10 Search Results for "Charbit, Pierre"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.53
Hardness and Approximation for Coloring Digraphs

Authors: Parinya Chalermsook, Harmender Gahlawat, Felix Klingelhoefer, Alantha Newman, and Chaoliang Tang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
The dichromatic number χ(D) of a digraph is the minimum number k such that V(D) can be partitioned into k subsets, each inducing an acyclic digraph. The acyclic number α(D) is the cardinality of a largest induced acyclic subdigraph of D. We study these problems from an approximation point of view. We begin with establishing that even when restricted to tournaments, approximating χ and α remain as challenging as their undirected counterparts on general graphs. Specifically, we establish that for every ε > 0, it is hard to approximate both α and χ up to a factor of n^{1-ε} even when restricted to tournaments. We next consider approximate coloring of digraphs in special cases. We begin with establishing that we can color 𝓁-dicolorable digraphs using at most 𝓁 ⋅ n^{1-1/(𝓁)} colors in time O(n^{2𝓁}); in particular, we can color 2-dicolorable digraphs with 2√n colors in polynomial time. We then focus on bounding the dichromatic number of dense digraphs as a function of the independence number α of the underlying graph. We consider two special cases in this regard: digraphs with χ(D) ≤ 2 and digraphs that do not contain any directed triangle. For these cases, we present algorithms which generalize and improve existing tools and results.
Cite as

Parinya Chalermsook, Harmender Gahlawat, Felix Klingelhoefer, Alantha Newman, and Chaoliang Tang. Hardness and Approximation for Coloring Digraphs. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chalermsook_et_al:LIPIcs.ICALP.2026.53,
  author =	{Chalermsook, Parinya and Gahlawat, Harmender and Klingelhoefer, Felix and Newman, Alantha and Tang, Chaoliang},
  title =	{{Hardness and Approximation for Coloring Digraphs}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{53:1--53:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.53},
  URN =		{urn:nbn:de:0030-drops-264421},
  doi =		{10.4230/LIPIcs.ICALP.2026.53},
  annote =	{Keywords: Graph Algorithms, Hardness of Approximation, Polynomial Time Approximation Algorithms, Structural Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.SAND.2026.7
Extending Ghouila-Houri’s Characterization of Comparability Graphs to Temporal Graphs

Authors: Pierre Charbit, Michel Habib, and Amalia Sorondo

Published in: LIPIcs, Volume 373, 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)

Abstract
An orientation of a static graph is called transitive if for any three vertices a,b,c, the presence of arcs (a,b) and (b,c) forces the presence of arc (a,c). If only the presence of an arc between a and c is required, but its orientation is unconstrained, the orientation is called quasi-transitive. A fundamental result due to Ghouila-Houri [Ghouila-Houri, 1962] states that any static graph admitting a quasi-transitive orientation also admits a transitive orientation. In a seminal work [Mertzios et al., 2025], Mertzios et al. introduced the notion of temporal transitivity in order to model information flows in simple temporal networks. We revisit the model introduced by Mertzios et al. and propose an analogous to Ghouila-Houri’s characterization for the temporal scenario. We present a structural theorem that will allow us to express by a 2-SAT formula all the constraints imposed on a temporal graph for it to admit a temporal transitive orientation. The latter produces an efficient recognition algorithm for graphs admitting such orientations, that we will call comparability temporal graphs. Inspired by the lexicographic strategy presented by Hell and Huang in [Hell and Huang, 1995] to transitively orient static graphs, we then propose an algorithm for constructing a temporal transitive orientation of a YES instance. This algorithm is straightforward and has a running-time complexity of O(nm + min{kn,m²}), with n, m and k being respectively the number of vertices, edges and monolabel triangles, i.e., triangles having the same unique time-label on their edges, in the temporal graph. This represents an improvement compared to the algorithm presented in [Mertzios et al., 2025]. Additionally, we extend the temporal transitivity model to temporal graphs having multiple time-labels associated to their edges and claim that the previous results hold in the multilabel setting. Finally, we propose a characterization of comparability temporal graphs by forbidden temporal ordered patterns.
Cite as

Pierre Charbit, Michel Habib, and Amalia Sorondo. Extending Ghouila-Houri’s Characterization of Comparability Graphs to Temporal Graphs. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{charbit_et_al:LIPIcs.SAND.2026.7,
  author =	{Charbit, Pierre and Habib, Michel and Sorondo, Amalia},
  title =	{{Extending Ghouila-Houri’s Characterization of Comparability Graphs to Temporal Graphs}},
  booktitle =	{5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-427-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{373},
  editor =	{Mertzios, George B. and Richa, Andr\'{e}a W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2026.7},
  URN =		{urn:nbn:de:0030-drops-262416},
  doi =		{10.4230/LIPIcs.SAND.2026.7},
  annote =	{Keywords: Temporal graphs, Transitive orientations, Graph algorithms}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.20
Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs

Authors: Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract
A disk graph is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit disk graphs, it is well known to be in P. The currently fastest algorithm runs in time O(n^{7/3+ o(1)}), where n denotes the number of disks [Jared Espenant et al., 2023; J. Mark Keil and Debajyoti Mondal, 2025]. Moreover, for the case of disk graphs with t distinct radii, the problem has also recently been shown to be in XP. More specifically, it is solvable in time O^*(n^{2t}) [J. Mark Keil and Debajyoti Mondal, 2025]. In this paper, we present algorithms with improved running times by allowing for approximate solutions and by using randomization: [(i)] 1) for unit disk graphs, we give an algorithm that, with constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(n/ε²); and 2) for disk graphs with t distinct radii, we give a parameterized approximation scheme that, with a constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(f(t)⋅ (1/ε)^{O(t)} ⋅ n), for some (exponential) function f(t).
Cite as

Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi. Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gao_et_al:LIPIcs.SWAT.2026.20,
  author =	{Gao, Jie and Gawrychowski, Pawe{\l} and Giannopoulos, Panos and Mulzer, Wolfgang and Singh, Satyam and Staals, Frank and Zehavi, Meirav},
  title =	{{Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.20},
  URN =		{urn:nbn:de:0030-drops-260563},
  doi =		{10.4230/LIPIcs.SWAT.2026.20},
  annote =	{Keywords: Maximum Clique, Disk Graphs, Unit Disk Graphs, FPT Approximation}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.20
Permutation Match Puzzles: How Young Tanvi Learned About Computational Complexity

Authors: Kshitij Gajjar and Neeldhara Misra

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a n × n grid is labeled with an ordering constraint - ascending (A) or descending (D) - and the goal is to fill the grid with the numbers 1 through n² such that each row and column respects its constraint. We provide a complete characterization of solvable puzzles: a puzzle admits a solution if and only if its associated constraint graph is acyclic, which translates to a simple "at most one switch" condition on the A/D labels. When solutions exist, we show that their count is given by a hook length formula. For unsolvable puzzles, we present an O(n) algorithm to compute the minimum number of label flips required to reach a solvable configuration. Finally, we consider a generalization where rows and columns may specify arbitrary permutations rather than simple orderings, and establish that finding minimal repairs in this setting is NP-complete by a reduction from feedback arc set.
Cite as

Kshitij Gajjar and Neeldhara Misra. Permutation Match Puzzles: How Young Tanvi Learned About Computational Complexity. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gajjar_et_al:LIPIcs.FUN.2026.20,
  author =	{Gajjar, Kshitij and Misra, Neeldhara},
  title =	{{Permutation Match Puzzles: How Young Tanvi Learned About Computational Complexity}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.20},
  URN =		{urn:nbn:de:0030-drops-257398},
  doi =		{10.4230/LIPIcs.FUN.2026.20},
  annote =	{Keywords: sorting match puzzles, permutation match puzzles, grid puzzles, constraint satisfaction, directed acyclic graphs, hook length formula, standard Young tableaux, NP-completeness, feedback arc set}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.1
Triangle Detection in H-Free Graphs

Authors: Amir Abboud, Ron Safier, and Nathan Wallheimer

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate the study of combinatorial algorithms for Triangle Detection in H-free graphs. The goal is to decide if a graph that forbids a fixed pattern H as a subgraph contains a triangle, using only "combinatorial" methods that notably exclude fast matrix multiplication. Our work aims to classify which patterns admit a subcubic speedup, working towards a dichotomy theorem. On the lower bound side, we show that if H is not 3-colorable or contains more than one triangle, the complexity of the problem remains unchanged, and no combinatorial speedup is likely possible. On the upper bound side, we develop an embedding approach that results in a strongly subcubic, combinatorial algorithm for a rich class of "embeddable" patterns. Specifically, for an embeddable pattern of size k, our algorithm runs in Õ(n^{3-1/(2^{k-3)}}) time, where Õ(⋅) hides poly-logarithmic factors. This algorithm also extends to listing all the triangles within the same time bound. We supplement this main result with two generalizations: - A generalization to patterns that are embeddable up to a single obstacle that arises from a triangle in the pattern. This completes our classification for small patterns, yielding a dichotomy theorem for all patterns of size up to eight. - An H-sensitive algorithm for embeddable patterns, which runs faster when the number of copies of H is significantly smaller than the maximum possible Ω(n^{k}). Finally, we focus on the special case of odd cycles. We present specialized Triangle Detection algorithms that are very efficient: - A combinatorial algorithm for C_{2k+1}-free graphs that runs in Õ(m+n^{1+2/k}) time for every k ≥ 2, where m is the number of edges in the graph. - A combinatorial C₅-sensitive algorithm that runs in Õ(n² + n^{4/3} t^{1/3}) time, where t is the number of 5-cycles in the graph.
Cite as

Amir Abboud, Ron Safier, and Nathan Wallheimer. Triangle Detection in H-Free Graphs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{abboud_et_al:LIPIcs.ITCS.2026.1,
  author =	{Abboud, Amir and Safier, Ron and Wallheimer, Nathan},
  title =	{{Triangle Detection in H-Free Graphs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.1},
  URN =		{urn:nbn:de:0030-drops-252885},
  doi =		{10.4230/LIPIcs.ITCS.2026.1},
  annote =	{Keywords: fine-grained complexity, triangle detection, H-free graphs}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.18
A Randomized Rounding Approach for DAG Edge Deletion

Authors: Sina Kalantarzadeh, Nathan Klein, and Victor Reis

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In the DAG Edge Deletion problem, we are given an edge-weighted directed acyclic graph and a parameter k, and the goal is to delete the minimum weight set of edges so that the resulting graph has no paths of length k. This problem, which has applications to scheduling, was introduced in 2015 by Kenkre, Pandit, Purohit, and Saket. They gave a k-approximation and showed that it is UGC-Hard to approximate better than ⌊0.5k⌋ for any constant k ≥ 4 using a work of Svensson from 2012. The approximation ratio was improved to 2/3(k+1) by Klein and Wexler in 2016. In this work, we introduce a randomized rounding framework based on distributions over vertex labels in [0,1]. The most natural distribution is to sample labels independently from the uniform distribution over [0,1]. We show this leads to a (2-√2)(k+1) ≈ 0.585(k+1)-approximation. By using a modified (but still independent) label distribution, we obtain a 0.549(k+1)-approximation for the problem, as well as show that no independent distribution over labels can improve our analysis to below 0.542(k+1). Finally, we show a 0.5(k+1)-approximation for bipartite graphs and for instances with structured LP solutions. Whether this ratio can be obtained in general is open.
Cite as

Sina Kalantarzadeh, Nathan Klein, and Victor Reis. A Randomized Rounding Approach for DAG Edge Deletion. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kalantarzadeh_et_al:LIPIcs.APPROX/RANDOM.2025.18,
  author =	{Kalantarzadeh, Sina and Klein, Nathan and Reis, Victor},
  title =	{{A Randomized Rounding Approach for DAG Edge Deletion}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  URN =		{urn:nbn:de:0030-drops-243840},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  annote =	{Keywords: Approximation Algorithms, Randomized Algorithms, Linear Programming, Graph Algorithms, Scheduling}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.74
Subcoloring of (Unit) Disk Graphs

Authors: Malory Marin and Rémi Watrigant

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

Abstract
A subcoloring of a graph is a partition of its vertex set into subsets (called colors), each inducing a disjoint union of cliques. It is a natural generalization of the classical proper coloring, in which each color must instead induce an independent set. Similarly to proper coloring, we define the subchromatic number of a graph as the minimum integer k such that it admits a subcoloring with k colors, and the corresponding problem k-Subcoloring which asks whether a graph has subchromatic number at most k. In this paper, we initiate the study of the subcoloring of (unit) disk graphs. One motivation stems from the fact that disk graphs can be seen as a dense generalization of planar graphs where, intuitively, each vertex can be blown into a large clique-much like subcoloring generalizes proper coloring. Interestingly, it can be observed that every unit disk graph admits a subcoloring with at most 7 colors. We first prove that the subchromatic number can be 3-approximated in polynomial-time in unit disk graphs. We then present several hardness results for special cases of unit disk graphs which somehow prevents the use of classical approaches for improving this result. We show in particular that 2-Subcoloring remains NP-hard in triangle-free unit disk graphs, as well as in unit disk graphs representable within a strip of bounded height. We also solve an open question of Broersma, Fomin, Nešetřil, and Woeginger (2002) by proving that 3-Subcoloring remains NP-hard in co-comparability graphs (which contain unit disk graphs representable within a strip of height √3/2). Finally, we prove that every n-vertex disk graph admits a subcoloring with at most O(log³(n)) colors and present a O(log²(n))-approximation algorithm for computing the subchromatic number of such graphs. This is achieved by defining a decomposition and a special type of co-comparability disk graph, called Δ-disk graphs, which might be of independent interest.
Cite as

Malory Marin and Rémi Watrigant. Subcoloring of (Unit) Disk Graphs. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{marin_et_al:LIPIcs.MFCS.2025.74,
  author =	{Marin, Malory and Watrigant, R\'{e}mi},
  title =	{{Subcoloring of (Unit) Disk Graphs}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{74:1--74:17},
  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.2025.74},
  URN =		{urn:nbn:de:0030-drops-241811},
  doi =		{10.4230/LIPIcs.MFCS.2025.74},
  annote =	{Keywords: subcoloring, algorithms, disk graphs, unit disk graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.63
The Maximum Clique Problem in a Disk Graph Made Easy

Authors: J. Mark Keil and Debajyoti Mondal

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
A disk graph is an intersection graph of disks in ℝ². Determining the computational complexity of finding a maximum clique in a disk graph is a long-standing open problem. In 1990, Clark, Colbourn, and Johnson gave a polynomial-time algorithm for computing a maximum clique in a unit disk graph. However, finding a maximum clique when disks are of arbitrary size is widely believed to be a challenging open problem. In this paper, we provide a new perspective to examine adjacencies in a disk graph that helps obtain the following results. - We design an 𝒪^*(n^{2k})-time algorithm, where 𝒪^* hides a polynomial factor, to find a maximum clique in a n-vertex disk graph with k different sizes of radii. This is polynomial for every fixed k, and thus settles the open question for the case when k = 2. - Given a set of n unit disks, we show how to compute a maximum clique inside each possible axis-aligned rectangle determined by the disk centers in O(n⁵log n)-time. This is at least a factor of n^{4/3} faster than applying the fastest known algorithm for finding a maximum clique in a unit disk graph for each rectangle independently. - We give an 𝒪^*(n^{2rk})-time algorithm to find a maximum clique in a n-vertex ball graph with k different sizes of radii where the ball centers lie on r parallel planes. This is polynomial for every fixed k and r, and thus contrasts the previously known NP-hardness result for finding a maximum clique in an arbitrary ball graph. - We design an 𝒪^*(n^{2k})-time algorithm to find a maximum clique in the intersection graph of a set S of n L-visible convex polygons, where k is the number of distinct shapes in S. This contrasts the known hardness result on finding a maximum clique in the intersection graph of unit disks and axis-aligned rectangles.
Cite as

J. Mark Keil and Debajyoti Mondal. The Maximum Clique Problem in a Disk Graph Made Easy. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 63:1-63:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{keil_et_al:LIPIcs.SoCG.2025.63,
  author =	{Keil, J. Mark and Mondal, Debajyoti},
  title =	{{The Maximum Clique Problem in a Disk Graph Made Easy}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{63:1--63:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.63},
  URN =		{urn:nbn:de:0030-drops-232155},
  doi =		{10.4230/LIPIcs.SoCG.2025.63},
  annote =	{Keywords: Geometric Intersection Graphs, Disk Graphs, Ball Graphs, Maximum Clique}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.117
On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games

Authors: Antonio Casares, Thomas Colcombet, and Karoliina Lehtinen

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
In this paper, we look at good-for-games Rabin automata that recognise a Muller language (a language that is entirely characterised by the set of letters that appear infinitely often in each word). We establish that minimal such automata are exactly of the same size as the minimal memory required for winning Muller games that have this language as their winning condition. We show how to effectively construct such minimal automata. Finally, we establish that these automata can be exponentially more succinct than equivalent deterministic ones, thus proving as a consequence that chromatic memory for winning a Muller game can be exponentially larger than unconstrained memory.
Cite as

Antonio Casares, Thomas Colcombet, and Karoliina Lehtinen. On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 117:1-117:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{casares_et_al:LIPIcs.ICALP.2022.117,
  author =	{Casares, Antonio and Colcombet, Thomas and Lehtinen, Karoliina},
  title =	{{On the Size of Good-For-Games Rabin Automata and Its Link with the Memory in Muller Games}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{117:1--117:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.117},
  URN =		{urn:nbn:de:0030-drops-164580},
  doi =		{10.4230/LIPIcs.ICALP.2022.117},
  annote =	{Keywords: Infinite duration games, Muller games, Rabin conditions, omega-regular languages, memory in games, good-for-games automata}
}
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DOI: 10.4230/LIPIcs.IPEC.2018.17
Parameterized Complexity of Independent Set in H-Free Graphs

Authors: Édouard Bonnet, Nicolas Bousquet, Pierre Charbit, Stéphan Thomassé, and Rémi Watrigant

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

Abstract
In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of H-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains NP-hard for most graphs H, we study its fixed-parameter tractability and make progress towards a dichotomy between FPT and W[1]-hard cases. We first show that MIS remains W[1]-hard in graphs forbidding simultaneously K_{1, 4}, any finite set of cycles of length at least 4, and any finite set of trees with at least two branching vertices. In particular, this answers an open question of Dabrowski et al. concerning C_4-free graphs. Then we extend the polynomial algorithm of Alekseev when H is a disjoint union of edges to an FPT algorithm when H is a disjoint union of cliques. We also provide a framework for solving several other cases, which is a generalization of the concept of iterative expansion accompanied by the extraction of a particular structure using Ramsey's theorem. Iterative expansion is a maximization version of the so-called iterative compression. We believe that our framework can be of independent interest for solving other similar graph problems. Finally, we present positive and negative results on the existence of polynomial (Turing) kernels for several graphs H.
Cite as

Édouard Bonnet, Nicolas Bousquet, Pierre Charbit, Stéphan Thomassé, and Rémi Watrigant. Parameterized Complexity of Independent Set in H-Free Graphs. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2018.17,
  author =	{Bonnet, \'{E}douard and Bousquet, Nicolas and Charbit, Pierre and Thomass\'{e}, St\'{e}phan and Watrigant, R\'{e}mi},
  title =	{{Parameterized Complexity of Independent Set in H-Free Graphs}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{17:1--17:13},
  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.2018.17},
  URN =		{urn:nbn:de:0030-drops-102183},
  doi =		{10.4230/LIPIcs.IPEC.2018.17},
  annote =	{Keywords: Parameterized Algorithms, Independent Set, H-Free Graphs}
}
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