7 Search Results for "Araújo, Júlio"

Document
DOI: 10.4230/LIPIcs.FUN.2026.4
The Closed Hull Game and the Closed Interval Game

Authors: Samuel N. Araújo, Fabrício Benevides, Nicolas Martins, Nicolas Nisse, and Rudini Sampaio

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

Abstract
Given a set S of vertices in a graph G, its geodesic interval is the set I(S) containing S and all vertices on a shortest path between vertices of S. A set S is convex if I(S) = S. Moreover, the convex hull ℋ(S) of S is the smallest convex set containing S. In 1984, Harary introduced convexity games where two players, Alice and Bob, alternately select vertices of a graph G = (V,E) such that, if the set of already selected vertices is S, the next player can only select a vertex in V ⧵ I(S) (closed interval game) or in V ⧵ ℋ(S) (closed hull game). Normal and misère versions of these games have been studied and here, we introduced the optimization variants of them. Formally, given a graph G and k ∈ ℕ, Alice wins if the game ends after at most k vertices have been selected and Bob wins otherwise. The corresponding problem consists of determining which player has a winning strategy. We prove that the closed interval optimization game is PSPACE-complete in graphs with diameter 4 and that the closed hull optimization game is NP-hard in bipartite graphs and in split graphs. On the positive side, we prove that both games can be solved in polynomial time in trees and that the closed hull optimization game can be solved in polynomial time in cobipartite graphs. We conjecture that the closed interval optimization game is NP-hard in cobipartite graphs and that the closed hull optimization game is PSPACE-complete in general graphs.
Cite as

Samuel N. Araújo, Fabrício Benevides, Nicolas Martins, Nicolas Nisse, and Rudini Sampaio. The Closed Hull Game and the Closed Interval Game. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{araujo_et_al:LIPIcs.FUN.2026.4,
  author =	{Ara\'{u}jo, Samuel N. and Benevides, Fabr{\'\i}cio and Martins, Nicolas and Nisse, Nicolas and Sampaio, Rudini},
  title =	{{The Closed Hull Game and the Closed Interval Game}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{4:1--4:12},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-257232},
  doi =		{10.4230/LIPIcs.FUN.2026.4},
  annote =	{Keywords: Combinatorial games in graphs, graph convexity, PSPACE}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.17
Realization of Temporally Connected Graphs Based on Degree Sequences

Authors: Arnaud Casteigts, Michelle Döring, and Nils Morawietz

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

Abstract
Given an undirected graph G, the problem of deciding whether G admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (Göbel et al., 1991). In this article, we relax this problem and ask whether a given degree sequence can be realized as a temporally connected graph. Our main results are a complete characterization of the feasible cases, and a recognition algorithm that runs in 𝒪(n) time for graphical degree sequences (realized as simple temporal graphs) and in 𝒪(n+m) time for multigraphical degree sequences (realized as non-simple temporal graphs, where the number of time labels on an edge corresponds to the multiplicity of the edge in the multigraph). In fact, these algorithms can be made constructive at essentially no cost. Namely, we give a constructive 𝒪(n+m) time algorithm that outputs, for a given (multi)graphical degree sequence 𝐝, a temporally connected graph whose underlying (multi)graph is a realization of 𝐝, if one exists.
Cite as

Arnaud Casteigts, Michelle Döring, and Nils Morawietz. Realization of Temporally Connected Graphs Based on Degree Sequences. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{casteigts_et_al:LIPIcs.ISAAC.2025.17,
  author =	{Casteigts, Arnaud and D\"{o}ring, Michelle and Morawietz, Nils},
  title =	{{Realization of Temporally Connected Graphs Based on Degree Sequences}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{17:1--17:18},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-249256},
  doi =		{10.4230/LIPIcs.ISAAC.2025.17},
  annote =	{Keywords: temporal paths, gossiping, (multi)graphical degree sequences, edge-disjoint spanning trees, linear time algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.5
Parameterized Saga of First-Fit and Last-Fit Coloring

Authors: Akanksha Agrawal, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, and Shaily Verma

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
The classic greedy coloring algorithm considers the vertices of an input graph G in a given order and assigns the first available color to each vertex v in G. In the Grundy Coloring problem, the task is to find an ordering of the vertices that will force the greedy algorithm to use as many colors as possible. In the Partial Grundy Coloring, the task is also to color the graph using as many colors as possible. This time, however, we may select both the ordering in which the vertices are considered and which color to assign the vertex. The only constraint is that the color assigned to a vertex v is a color previously used for another vertex if such a color is available. Whether Grundy Coloring and Partial Grundy Coloring admit fixed-parameter tractable (FPT) algorithms, algorithms with running time f(k)n^O(1), where k is the number of colors, was posed as an open problem by Zaker and by Effantin et al., respectively. Recently, Aboulker et al. (STACS 2020 and Algorithmica 2022) resolved the question for Grundy Coloring in the negative by showing that the problem is W[1]-hard. For Partial Grundy Coloring, they obtain an FPT algorithm on graphs that do not contain K_{i,j} as a subgraph (a.k.a. K_{i,j}-free graphs). Aboulker et al. re-iterate the question of whether there exists an FPT algorithm for Partial Grundy Coloring on general graphs and also asks whether Grundy Coloring admits an FPT algorithm on K_{i,j}-free graphs. We give FPT algorithms for Partial Grundy Coloring on general graphs and for Grundy Coloring on K_{i,j}-free graphs, resolving both the questions in the affirmative. We believe that our new structural theorems for partial Grundy coloring and "representative-family" like sets for K_{i,j}-free graphs that we use in obtaining our results may have wider algorithmic applications.
Cite as

Akanksha Agrawal, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, and Shaily Verma. Parameterized Saga of First-Fit and Last-Fit Coloring. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{agrawal_et_al:LIPIcs.STACS.2025.5,
  author =	{Agrawal, Akanksha and Lokshtanov, Daniel and Panolan, Fahad and Saurabh, Saket and Verma, Shaily},
  title =	{{Parameterized Saga of First-Fit and Last-Fit Coloring}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.5},
  URN =		{urn:nbn:de:0030-drops-228304},
  doi =		{10.4230/LIPIcs.STACS.2025.5},
  annote =	{Keywords: Grundy Coloring, Partial Grundy Coloring, FPT Algorithm, K\underline\{i,j\}-free graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.36
MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal

Authors: Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal st-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In the Maximum Minimal st-Separator problem, given a graph G, two distinct vertices s and t and a positive integer k, the goal is to determine whether there exists a minimal st-separator in G of size at least k. Similarly, the Maximum Minimal OCT problem seeks to determine if there exists a minimal set of vertices whose deletion results in a bipartite graph, and whose size is at least k. We demonstrate that both problems are fixed-parameter tractable parameterized by k. Our FPT algorithm for Maximum Minimal st-Separator answers the open question by Hanaka, Bodlaender, van der Zanden & Ono [TCS 2019]. One unique insight from this work is the following. We use the meta-result of Lokshtanov, Ramanujan, Saurabh & Zehavi [ICALP 2018] that enables us to reduce our problems to highly unbreakable graphs. This is interesting, as an explicit use of the recursive understanding and randomized contractions framework of Chitnis, Cygan, Hajiaghayi, Pilipczuk & Pilipczuk [SICOMP 2016] to reduce to the highly unbreakable graphs setting (which is the result that Lokshtanov et al. tries to abstract out in their meta-theorem) does not seem obvious because certain "extension" variants of our problems are W[1]-hard.
Cite as

Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma. MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gaikwad_et_al:LIPIcs.STACS.2025.36,
  author =	{Gaikwad, Ajinkya and Kumar, Hitendra and Maity, Soumen and Saurabh, Saket and Sharma, Roohani},
  title =	{{MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{36:1--36:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.36},
  URN =		{urn:nbn:de:0030-drops-228622},
  doi =		{10.4230/LIPIcs.STACS.2025.36},
  annote =	{Keywords: Parameterized Complexity, FPT, MaxMin problems, Maximum Minimal st-separator, Maximum Minimal Odd Cycle Transversal, Unbreakable Graphs, CMSO, Long Induced Odd Cycles, Sunflower Lemma}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.4
A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover

Authors: Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau

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

Abstract
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph G and a positive integer k, and the objective is to decide whether G contains a minimal vertex cover of size at least k. Motivated by the kernelization of MMVC with parameter k, our main contribution is to introduce a simple general framework to obtain lower bounds on the degrees of a certain type of polynomial kernels for vertex-optimization problems, which we call {lop-kernels}. Informally, this type of kernels is required to preserve large optimal solutions in the reduced instance, and captures the vast majority of existing kernels in the literature. As a consequence of this framework, we show that the trivial quadratic kernel for MMVC is essentially optimal, answering a question of Boria et al. [Discret. Appl. Math. 2015], and that the known cubic kernel for Maximum Minimal Feedback Vertex Set is also essentially optimal. On the positive side, given the (plausible) non-existence of subquadratic kernels for MMVC on general graphs, we provide subquadratic kernels on H-free graphs for several graphs H, such as the bull, the paw, or the complete graphs, by making use of the Erdős-Hajnal property in order to find an appropriate decomposition. Finally, we prove that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover of the input graph, even on bipartite graphs, unless NP ⊆ coNP / poly. This indicates that parameters smaller than the solution size are unlike to yield polynomial kernels for MMVC.
Cite as

Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau. A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{araujo_et_al:LIPIcs.IPEC.2021.4,
  author =	{Ara\'{u}jo, J\'{u}lio and Bougeret, Marin and Campos, Victor and Sau, Ignasi},
  title =	{{A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.4},
  URN =		{urn:nbn:de:0030-drops-153879},
  doi =		{10.4230/LIPIcs.IPEC.2021.4},
  annote =	{Keywords: Maximum minimal vertex cover, parameterized complexity, polynomial kernel, kernelization lower bound, Erd\H{o}s-Hajnal property, induced subgraphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2018.12
Dual Parameterization of Weighted Coloring

Authors: Júlio Araújo, Victor A. Campos, Carlos Vinícius G. C. Lima, Vinícius Fernandes dos Santos, Ignasi Sau, and Ana Silva

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

Abstract
Given a graph G, a proper k-coloring of G is a partition c = (S_i)_{i in [1,k]} of V(G) into k stable sets S_1,..., S_k. Given a weight function w: V(G) -> R^+, the weight of a color S_i is defined as w(i) = max_{v in S_i} w(v) and the weight of a coloring c as w(c) = sum_{i=1}^{k} w(i). Guan and Zhu [Inf. Process. Lett., 1997] defined the weighted chromatic number of a pair (G,w), denoted by sigma(G,w), as the minimum weight of a proper coloring of G. The problem of determining sigma(G,w) has received considerable attention during the last years, and has been proved to be notoriously hard: for instance, it is NP-hard on split graphs, unsolvable on n-vertex trees in time n^{o(log n)} unless the ETH fails, and W[1]-hard on forests parameterized by the size of a largest tree. We focus on the so-called dual parameterization of the problem: given a vertex-weighted graph (G,w) and an integer k, is sigma(G,w) <= sum_{v in V(G)} w(v) - k? This parameterization has been recently considered by Escoffier [WG, 2016], who provided an FPT algorithm running in time 2^{O(k log k)} * n^{O(1)}, and asked which kernel size can be achieved for the problem. We provide an FPT algorithm running in time 9^k * n^{O(1)}, and prove that no algorithm in time 2^{o(k)} * n^{O(1)} exists under the ETH. On the other hand, we present a kernel with at most (2^{k-1}+1) (k-1) vertices, and rule out the existence of polynomial kernels unless NP subseteq coNP/poly, even on split graphs with only two different weights. Finally, we identify some classes of graphs on which the problem admits a polynomial kernel, in particular interval graphs and subclasses of split graphs, and in the latter case we present lower bounds on the degrees of the polynomials.
Cite as

Júlio Araújo, Victor A. Campos, Carlos Vinícius G. C. Lima, Vinícius Fernandes dos Santos, Ignasi Sau, and Ana Silva. Dual Parameterization of Weighted Coloring. In 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 115, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{araujo_et_al:LIPIcs.IPEC.2018.12,
  author =	{Ara\'{u}jo, J\'{u}lio and Campos, Victor A. and Lima, Carlos Vin{\'\i}cius G. C. and Fernandes dos Santos, Vin{\'\i}cius and Sau, Ignasi and Silva, Ana},
  title =	{{Dual Parameterization of Weighted Coloring}},
  booktitle =	{13th International Symposium on Parameterized and Exact Computation (IPEC 2018)},
  pages =	{12:1--12:14},
  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.2018.12},
  URN =		{urn:nbn:de:0030-drops-102134},
  doi =		{10.4230/LIPIcs.IPEC.2018.12},
  annote =	{Keywords: weighted coloring, max coloring, parameterized complexity, dual parameterization, FPT algorithms, polynomial kernels, split graphs, interval graphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.75
Weighted Coloring in Trees

Authors: Julio Araujo, Nicolas Nisse, and Stéphane Pérennes

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract
A proper coloring of a graph is a partition of its vertex set into stable sets, where each part corresponds to a color. For a vertex-weighted graph, the weight of a color is the maximum weight of its vertices. The weight of a coloring is the sum of the weights of its colors. Guan and Zhu (1997) defined the weighted chromatic number of a vertex-weighted graph G as the smallest weight of a proper coloring of G. If vertices of a graph have weight 1, its weighted chromatic number coincides with its chromatic number. Thus, the problem of computing the weighted chromatic number, a.k.a. Max Coloring Problem, is NP-hard in general graphs. It remains NP-hard in some graph classes as bipartite graphs. Approximation algorithms have been designed in several graph classes, in particular, there exists a PTAS for trees. Surprisingly, the time-complexity of computing this parameter in trees is still open. The Exponential Time Hypothesis (ETH) states that 3-SAT cannot be solved in sub-exponential time. We show that, assuming ETH, the best algorithm to compute the weighted chromatic number of n-node trees has time-complexity n O(log(n)). Our result mainly relies on proving that, when computing an optimal proper weighted coloring of a graph G, it is hard to combine colorings of its connected components.
Cite as

Julio Araujo, Nicolas Nisse, and Stéphane Pérennes. Weighted Coloring in Trees. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 75-86, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{araujo_et_al:LIPIcs.STACS.2014.75,
  author =	{Araujo, Julio and Nisse, Nicolas and P\'{e}rennes, St\'{e}phane},
  title =	{{Weighted Coloring in Trees}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{75--86},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.75},
  URN =		{urn:nbn:de:0030-drops-44484},
  doi =		{10.4230/LIPIcs.STACS.2014.75},
  annote =	{Keywords: Weighted Coloring, Max Coloring, Exponential Time Hypothesis, 3-SAT}
}
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