130 Search Results for "Golovach, Petr"

Volume

LIPIcs, Volume 214

16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

IPEC 2021, September 8-10, 2021, Lisbon, Portugal

Editors: Petr A. Golovach and Meirav Zehavi

Document
DOI: 10.4230/LIPIcs.ESA.2025.7
Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion

Authors: Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A replacement action is a function ℒ that maps each graph H to a collection of graphs of size at most |V(H)|. Given a graph class ℋ, we consider a general family of graph modification problems, called ℒ-Replacement to ℋ, where the input is a graph G and the question is whether it is possible to replace some induced subgraph H₁ of G on at most k vertices by a graph H₂ in ℒ(H₁) so that the resulting graph belongs to ℋ. ℒ-Replacement to ℋ can simulate many graph modification problems including vertex deletion, edge deletion/addition/edition/contraction, vertex identification, subgraph complementation, independent set deletion, (induced) matching deletion/contraction, etc. We present two algorithms. The first one solves ℒ-Replacement to ℋ in time 2^poly(k) ⋅ |V(G)|² for every minor-closed graph class ℋ, where poly is a polynomial whose degree depends on ℋ, under a mild technical condition on ℒ. This generalizes the results of Morelle, Sau, Stamoulis, and Thilikos [ICALP 2020, ICALP 2023] for the particular case of Vertex Deletion to ℋ within the same running time. Our second algorithm is an improvement of the first one when ℋ is the class of graphs embeddable in a surface of Euler genus at most g and runs in time 2^𝒪(k⁹) ⋅ |V(G)|², where the 𝒪(⋅) notation depends on g. To the best of our knowledge, these are the first parameterized algorithms with a reasonable parametric dependence for such a general family of graph modification problems to minor-closed classes.
Cite as

Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos. Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{morelle_et_al:LIPIcs.ESA.2025.7,
  author =	{Morelle, Laure and Sau, Ignasi and Thilikos, Dimitrios M.},
  title =	{{Graph Modification of Bounded Size to Minor-Closed Classes as Fast as Vertex Deletion}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.7},
  URN =		{urn:nbn:de:0030-drops-244751},
  doi =		{10.4230/LIPIcs.ESA.2025.7},
  annote =	{Keywords: Graph modification problems, Parameterized complexity, Graph minors, Flat Wall theorem, Irrelevant vertex technique, Algorithmic meta-theorem, Parametric dependence, Dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.46
Max-Distance Sparsification for Diversification and Clustering

Authors: Soh Kumabe

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Let 𝒟 be a set family that is the solution domain of some combinatorial problem. The max-min diversification problem on 𝒟 is the problem to select k sets from 𝒟 such that the Hamming distance between any two selected sets is at least d. FPT algorithms parameterized by k+𝓁, where 𝓁 = max_{D ∈ 𝒟}|D|, and k+d have been actively studied recently for several specific domains. This paper provides unified algorithmic frameworks to solve this problem. Specifically, for each parameterization k+𝓁 and k+d, we provide an FPT oracle algorithm for the max-min diversification problem using oracles related to 𝒟. We then demonstrate that our frameworks provide the first FPT algorithms on several new domains 𝒟, including the domain of t-linear matroid intersection, almost 2-SAT, minimum edge s,t-flows, vertex sets of s,t-mincut, vertex sets of edge bipartization, and Steiner trees. We also demonstrate that our frameworks generalize most of the existing domain-specific tractability results. Our main technical breakthrough is introducing the notion of max-distance sparsifier of 𝒟, a domain on which the max-min diversification problem is equivalent to the same problem on the original domain 𝒟. The core of our framework is to design FPT oracle algorithms that construct a constant-size max-distance sparsifier of 𝒟. Using max-distance sparsifiers, we provide FPT algorithms for the max-min and max-sum diversification problems on 𝒟, as well as k-center and k-sum-of-radii clustering problems on 𝒟, which are also natural problems in the context of diversification and have their own interests.
Cite as

Soh Kumabe. Max-Distance Sparsification for Diversification and Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kumabe:LIPIcs.ESA.2025.46,
  author =	{Kumabe, Soh},
  title =	{{Max-Distance Sparsification for Diversification and Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.46},
  URN =		{urn:nbn:de:0030-drops-245146},
  doi =		{10.4230/LIPIcs.ESA.2025.46},
  annote =	{Keywords: Fixed-Parameter Tractability, Diversification, Clustering}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.29
The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration

Authors: Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A dominating set of a graph G = (V,E) is a set of vertices D ⊆ V whose closed neighborhood is V, i.e., N[D] = V. We view a dominating set as a collection of tokens placed on the vertices of D. In the token sliding variant of the Dominating Set Reconfiguration problem (TS-DSR), we seek to transform a source dominating set into a target dominating set in G by sliding tokens along edges, and while maintaining a dominating set all along the transformation. TS-DSR is known to be PSPACE-complete even restricted to graphs of pathwidth w, for some non-explicit constant w and to be XL-complete parameterized by the size k of the solution. The first contribution of this article consists in using a novel approach to provide the first explicit constant for which the TS-DSR problem is PSPACE-complete, a question that was left open in the literature. From a parameterized complexity perspective, the token jumping variant of DSR, i.e., where tokens can jump to arbitrary vertices, is known to be FPT when parameterized by the size of the dominating sets on nowhere dense classes of graphs. But, in contrast, no non-trivial result was known about TS-DSR. We prove that DSR is actually much harder in the sliding model since it is XL-complete when restricted to bounded pathwidth graphs and even when parameterized by k plus the feedback vertex set number of the graph. This gives, for the first time, a difference of behavior between the complexity under token sliding and token jumping for some problem on graphs of bounded treewidth. All our results are obtained using a brand new method, based on the hardness of the so-called Tape Reconfiguration problem, a problem we believe to be of independent interest. We complement these hardness results with a positive result showing that DSR (parameterized by k) in the sliding model is FPT on planar graphs, also answering an open problem from the literature.
Cite as

Nicolas Bousquet, Quentin Deschamps, Arnaud Mary, Amer E. Mouawad, and Théo Pierron. The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bousquet_et_al:LIPIcs.ESA.2025.29,
  author =	{Bousquet, Nicolas and Deschamps, Quentin and Mary, Arnaud and Mouawad, Amer E. and Pierron, Th\'{e}o},
  title =	{{The Tape Reconfiguration Problem and Its Consequences for Dominating Set Reconfiguration}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.29},
  URN =		{urn:nbn:de:0030-drops-244974},
  doi =		{10.4230/LIPIcs.ESA.2025.29},
  annote =	{Keywords: combinatorial reconfiguration, parameterized complexity, structural graph parameters, treewidth, dominating set}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.16
On Algorithmic Applications of ℱ-Branchwidth

Authors: Benjamin Bergougnoux, Thekla Hamm, Lars Jaffke, and Paloma T. Lima

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
F-branchwidth is a framework for width measures of graphs, recently introduced by Eiben et al. [ITCS 2022], that captures tree-width, co-tree-width, clique-width, and mim-width, and several of their generalizations and interpolations. In this work, we search for algorithmic applications of F-branchwidth measures that do not have an equivalent counterpart in the literature so far. Our first contribution is a minimal set of eleven F-branchwidth measures such that each of the infinitely many F-branchwidth measures is equivalent to one of the eleven. We observe that for the FO Model Checking problem, each F-branchwidth is either equivalent to clique-width (and therefore has an FPT-algorithm by formula length plus the width) or the problem remains as hard as on general graphs even on graphs of constant width. Next, we study the number of equivalence classes of the neighborhood equivalence in a decomposition, which upper bounds the run time of the model checking algorithm for ACDN logic recently introduced by Bergougnoux et al. [SODA 2023]. We give structural lower bounds that show that for each F-branchwidth, an efficient model checking algorithm was already known or cannot be obtained via this method. Lastly, we classify the complexity of Independent Set parameterized by any F-branchwidth except for one open case. Also here, our contributions are lower bounds. In this context, we also prove that Independent Set on graphs of mim-width w cannot be solved in time n^o(w) unless the Exponential Time Hypothesis fails, answering an open question in the literature.
Cite as

Benjamin Bergougnoux, Thekla Hamm, Lars Jaffke, and Paloma T. Lima. On Algorithmic Applications of ℱ-Branchwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bergougnoux_et_al:LIPIcs.ESA.2025.16,
  author =	{Bergougnoux, Benjamin and Hamm, Thekla and Jaffke, Lars and Lima, Paloma T.},
  title =	{{On Algorithmic Applications of ℱ-Branchwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.16},
  URN =		{urn:nbn:de:0030-drops-244849},
  doi =		{10.4230/LIPIcs.ESA.2025.16},
  annote =	{Keywords: Graph width parameters, parameterized complexity, F-branchwidth, tree-width, clique-width, rank-width, mim-width, FO model checking, DN logic, Independent Set, ETH}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.110
Faster Exponential Algorithms for Cut Problems via Geometric Data Structures

Authors: László Kozma and Junqi Tan

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
For many hard computational problems, simple algorithms that run in time 2ⁿ ⋅ n^O(1) arise, say, from enumerating all subsets of a size-n set. Finding (exponentially) faster algorithms is a natural goal that has driven much of the field of exact exponential algorithms (e.g., see Fomin and Kratsch, 2010). In this paper we obtain algorithms with running time O(1.9999977ⁿ) on input graphs with n vertices, for the following well-studied problems: - d-Cut: find a proper cut in which no vertex has more than d neighbors on the other side of the cut; - Internal Partition: find a proper cut in which every vertex has at least as many neighbors on its side of the cut as on the other side; and - (α,β)-Domination: given intervals α,β ⊆ [0,n], find a subset S of the vertices, so that for every vertex v ∈ S the number of neighbors of v in S is from α and for every vertex v ∉ S, the number of neighbors of v in S is from β. Our algorithms are exceedingly simple, combining the split and list technique (Horowitz and Sahni, 1974; Williams, 2005) with a tool from computational geometry: orthogonal range searching in the moderate dimensional regime (Chan, 2017). Our technique is applicable to the decision, optimization and counting versions of these problems and easily extends to various generalizations with more fine-grained, vertex-specific constraints, as well as to directed, balanced, and other variants. Algorithms with running times of the form cⁿ, for c < 2, were known for the first problem only for constant d, and for the third problem for certain special cases of α and β; for the second problem we are not aware of such results.
Cite as

László Kozma and Junqi Tan. Faster Exponential Algorithms for Cut Problems via Geometric Data Structures. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 110:1-110:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kozma_et_al:LIPIcs.ESA.2025.110,
  author =	{Kozma, L\'{a}szl\'{o} and Tan, Junqi},
  title =	{{Faster Exponential Algorithms for Cut Problems via Geometric Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{110:1--110:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.110},
  URN =		{urn:nbn:de:0030-drops-245796},
  doi =		{10.4230/LIPIcs.ESA.2025.110},
  annote =	{Keywords: graph algorithms, cuts, exponential time, data structures}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.40
Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs

Authors: Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We show that, for every fixed positive integers r and k, Max-Weight List r-Colorable Induced Subgraph admits a polynomial-time algorithm on kP₃-free graphs. This problem is a common generalization of Max-Weight Independent Set, Odd Cycle Transversal and List r-Coloring, among others. Our result has several consequences. First, it implies that, for every fixed r ≥ 5, assuming 𝖯 ≠ NP, Max-Weight List r-Colorable Induced Subgraph is polynomial-time solvable on H-free graphs if and only if H is an induced subgraph of either kP₃ or P₅+kP₁, for some k ≥ 1. Second, it makes considerable progress toward a complexity dichotomy for Odd Cycle Transversal on H-free graphs, allowing to answer a question of Agrawal, Lima, Lokshtanov, Rzążewski, Saurabh, and Sharma [ACM Trans. Algorithms 2025]. Third, it gives a short and self-contained proof of the known result of Chudnovsky, Hajebi, and Spirkl [Combinatorica 2024] that List r-Coloring on kP₃-free graphs is polynomial-time solvable for every fixed r and k. We also consider two natural distance-d generalizations of Max-Weight Independent Set and List r-Coloring and provide polynomial-time algorithms on kP₃-free graphs for every fixed integers r, k, and d ≥ 6.
Cite as

Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi. Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{galby_et_al:LIPIcs.ESA.2025.40,
  author =	{Galby, Esther and Lima, Paloma T. and Munaro, Andrea and Nikabadi, Amir},
  title =	{{Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{40:1--40:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.40},
  URN =		{urn:nbn:de:0030-drops-245086},
  doi =		{10.4230/LIPIcs.ESA.2025.40},
  annote =	{Keywords: Hereditary classes, list coloring, odd cycle transversal, independent set}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.43
Edge Clique Partition and Cover Beyond Independence

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses. Despite the well-known fixed-parameter tractability of these problems when parameterized by the total number of cliques, such a parameterization often fails to be meaningful for sparse graphs. In many real-world instances, on the other hand, the minimum number of cliques in an edge cover or partition can be very close to the size of a maximum independent set α(G). Motivated by this observation, we investigate above-α parameterizations of the edge clique cover and partition problems. Concretely, we introduce and study Edge Clique Cover Above Independent Set (ECC/α) and Edge Clique Partition Above Independent Set (ECP/α), where the goal is to cover or partition all edges of a graph using at most α(G) + k cliques, and k is the parameter. Our main results reveal a distinct complexity landscape for the two variants. We show that ECP/α is fixed-parameter tractable, whereas ECC/α is NP-complete for all k ≥ 2, yet can be solved in polynomial time for k ∈ {0,1}. These findings highlight intriguing differences between the two problems when viewed through the lens of parameterization above a natural lower bound. Finally, we demonstrate that ECC/α becomes fixed-parameter tractable when parameterized by k + ω(G), where ω(G) is the size of a maximum clique of the graph G. This result is particularly relevant for sparse graphs, in which ω is typically small. For H-minor free graphs, we design a subexponential algorithm of running time f(H)^√k ⋅ n^𝒪(1).
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Edge Clique Partition and Cover Beyond Independence. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fomin_et_al:LIPIcs.ESA.2025.43,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Edge Clique Partition and Cover Beyond Independence}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.43},
  URN =		{urn:nbn:de:0030-drops-245113},
  doi =		{10.4230/LIPIcs.ESA.2025.43},
  annote =	{Keywords: edge clique partition, edge clique cover, independence number, parameterized complexity, above guarantee}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.83
Fault-Tolerant Matroid Bases

Authors: Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We investigate the problem of constructing fault-tolerant bases in matroids. Given a matroid ℳ and a redundancy parameter k, a k-fault-tolerant basis is a minimum-size set of elements such that, even after the removal of any k elements, the remaining subset still spans the entire ground set. Since matroids generalize linear independence across structures such as vector spaces, graphs, and set systems, this problem unifies and extends several fault-tolerant concepts appearing in prior research. Our main contribution is a fixed-parameter tractable (FPT) algorithm for the k-fault-tolerant basis problem, parameterized by both k and the rank r of the matroid. This two-variable parameterization by k + r is shown to be tight in the following sense. On the one hand, the problem is already NP-hard for k = 1. On the other hand, it is Para-NP-hard for r ≥ 3 and polynomial-time solvable for r ≤ 2.
Cite as

Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, and Laure Morelle. Fault-Tolerant Matroid Bases. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 83:1-83:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bentert_et_al:LIPIcs.ESA.2025.83,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A. and Morelle, Laure},
  title =	{{Fault-Tolerant Matroid Bases}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{83:1--83:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.83},
  URN =		{urn:nbn:de:0030-drops-245511},
  doi =		{10.4230/LIPIcs.ESA.2025.83},
  annote =	{Keywords: Parameterized Complexity, matroids, robust bases}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.15
Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs

Authors: Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Enumerating minimal dominating sets with polynomial delay in bipartite graphs is a long-standing open problem. To date, even the subcase of chordal bipartite graphs is open, with the best known algorithm due to Golovach, Heggernes, Kanté, Kratsch, Sæther, and Villanger running in incremental-polynomial time. We improve on this result by providing a polynomial delay and space algorithm enumerating minimal dominating sets in chordal bipartite graphs. Additionally, we show that the total and connected variants admit polynomial and incremental-polynomial delay algorithms, respectively, within the same class. This provides an alternative proof of a result by Golovach et al. for total dominating sets, and answers an open question for the connected variant. Finally, we give evidence that the techniques used in this paper cannot be generalized to bipartite graphs for (total) minimal dominating sets, unless P = NP, and show that enumerating minimal connected dominating sets in bipartite graphs is harder than enumerating minimal transversals in general hypergraphs.
Cite as

Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes. Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{castelo_et_al:LIPIcs.WADS.2025.15,
  author =	{Castelo, Emanuel and Defrain, Oscar and C. M. Gomes, Guilherme},
  title =	{{Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.15},
  URN =		{urn:nbn:de:0030-drops-242467},
  doi =		{10.4230/LIPIcs.WADS.2025.15},
  annote =	{Keywords: algorithmic enumeration, minimal dominating sets, connected dominating sets, total dominating sets, chordal bipartite graphs, sequential method, polynomial delay}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.19
On the Enumeration of Signatures of XOR-CNF’s

Authors: Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Given a CNF formula φ with clauses C_1, … , C_m over a set of variables V, a truth assignment 𝐚: V → {0, 1} generates a binary sequence σ_φ(𝐚) = (C_1(𝐚), …, C_m(𝐚)), called a signature of φ, where C_i(𝐚) = 1 if clause C_i evaluates to 1 under assignment 𝐚, and C_i(𝐚) = 0 otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, Bérczi et al. interestingly proved that generating signatures of a CNF is tractable despite the fact that verifying a solution is hard. They also showed the hardness of finding maximal signatures of an arbitrary CNF due to the intractability of satisfiability in general. Their contribution leaves open the problem of efficiently generating maximal signatures for tractable classes of CNFs, i.e., those for which satisfiability can be solved in polynomial time. Stepping into that direction, we completely characterize the complexity of generating all, minimal, and maximal signatures for XOR-CNF’s.
Cite as

Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin. On the Enumeration of Signatures of XOR-CNF’s. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{creignou_et_al:LIPIcs.WADS.2025.19,
  author =	{Creignou, Nadia and Defrain, Oscar and Olive, Fr\'{e}d\'{e}ric and Vilmin, Simon},
  title =	{{On the Enumeration of Signatures of XOR-CNF’s}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.19},
  URN =		{urn:nbn:de:0030-drops-242508},
  doi =		{10.4230/LIPIcs.WADS.2025.19},
  annote =	{Keywords: Algorithmic enumeration, XOR-CNF, signatures, maximal bipartite subgraphs enumeration, extension, proximity search}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.36
On the Complexity of Minimising the Moving Distance for Dispersing Objects

Authors: Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an O(n log n)-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the L₁ and L₂ distances.
Cite as

Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. On the Complexity of Minimising the Moving Distance for Dispersing Objects. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{honoratodroguett_et_al:LIPIcs.WADS.2025.36,
  author =	{Honorato-Droguett, Nicol\'{a}s and Kurita, Kazuhiro and Hanaka, Tesshu and Ono, Hirotaka},
  title =	{{On the Complexity of Minimising the Moving Distance for Dispersing Objects}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.36},
  URN =		{urn:nbn:de:0030-drops-242673},
  doi =		{10.4230/LIPIcs.WADS.2025.36},
  annote =	{Keywords: Intersection graphs, Optimisation, Graph modification}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.38
Clustering Point Sets Revisited

Authors: Md. Billal Hossain and Benjamin Raichel

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In the sets clustering problem one is given a collection of point sets 𝒫 = {P_1,… P_m} in ℝ^d, where for any set of k centers in ℝ^d, each P_i is assigned to its nearest center as determine by some local cost functions. The goal is then to select a set of k centers to minimize some global cost function of the corresponding local assignment costs. Specifically, we consider either summing or taking the maximum cost over all P_i, where for each P_i the cost of assigning it to a center c is either max_{p ∈ P_i} ‖c-p‖, ∑_{p ∈ P_i} ‖c-p‖, or ∑_{p ∈ P_i} ‖c-p‖². Different combinations of the global and local cost functions naturally generalize the k-center, k-median, and k-means clustering problems. In this paper, we improve the prior results for the natural generalization of k-center, give the first result for the natural generalization of k-means, and give results for generalizations of k-median and k-center which differ from those previously studied.
Cite as

Md. Billal Hossain and Benjamin Raichel. Clustering Point Sets Revisited. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{hossain_et_al:LIPIcs.WADS.2025.38,
  author =	{Hossain, Md. Billal and Raichel, Benjamin},
  title =	{{Clustering Point Sets Revisited}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.38},
  URN =		{urn:nbn:de:0030-drops-242693},
  doi =		{10.4230/LIPIcs.WADS.2025.38},
  annote =	{Keywords: Clustering, k-center, k-median, k-means}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.13
Solving Partial Dominating Set and Related Problems Using Twin-Width

Authors: Jakub Balabán, Daniel Mock, and Peter Rossmanith

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are W[1]-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including nowhere-dense classes. In this paper, we demonstrate that these problems are also fixed-parameter tractable with respect to the twin-width of a graph. Indeed, we establish a more general result: every graph property that can be expressed by a logical formula of the form ϕ≡∃ x₁⋯ ∃ x_k ∑_{α ∈ I} #y ψ_α(x₁,…,x_k,y) ≥ t, where ψ_α is a quantifier-free formula for each α ∈ I, t is an arbitrary number, and #y is a counting quantifier, can be evaluated in time f(d,k)n, where n is the number of vertices and d is the width of a contraction sequence that is part of the input. In addition to the aforementioned problems, this includes also connected partial dominating set and independent partial dominating set.
Cite as

Jakub Balabán, Daniel Mock, and Peter Rossmanith. Solving Partial Dominating Set and Related Problems Using Twin-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.13,
  author =	{Balab\'{a}n, Jakub and Mock, Daniel and Rossmanith, Peter},
  title =	{{Solving Partial Dominating Set and Related Problems Using Twin-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.13},
  URN =		{urn:nbn:de:0030-drops-241203},
  doi =		{10.4230/LIPIcs.MFCS.2025.13},
  annote =	{Keywords: Partial Dominating Set, Partial Vertex Cover, meta-algorithm, counting logic, twin-width}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.52
On the Complexity of Recoverable Robust Optimization in the Polynomial Hierarchy

Authors: Christoph Grüne and Lasse Wulf

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Recoverable robust optimization is a popular multi-stage approach, in which it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We consider recoverable robust optimization in combination with discrete budgeted uncertainty. In this setting, it seems plausible that many problems become Σ^p₃-complete and therefore it is impossible to find compact IP formulations of them (unless the unlikely conjecture NP = Σ^p₃ holds). Even though this seems plausible, few concrete results of this kind are known. In this paper, we fill that gap of knowledge. We consider recoverable robust optimization for the nominal problems of Sat, 3Sat, vertex cover, dominating set, set cover, hitting set, feedback vertex set, feedback arc set, uncapacitated facility location, p-center, p-median, independent set, clique, subset sum, knapsack, partition, scheduling, Hamiltonian path/cycle (directed/undirected), TSP, k-directed disjoint path (k ≥ 2), and Steiner tree. We show that for each of these problems, and for each of three widely used distance measures, the recoverable robust problem becomes Σ^p₃-complete. Concretely, we show that all these problems share a certain abstract property and prove that this property implies that their robust recoverable counterpart is Σ^p₃-complete. This reveals the insight that all the above problems are Σ^p₃-complete "for the same reason". Our result extends a recent framework by Grüne and Wulf.
Cite as

Christoph Grüne and Lasse Wulf. On the Complexity of Recoverable Robust Optimization in the Polynomial Hierarchy. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 52:1-52:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{grune_et_al:LIPIcs.MFCS.2025.52,
  author =	{Gr\"{u}ne, Christoph and Wulf, Lasse},
  title =	{{On the Complexity of Recoverable Robust Optimization in the Polynomial Hierarchy}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{52:1--52:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.52},
  URN =		{urn:nbn:de:0030-drops-241596},
  doi =		{10.4230/LIPIcs.MFCS.2025.52},
  annote =	{Keywords: Complexity, Robust Optimization, Recoverable Robust Optimization, Two-Stage Problems, Polynomial Hierarchy, Sigma 2, Sigma 3}
}
  • Refine by Type
  • 129 Document/PDF
  • 32 Document/HTML
  • 1 Volume

  • Refine by Publication Year
  • 32 2025
  • 6 2024
  • 6 2023
  • 6 2022
  • 43 2021
  • Show More...

  • Refine by Author
  • 61 Golovach, Petr A.
  • 52 Fomin, Fedor V.
  • 22 Saurabh, Saket
  • 10 Inamdar, Tanmay
  • 10 Simonov, Kirill
  • Show More...

  • Refine by Series/Journal
  • 126 LIPIcs
  • 1 OASIcs
  • 1 DagRep
  • 1 DagSemProc

  • Refine by Classification
  • 50 Theory of computation → Parameterized complexity and exact algorithms
  • 37 Mathematics of computing → Graph algorithms
  • 21 Theory of computation → Fixed parameter tractability
  • 20 Theory of computation → Graph algorithms analysis
  • 8 Theory of computation → Design and analysis of algorithms
  • Show More...

  • Refine by Keyword
  • 19 parameterized complexity
  • 13 kernelization
  • 10 fixed-parameter tractability
  • 9 Parameterized Complexity
  • 9 Parameterized complexity
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact