47 Search Results for "Ordyniak, Sebastian"

Document
DOI: 10.4230/LIPIcs.STACS.2026.42
Computing Twin-Width via Treedepth and Vertex Integrity

Authors: Robert Ganian and Mathis Rocton

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Twin-width is a graph parameter that has become central to explaining the fixed-parameter tractability of first-order model checking across many graph classes. Despite its algorithmic importance, computing twin-width remains poorly understood: even recognizing graphs of twin-width at most four is NP-hard, and no fixed-parameter approximations parameterized by twin-width itself are known. A recent approach towards breaking this barrier focuses on first developing fixed-parameter algorithms for computing or approximating twin-width under parameterizations distinct from twin-width. Our first result establishes that approximating twin-width is fixed-parameter tractable when parameterized by treedepth, thereby breaking the long-standing barrier that all previous tractable parameterizations were based on deletion distance. The proof proceeds via oriented twin-width, yielding the first constructive evidence that this variant may be easier to handle algorithmically. As our second main result, we show that computing twin-width exactly is fixed-parameter tractable with respect to vertex integrity. This constitutes the first non-trivial parameterized algorithm for computing optimal contraction sequences.
Cite as

Robert Ganian and Mathis Rocton. Computing Twin-Width via Treedepth and Vertex Integrity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.STACS.2026.42,
  author =	{Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width via Treedepth and Vertex Integrity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.42},
  URN =		{urn:nbn:de:0030-drops-255318},
  doi =		{10.4230/LIPIcs.STACS.2026.42},
  annote =	{Keywords: twin-width, fixed-parameter algorithms, treedepth, vertex integrity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.51
Structural Parameterization of Steiner Tree Packing

Authors: Niko Hastrich and Kirill Simonov

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms. In this paper, we show the first FPT algorithms for STP parameterized by structural parameters of the input graph. In particular, we show that STP is fixed-parameter tractable by the tree-cut width as well as the fracture number of the input graph. To achieve our results, we generalize techniques from Edge-Disjoint Paths (EDP) to Generalized Steiner Tree Packing (GSTP), which generalizes both STP and EDP. First, we derive the notion of the augmented graph for GSTP analogous to EDP. We then show that GSTP is FPT by - the tree-cut width of the augmented graph, - the fracture number of the augmented graph, - the slim tree-cut width of the input graph. The latter two results were previously known for EDP; our results generalize these to GSTP and improve the running time for the parameter fracture number. On the other hand, it was open whether EDP is FPT parameterized by the tree-cut width of the augmented graph, despite extensive research on the structural complexity of the problem. We settle this question affirmatively.
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Niko Hastrich and Kirill Simonov. Structural Parameterization of Steiner Tree Packing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hastrich_et_al:LIPIcs.STACS.2026.51,
  author =	{Hastrich, Niko and Simonov, Kirill},
  title =	{{Structural Parameterization of Steiner Tree Packing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.51},
  URN =		{urn:nbn:de:0030-drops-255405},
  doi =		{10.4230/LIPIcs.STACS.2026.51},
  annote =	{Keywords: Steiner tree packing, structural parameters, fixed-parameter tractability}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
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Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.30
A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers

Authors: Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems Hamiltonian Path and Hamiltonian Cycle are in FPT. In particular, we focus on parameters that describe how many vertices and edges have to be deleted to become a member of a certain graph class. We show that the problems are W[1]-hard for such restricted cases as vertex distance to path and vertex distance to clique. We complement these results by showing that the problems can be solved in XP time for vertex distance to outerplanar and vertex distance to block. Furthermore, we present some FPT algorithms, e.g., for edge distance to block. Additionally, we prove para-NP-hardness when considered with the edge clique cover number.
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Jesse Beisegel, Katharina Klost, Kristin Knorr, Fabienne Ratajczak, and Robert Scheffler. A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beisegel_et_al:LIPIcs.IPEC.2025.30,
  author =	{Beisegel, Jesse and Klost, Katharina and Knorr, Kristin and Ratajczak, Fabienne and Scheffler, Robert},
  title =	{{A Graph Width Perspective on Partially Ordered Hamiltonian Paths and Cycles II: Vertex and Edge Deletion Numbers}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.30},
  URN =		{urn:nbn:de:0030-drops-251623},
  doi =		{10.4230/LIPIcs.IPEC.2025.30},
  annote =	{Keywords: Hamiltonian path, Hamiltonian cycle, partial order, graph width parameter, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.26
Complexity of Local Search for CSPs Parameterized by Constraint Difference

Authors: Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
In this paper, we study the parameterized complexity of local search, whose goal is to find a good nearby solution from the given current solution. Formally, given an optimization problem where the goal is to find the largest feasible subset S of a universe U, the new input consists of a current solution P (not necessarily feasible) as well as an ordinary input for the problem. Given the existence of a feasible solution S^*, the goal is to find a feasible solution as good as S^* in parameterized time f(k)⋅n^O(1), where k denotes the distance |PΔ S^*|. This model generalizes numerous classical parameterized optimization problems whose parameter k is the minimum number of elements removed from U to make it feasible, which corresponds to the case P = U. We apply this model to widely studied Constraint Satisfaction Problems (CSPs), where U is the set of constraints, and a subset U' of constraints is feasible if there is an assignment to the variables satisfying all constraints in U'. We give a complete characterization of the parameterized complexity of all boolean-alphabet symmetric CSPs, where the predicate’s acceptance depends on the number of true literals.
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Aditya Anand, Vincent Cohen-Addad, Tommaso D'Orsi, Anupam Gupta, Euiwoong Lee, Debmalya Panigrahi, and Sijin Peng. Complexity of Local Search for CSPs Parameterized by Constraint Difference. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.IPEC.2025.26,
  author =	{Anand, Aditya and Cohen-Addad, Vincent and D'Orsi, Tommaso and Gupta, Anupam and Lee, Euiwoong and Panigrahi, Debmalya and Peng, Sijin},
  title =	{{Complexity of Local Search for CSPs Parameterized by Constraint Difference}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.26},
  URN =		{urn:nbn:de:0030-drops-251586},
  doi =		{10.4230/LIPIcs.IPEC.2025.26},
  annote =	{Keywords: Constraint Satisfaction Problems, Parameterized Local Search, Optimization}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
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Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.IPEC.2025.1
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)

Authors: Martin Koutecký

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
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Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
  author =	{Kouteck\'{y}, Martin},
  title =	{{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
  URN =		{urn:nbn:de:0030-drops-251338},
  doi =		{10.4230/LIPIcs.IPEC.2025.1},
  annote =	{Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.29
Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division

Authors: Ajaykrishnan E S and Daniel Lokshtanov

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent’s share. Focusing on agents with additive valuations, we show that the problem remains computationally hard when parameterized by p and the number of agents. This result holds even for star graphs and with the input numbers given in unary representation, thereby resolving an open problem posed by Gahlawat and Zehavi (FSTTCS 2023). In stark contrast, we show that if one is willing to tolerate even the slightest amount of envy, then the problem becomes efficient with respect to the natural parameters. Specifically, we design an Efficient Parameterized Approximation Scheme parameterized by p and the number of agent types. Our algorithm works on general graphs and remains efficient even when the input numbers are provided in binary representation.
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Ajaykrishnan E S and Daniel Lokshtanov. Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{es_et_al:LIPIcs.FSTTCS.2025.29,
  author =	{E S, Ajaykrishnan and Lokshtanov, Daniel},
  title =	{{Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.29},
  URN =		{urn:nbn:de:0030-drops-251101},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.29},
  annote =	{Keywords: Envy-Free Incomplete Connected Fair Division, Efficient Parameterized Approximation Scheme, W\lbrack1\rbrack-hardness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.5
Graph Coloring Below Guarantees via Co-Triangle Packing

Authors: Shyan Akmal and Tomohiro Koana

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
In the 𝓁-Coloring problem, we are given a graph on n nodes, and tasked with determining if its vertices can be properly colored using 𝓁 colors. In this paper we study below-guarantee graph coloring, which tests whether an n-vertex graph can be properly colored using g-k colors, where g is a trivial upper bound such as n. We introduce an algorithmic framework that builds on a packing of co-triangles K₃ (independent sets of three vertices): the algorithm greedily finds co-triangles and employs a win-win analysis. If many are found, we immediately return yes; otherwise these co-triangles form a small co-triangle modulator, whose deletion makes the graph co-triangle-free. Extending the work of [Gutin et al., SIDMA 2021], who solved 𝓁-Coloring (for any 𝓁) in randomized O^∗(2^k) time when given a K₂-free modulator of size k, we show that this problem can likewise be solved in randomized O^*(2^{k}) time when given a K₃-free modulator of size k. This result in turn yields a randomized O^*(2^{3k/2}) algorithm for (n-k)-Coloring (also known as Dual Coloring), improving the previous O^*(4^k) bound. We then introduce a smaller parameterization, (ω+μ-k)-Coloring, where ω is the clique number and μ is the size of a maximum matching in the complement graph; since ω+μ ≤ n for any graph, this problem is strictly harder. Using the same co-triangle-packing argument, we obtain a randomized O^*(2^{6k}) algorithm, establishing its fixed-parameter tractability for a smaller parameter. Complementing this finding, we show that no fixed-parameter tractable algorithm exists for (ω-k)-Coloring or (μ-k)-Coloring under standard complexity assumptions.
Cite as

Shyan Akmal and Tomohiro Koana. Graph Coloring Below Guarantees via Co-Triangle Packing. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akmal_et_al:LIPIcs.ISAAC.2025.5,
  author =	{Akmal, Shyan and Koana, Tomohiro},
  title =	{{Graph Coloring Below Guarantees via Co-Triangle Packing}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.5},
  URN =		{urn:nbn:de:0030-drops-249130},
  doi =		{10.4230/LIPIcs.ISAAC.2025.5},
  annote =	{Keywords: coloring, parameterized algorithms, algebraic algorithms, above-guarantee, below-guarantee, subset convolution, determinants}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.23
Precoloring Extension with Demands on Paths

Authors: Arun Kumar Das, Michal Opler, and Tomáš Valla

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Let G be a graph with a set of precolored vertices, and let us be given an integer distance parameter d and a set of integer demands d₁,… ,d_c. The Distance Precoloring Extension with Demands (DPED) problem is to compute a vertex c-coloring of G such that the following three conditions hold: (i) the resulting coloring respects the colors of the precolored vertices, (ii) the distance of two vertices of the same color is at least d, and (iii) the number of vertices colored by color i is exactly d_i. This problem is motivated by a program scheduling in commercial broadcast channels with constraints on content repetition and placement, which leads precisely to the DPED problem for paths. In this paper, we study DPED on paths and present a polynomial time exact algorithm when precolored vertices are restricted to the two ends of the path and devise an approximation algorithm for DPED with an additive approximation factor polynomially bounded by d and the number of precolored vertices. Then, we prove that the Distance Precoloring Extension problem on paths, a less restrictive version of DPED without the demand constraints, and then DPED itself, is NP-complete. Motivated by this result, we further study the parameterized complexity of DPED on paths. We establish that the DPED problem on paths is W[1]-hard when parameterized by the number of colors and the distance. On the positive side, we devise a fixed parameter tractable (FPT) algorithm for DPED on paths when the number of colors, the distance, and the number of precolored vertices are considered as the parameters. Moreover, we prove that Distance Precoloring Extension is FPT parameterized by the distance. As a byproduct, we also obtain several results for the Distance List Coloring problem on paths.
Cite as

Arun Kumar Das, Michal Opler, and Tomáš Valla. Precoloring Extension with Demands on Paths. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{das_et_al:LIPIcs.ISAAC.2025.23,
  author =	{Das, Arun Kumar and Opler, Michal and Valla, Tom\'{a}\v{s}},
  title =	{{Precoloring Extension with Demands on Paths}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.23},
  URN =		{urn:nbn:de:0030-drops-249319},
  doi =		{10.4230/LIPIcs.ISAAC.2025.23},
  annote =	{Keywords: precoloring extension, distance coloring, FPT, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.25
Structural Parameterizations of Simultaneous Planarity

Authors: Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Given a set of graphs on the same vertex set, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks, whether there exist planar drawings of all input graphs, such that every pair of drawings coincides on their shared subgraph. It is known that SEFE is NP-complete [Elisabeth Gassner et al., 2006], even in the so-called sunflower case, where all pairs of input graphs have the same shared graph G_∩ [Marcus Schaefer, 2012]. Fink, Pfretzschner, and Rutter [Simon D. Fink et al., 2023] recently initiated the study of the parameterized complexity of SEFE in the sunflower case, mainly focusing on structural parameters of G_∩. In this work, we shift the focus towards parameters of the union graph G_∪ that contains the edges of all input graphs. On the positive side, we establish fixed-parameter tractability for the problem with respect to the feedback edge set number of G_∪. We complement this result by showing that it, surprisingly, remains NP-complete even if G_∪ has constant vertex cover number. These results settle two open questions posed by Fink et al. [Simon D. Fink et al., 2023].
Cite as

Thomas Depian, Simon D. Fink, Alexander Firbas, Robert Ganian, Matthias Pfretzschner, and Ignaz Rutter. Structural Parameterizations of Simultaneous Planarity. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ISAAC.2025.25,
  author =	{Depian, Thomas and Fink, Simon D. and Firbas, Alexander and Ganian, Robert and Pfretzschner, Matthias and Rutter, Ignaz},
  title =	{{Structural Parameterizations of Simultaneous Planarity}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.25},
  URN =		{urn:nbn:de:0030-drops-249332},
  doi =		{10.4230/LIPIcs.ISAAC.2025.25},
  annote =	{Keywords: SEFE, Simultaneous Planarity, Fixed-Parameter Tractability, NP-hardness}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.16
Structural Parameterizations of k-Planarity

Authors: Tatsuya Gima, Yasuaki Kobayashi, and Yuto Okada

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
The concept of k-planarity is extensively studied in the context of Beyond Planarity. A graph is k-planar if it admits a drawing in the plane in which each edge is crossed at most k times. The local crossing number of a graph is the minimum integer k such that it is k-planar. The problem of determining whether an input graph is 1-planar is known to be NP-complete even for near-planar graphs [Cabello and Mohar, SIAM J. Comput. 2013], that is, the graphs obtained from planar graphs by adding a single edge. Moreover, the local crossing number is hard to approximate within a factor 2 - ε for any ε > 0 [Urschel and Wellens, IPL 2021]. To address this computational intractability, Bannister, Cabello, and Eppstein [JGAA 2018] investigated the parameterized complexity of the case of k = 1, particularly focusing on structural parameterizations on input graphs, such as treedepth, vertex cover number, and feedback edge number. In this paper, we extend their approach by considering the general case k ≥ 1 and give (tight) parameterized upper and lower bound results. In particular, we strengthen the aforementioned lower bound results to subclasses of constant-treewidth graphs: we show that testing 1-planarity is NP-complete even for near-planar graphs with feedback vertex set number at most 3 and pathwidth at most 4, and the local crossing number is hard to approximate within any constant factor for graphs with feedback vertex set number at most 2.
Cite as

Tatsuya Gima, Yasuaki Kobayashi, and Yuto Okada. Structural Parameterizations of k-Planarity. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gima_et_al:LIPIcs.GD.2025.16,
  author =	{Gima, Tatsuya and Kobayashi, Yasuaki and Okada, Yuto},
  title =	{{Structural Parameterizations of k-Planarity}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.16},
  URN =		{urn:nbn:de:0030-drops-250021},
  doi =		{10.4230/LIPIcs.GD.2025.16},
  annote =	{Keywords: 1-planar graphs, local crossing number, beyond planarity, parameterized complexity, kernelization}
}
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)

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@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.2025.15
Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms

Authors: Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan

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

Abstract
In spite of the extensive study of stack and queue layouts, many fundamental questions remain open concerning the complexity-theoretic frontiers for computing stack and queue layouts. A stack (resp. queue) layout places vertices along a line and assigns edges to pages so that no two edges on the same page are crossing (resp. nested). We provide three new algorithms which together substantially expand our understanding of these problems: 1) A fixed-parameter algorithm for computing minimum-page stack and queue layouts w.r.t. the vertex integrity of an n-vertex graph G. This result is motivated by an open question in the literature and generalizes the previous algorithms parameterizing by the vertex cover number of G. The proof relies on a newly developed Ramsey pruning technique. Vertex integrity intuitively measures the vertex deletion distance to a subgraph with only small connected components. 2) An n^𝒪(q 𝓁) algorithm for computing 𝓁-page stack and queue layouts of page width at most q. This is the first algorithm avoiding a double-exponential dependency on the parameters. The page width of a layout measures the maximum number of edges one needs to cross on any page to reach the outer face. 3) A 2^𝒪(n) algorithm for computing 1-page queue layouts. This improves upon the previously fastest n^𝒪(n) algorithm and can be seen as a counterpart to the recent subexponential algorithm for computing 2-page stack layouts [ICALP'24], but relies on an entirely different technique.
Cite as

Thomas Depian, Simon D. Fink, Robert Ganian, and Vaishali Surianarayanan. Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{depian_et_al:LIPIcs.ESA.2025.15,
  author =	{Depian, Thomas and Fink, Simon D. and Ganian, Robert and Surianarayanan, Vaishali},
  title =	{{Linear Layouts Revisited: Stacks, Queues, and Exact Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-244835},
  doi =		{10.4230/LIPIcs.ESA.2025.15},
  annote =	{Keywords: stack layouts, queue layouts, parameterized algorithms, vertex integrity, Ramsey theory}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.13
Tight Bounds for Some Classical Problems Parameterized by Cutwidth

Authors: Narek Bojikian, Vera Chekan, and Stefan Kratsch

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

Abstract
Cutwidth is a widely studied parameter and it quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth upper-bounds pathwidth. The SETH-tight parameterized complexity of problems on graphs of bounded pathwidth (and treewidth) has been actively studied over the past decade while for cutwidth the complexity of many classical problems remained open. For Hamiltonian Cycle, it is known that a (2+√2)^{pw} n^𝒪(1) algorithm is optimal for pathwidth under SETH [Cygan et al. JACM 2018]. Van Geffen et al. [J. Graph Algorithms Appl. 2020] and Bojikian et al. [STACS 2023] asked which running time is optimal for this problem parameterized by cutwidth. We answer this question with (1+√2)^{ctw} n^𝒪(1) by providing matching upper and lower bounds. Second, as our main technical contribution, we close the gap left by van Heck [2018] for Partition Into Triangles (and Triangle Packing) by improving both upper and lower bound and getting a tight bound of ∛{3}^{ctw} n^𝒪(1), which to our knowledge exhibits the only known tight non-integral basis apart from Hamiltonian Cycle [Cygan et al. JACM 2018] and C₄-Hitting Set [SODA 2025]. We show that the cuts inducing a disjoint union of paths of length three (unions of so-called Z-cuts) lie at the core of the complexity of the problem - usually lower-bound constructions use simpler cuts inducing either a matching or a disjoint union of bicliques. Finally, we determine the optimal running times for Max Cut (2^{ctw} n^𝒪(1)) and Induced Matching (3^{ctw} n^𝒪(1)) by providing matching lower bounds for the existing algorithms - the latter result also answers an open question for treewidth by Chaudhary and Zehavi [WG 2023].
Cite as

Narek Bojikian, Vera Chekan, and Stefan Kratsch. Tight Bounds for Some Classical Problems Parameterized by Cutwidth. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bojikian_et_al:LIPIcs.ESA.2025.13,
  author =	{Bojikian, Narek and Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Bounds for Some Classical Problems Parameterized by Cutwidth}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{13:1--13:17},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-244815},
  doi =		{10.4230/LIPIcs.ESA.2025.13},
  annote =	{Keywords: Parameterized complexity, cutwidth, Hamiltonian cycle, triangle packing, max cut, induced matching}
}
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