewicz, and Frances A. Rosamond

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
In this article, the steering committee of the Parameterized Algorithms and Computational Experiments challenge (PACE) reports on the first iteration of the challenge. Where did PACE come from, how did it go, who won, and what's next?
Cite as

Holger Dell, Thore Husfeldt, Bart M. P. Jansen, Petteri Kaski, Christian Komusiewicz, and Frances A. Rosamond. The First Parameterized Algorithms and Computational Experiments Challenge. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 30:1-30:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dell_et_al:LIPIcs.IPEC.2016.30,
  author =	{Dell, Holger and Husfeldt, Thore and Jansen, Bart M. P. and Kaski, Petteri and Komusiewicz, Christian and Rosamond, Frances A.},
  title =	{{The First Parameterized Algorithms and Computational Experiments Challenge}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{30:1--30:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.30},
  URN =		{urn:nbn:de:0030-drops-69310},
  doi =		{10.4230/LIPIcs.IPEC.2016.30},
  annote =	{Keywords: treewidth, feedback vertex set, contest, implementation challenge, FPT}
}
Document
DOI: 10.4230/LIPIcs.CPM.2016.7
Graph Motif Problems Parameterized by Dual

Authors: Guillaume Fertin and Christian Komusiewicz

Published in: LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

Abstract
Let G=(V,E) be a vertex-colored graph, where C is the set of colors used to color V. The Graph Motif (or GM) problem takes as input G, a multiset M of colors built from C, and asks whether there is a subset S subseteq V such that (i) G[S] is connected and (ii) the multiset of colors obtained from S equals M. The Colorful Graph Motif problem (or CGM) is a constrained version of GM in which M=C, and the List-Colored Graph Motif problem (or LGM) is the extension of GM in which each vertex v of V may choose its color from a list L(v) of colors. We study the three problems GM, CGM and LGM, parameterized by l:=|V|-|M|. In particular, for general graphs, we show that, assuming the strong exponential-time hypothesis, CGM has no (2-epsilon)^l * |V|^{O(1)}-time algorithm, which implies that a previous algorithm, running in O(2^l\cdot |E|) time is optimal. We also prove that LGM is W[1]-hard even if we restrict ourselves to lists of at most two colors. If we constrain the input graph to be a tree, then we show that, in contrast to CGM, GM can be solved in O(4^l *|V|) time but admits no polynomial kernel, while CGM can be solved in O(sqrt{2}^l + |V|) time and admits a polynomial kernel.
Cite as

Guillaume Fertin and Christian Komusiewicz. Graph Motif Problems Parameterized by Dual. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 7:1-7:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{fertin_et_al:LIPIcs.CPM.2016.7,
  author =	{Fertin, Guillaume and Komusiewicz, Christian},
  title =	{{Graph Motif Problems Parameterized by Dual}},
  booktitle =	{27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)},
  pages =	{7:1--7:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-012-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{54},
  editor =	{Grossi, Roberto and Lewenstein, Moshe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.7},
  URN =		{urn:nbn:de:0030-drops-60837},
  doi =		{10.4230/LIPIcs.CPM.2016.7},
  annote =	{Keywords: NP-hard problem, subgraph problem, fixed-parameter algorithm, lowerbounds, kernelization}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.14
Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs

Authors: Iyad Kanj, Christian Komusiewicz, Manuel Sorge, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
We consider the recognition problem for two graph classes that generalize split and unipolar graphs, respectively. First, we consider the recognizability of graphs that admit a monopolar partition: a partition of the vertex set into sets A,B such that G[A] is a disjoint union of cliques and G[B] an independent set. If in such a partition G[A] is a single clique, then G is a split graph. We show that in O(2^k * k^3 * (|V(G)| + |E(G)|)) time we can decide whether G admits a monopolar partition (A,B) where G[A] has at most k cliques. This generalizes the linear-time algorithm for recognizing split graphs corresponding to the case when k=1. Second, we consider the recognizability of graphs that admit a 2-subcoloring: a partition of the vertex set into sets A,B such that each of G[A] and G[B] is a disjoint union of cliques. If in such a partition G[A] is a single clique, then G is a unipolar graph. We show that in O(k^(2k+2) * (|V(G)|^2+|V(G)| * |E(G)|)) time we can decide whether G admits a 2-subcoloring (A,B) where G[A] has at most k cliques. This generalizes the polynomial-time algorithm for recognizing unipolar graphs corresponding to the case when k=1. We also show that in O(4^k) time we can decide whether G admits a 2-subcoloring (A,B) where G[A] and G[B] have at most k cliques in total. To obtain the first two results above, we formalize a technique, which we dub inductive recognition, that can be viewed as an adaptation of iterative compression to recognition problems. We believe that the formalization of this technique will prove useful in general for designing parameterized algorithms for recognition problems. Finally, we show that, unless the Exponential Time Hypothesis fails, no subexponential-time algorithms for the above recognition problems exist, and that, unless P=NP, no generic fixed-parameter algorithm exists for the recognizability of graphs whose vertex set can be bipartitioned such that one part is a disjoint union of k cliques.
Cite as

Iyad Kanj, Christian Komusiewicz, Manuel Sorge, and Erik Jan van Leeuwen. Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{kanj_et_al:LIPIcs.SWAT.2016.14,
  author =	{Kanj, Iyad and Komusiewicz, Christian and Sorge, Manuel and Jan van Leeuwen, Erik},
  title =	{{Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.14},
  URN =		{urn:nbn:de:0030-drops-60360},
  doi =		{10.4230/LIPIcs.SWAT.2016.14},
  annote =	{Keywords: vertex-partition problems, monopolar graphs, subcolorings, split graphs, unipolar graphs, fixed-parameter algorithms}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2015.343
Parameterized Complexity of Critical Node Cuts

Authors: Danny Hermelin, Moshe Kaspi, Christian Komusiewicz, and Barak Navon

Published in: LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)

Abstract
We consider the following graph cut problem called Critical Node Cut (CNC): Given a graph G on n vertices, and two positive integers k and x, determine whether G has a set of k vertices whose removal leaves G with at most x connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in f(kappa) * n^{O(1)} time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters kappa. We consider four such parameters: - The size k of the required cut. - The upper bound x on the number of remaining connected pairs. - The lower bound y on the number of connected pairs to be removed. - The treewidth w of G. We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from w+k. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size kappa^{O(1)}, where kappa is the given parameter.
Cite as

Danny Hermelin, Moshe Kaspi, Christian Komusiewicz, and Barak Navon. Parameterized Complexity of Critical Node Cuts. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 343-354, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hermelin_et_al:LIPIcs.IPEC.2015.343,
  author =	{Hermelin, Danny and Kaspi, Moshe and Komusiewicz, Christian and Navon, Barak},
  title =	{{Parameterized Complexity of Critical Node Cuts}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{343--354},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Husfeldt, Thore and Kanj, Iyad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.343},
  URN =		{urn:nbn:de:0030-drops-55950},
  doi =		{10.4230/LIPIcs.IPEC.2015.343},
  annote =	{Keywords: graph cut problem, NP-hard problem, treewidth}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.130
Approximation Algorithms for Mixed, Windy, and Capacitated Arc Routing Problems

Authors: René van Bevern, Christian Komusiewicz, and Manuel Sorge

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
We show that any alpha(n)-approximation algorithm for the n-vertex metric asymmetric Traveling Salesperson problem yields O(alpha(C))-approximation algorithms for various mixed, windy, and capacitated arc routing problems. Herein, C is the number of weakly-connected components in the subgraph induced by the positive-demand arcs, a number that can be expected to be small in applications. In conjunction with known results, we derive constant-factor approximations if C is in O(log n) and O(log(C)/log(log(C)))-approximations in general.
Cite as

René van Bevern, Christian Komusiewicz, and Manuel Sorge. Approximation Algorithms for Mixed, Windy, and Capacitated Arc Routing Problems. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 130-143, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{vanbevern_et_al:OASIcs.ATMOS.2015.130,
  author =	{van Bevern, Ren\'{e} and Komusiewicz, Christian and Sorge, Manuel},
  title =	{{Approximation Algorithms for Mixed, Windy, and Capacitated Arc Routing Problems}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{130--143},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.130},
  URN =		{urn:nbn:de:0030-drops-54575},
  doi =		{10.4230/OASIcs.ATMOS.2015.130},
  annote =	{Keywords: vehicle routing, transportation, Rural Postman, Chinese Postman, NP- hard problem, parameterized algorithm, combinatorial optimization}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2008.1760
A Cubic-Vertex Kernel for Flip Consensus Tree

Authors: Christian Komusiewicz and Johannes Uhlmann

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

Abstract
Given a bipartite graph G=(V_c,V_t,E) and a non-negative integer k, the NP-complete Minimum-Flip Consensus Tree problem asks whether G can be transformed, using up to k edge insertions and deletions, into a graph that does not contain an induced P_5 with its first vertex in V_t (a so-called M-graph or Sigma-graph). This problem plays an important role in computational phylogenetics, V_c standing for the characters and V_t standing for taxa. Chen et al. [IEEE/ACM TCBB 2006] showed that Minimum-Flip Consensus Tree is NP-complete and presented a parameterized algorithm with running time O(6^k\cdot |V_t|\cdot |V_c|). Recently, Boecker et al. [IWPEC'08] presented a refined search tree algorithm with running time O(4.83^k(|V_t|+|V_c|) + |V_t|\cdot |V_c|). We complement these results by polynomial-time executable data reduction rules yielding a problem kernel with O(k^3) vertices.
Cite as

Christian Komusiewicz and Johannes Uhlmann. A Cubic-Vertex Kernel for Flip Consensus Tree. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 280-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{komusiewicz_et_al:LIPIcs.FSTTCS.2008.1760,
  author =	{Komusiewicz, Christian and Uhlmann, Johannes},
  title =	{{A Cubic-Vertex Kernel for Flip Consensus Tree}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{280--291},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1760},
  URN =		{urn:nbn:de:0030-drops-17600},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1760},
  annote =	{Keywords: Fixed-parameter algorithm, problem kernel, NP-hard problem, graph modification problem, computational phylogenetics}
}
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