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Documents authored by Souza, Uéverton S.

Found 2 Possible Name Variants:

Souza, Uéverton S.

Document
DOI: 10.4230/LIPIcs.ESA.2022.58
Taming Graphs with No Large Creatures and Skinny Ladders

Authors: Jakub Gajarský, Lars Jaffke, Paloma T. Lima, Jana Novotná, Marcin Pilipczuk, Paweł Rzążewski, and Uéverton S. Souza

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class 𝒢 there exists a constant k such that no member of 𝒢 contains a k-creature as an induced subgraph or a k-skinny-ladder as an induced minor, then there exists a polynomial p such that every G ∈ 𝒢 contains at most p(|V(G)|) minimal separators. By a result of Fomin, Todinca, and Villanger [SIAM J. Comput. 2015] the latter entails the existence of polynomial-time algorithms for Maximum Weight Independent Set, Feedback Vertex Set and many other problems, when restricted to an input graph from 𝒢. Furthermore, as shown by Gartland and Lokshtanov, our result implies a full dichotomy of hereditary graph classes defined by a finite set of forbidden induced subgraphs into tame (admitting a polynomial bound of the number of minimal separators) and feral (containing infinitely many graphs with exponential number of minimal separators).
Cite as

Jakub Gajarský, Lars Jaffke, Paloma T. Lima, Jana Novotná, Marcin Pilipczuk, Paweł Rzążewski, and Uéverton S. Souza. Taming Graphs with No Large Creatures and Skinny Ladders. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 58:1-58:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gajarsky_et_al:LIPIcs.ESA.2022.58,
  author =	{Gajarsk\'{y}, Jakub and Jaffke, Lars and Lima, Paloma T. and Novotn\'{a}, Jana and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l} and Souza, U\'{e}verton S.},
  title =	{{Taming Graphs with No Large Creatures and Skinny Ladders}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{58:1--58:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.58},
  URN =		{urn:nbn:de:0030-drops-169969},
  doi =		{10.4230/LIPIcs.ESA.2022.58},
  annote =	{Keywords: Minimal separator, hereditary graph class}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.69
Reducing the Vertex Cover Number via Edge Contractions

Authors: Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, Uéverton S. Souza, and Prafullkumar Tale

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
The Contraction(vc) problem takes as input a graph G on n vertices and two integers k and d, and asks whether one can contract at most k edges to reduce the size of a minimum vertex cover of G by at least d. Recently, Lima et al. [MFCS 2020, JCSS 2021] proved, among other results, that unlike most of the so-called blocker problems, Contraction(vc) admits an XP algorithm running in time f(d) ⋅ n^O(d). They left open the question of whether this problem is FPT under this parameterization. In this article, we continue this line of research and prove the following results: - Contraction(vc) is W[1]-hard parameterized by k + d. Moreover, unless the ETH fails, the problem does not admit an algorithm running in time f(k + d) ⋅ n^o(k + d) for any function f. In particular, this answers the open question stated in Lima et al. [MFCS 2020] in the negative. - It is NP-hard to decide whether an instance (G, k, d) of {Contraction(vc)} is a Yes-instance even when k = d, hence enhancing our understanding of the classical complexity of the problem. - Contraction(vc) can be solved in time 2^O(d) ⋅ n^{k - d + O(1)}. This XP algorithm improves the one of Lima et al. [MFCS 2020], which uses Courcelle’s theorem as a subroutine and hence, the f(d)-factor in the running time is non-explicit and probably very large. On the other hand, this shows that when k = d, the problem is FPT parameterized by d (or by k).
Cite as

Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, Uéverton S. Souza, and Prafullkumar Tale. Reducing the Vertex Cover Number via Edge Contractions. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lima_et_al:LIPIcs.MFCS.2022.69,
  author =	{Lima, Paloma T. and dos Santos, Vinicius F. and Sau, Ignasi and Souza, U\'{e}verton S. and Tale, Prafullkumar},
  title =	{{Reducing the Vertex Cover Number via Edge Contractions}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{69:1--69:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.69},
  URN =		{urn:nbn:de:0030-drops-168671},
  doi =		{10.4230/LIPIcs.MFCS.2022.69},
  annote =	{Keywords: Blocker problems, edge contraction, vertex cover, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.42
Co-Degeneracy and Co-Treewidth: Using the Complement to Solve Dense Instances

Authors: Gabriel L. Duarte, Mateus de Oliveira Oliveira, and Uéverton S. Souza

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Clique-width and treewidth are two of the most important and useful graph parameters, and several problems can be solved efficiently when restricted to graphs of bounded clique-width or treewidth. Bounded treewidth implies bounded clique-width, but not vice versa. Problems like Longest Cycle, Longest Path, MaxCut, Edge Dominating Set, and Graph Coloring are fixed-parameter tractable when parameterized by the treewidth, but they cannot be solved in FPT time when parameterized by the clique-width unless FPT = W[1], as shown by Fomin, Golovach, Lokshtanov, and Saurabh [SIAM J. Comput. 2010, SIAM J. Comput. 2014]. For a given problem that is fixed-parameter tractable when parameterized by treewidth, but intractable when parameterized by clique-width, there may exist infinite families of instances of bounded clique-width and unbounded treewidth where the problem can be solved efficiently. In this work, we initiate a systematic study of the parameters co-treewidth (the treewidth of the complement of the input graph) and co-degeneracy (the degeneracy of the complement of the input graph). We show that Longest Cycle, Longest Path, and Edge Dominating Set are FPT when parameterized by co-degeneracy. On the other hand, Graph Coloring is para-NP-complete when parameterized by co-degeneracy but FPT when parameterized by the co-treewidth. Concerning MaxCut, we give an FPT algorithm parameterized by co-treewidth, while we leave open the complexity of the problem parameterized by co-degeneracy. Additionally, we show that Precoloring Extension is fixed-parameter tractable when parameterized by co-treewidth, while this problem is known to be W[1]-hard when parameterized by treewidth. These results give evidence that co-treewidth is a useful width parameter for handling dense instances of problems for which an FPT algorithm for clique-width is unlikely to exist. Finally, we develop an algorithmic framework for co-degeneracy based on the notion of Bondy-Chvátal closure.
Cite as

Gabriel L. Duarte, Mateus de Oliveira Oliveira, and Uéverton S. Souza. Co-Degeneracy and Co-Treewidth: Using the Complement to Solve Dense Instances. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{duarte_et_al:LIPIcs.MFCS.2021.42,
  author =	{Duarte, Gabriel L. and de Oliveira Oliveira, Mateus and Souza, U\'{e}verton S.},
  title =	{{Co-Degeneracy and Co-Treewidth: Using the Complement to Solve Dense Instances}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{42:1--42:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.42},
  URN =		{urn:nbn:de:0030-drops-144828},
  doi =		{10.4230/LIPIcs.MFCS.2021.42},
  annote =	{Keywords: FPT, treewidth, degeneracy, complement graph, Bondy-Chv\'{a}tal closure}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.64
Reducing Graph Transversals via Edge Contractions

Authors: Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, and Uéverton S. Souza

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
For a graph parameter π, the Contraction(π) problem consists in, given a graph G and two positive integers k,d, deciding whether one can contract at most k edges of G to obtain a graph in which π has dropped by at least d. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where π is the size of a minimum dominating set. We focus on graph parameters defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection ℋ according to a fixed containment relation. We prove co-NP-hardness results under some assumptions on the graphs in ℋ, which in particular imply that Contraction(π) is co-NP-hard even for fixed k = d = 1 when π is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when π is the size of a minimum vertex cover, the problem is in XP parameterized by d.
Cite as

Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, and Uéverton S. Souza. Reducing Graph Transversals via Edge Contractions. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 64:1-64:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lima_et_al:LIPIcs.MFCS.2020.64,
  author =	{Lima, Paloma T. and dos Santos, Vinicius F. and Sau, Ignasi and Souza, U\'{e}verton S.},
  title =	{{Reducing Graph Transversals via Edge Contractions}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{64:1--64:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.64},
  URN =		{urn:nbn:de:0030-drops-127346},
  doi =		{10.4230/LIPIcs.MFCS.2020.64},
  annote =	{Keywords: blocker problem, edge contraction, graph transversal, parameterized complexity, vertex cover, feedback vertex set, odd cycle transversal}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2019.2
Width Parameterizations for Knot-Free Vertex Deletion on Digraphs

Authors: Stéphane Bessy, Marin Bougeret, Alan D. A. Carneiro, Fábio Protti, and Uéverton S. Souza

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
A knot in a directed graph G is a strongly connected subgraph Q of G with at least two vertices, such that no vertex in V(Q) is an in-neighbor of a vertex in V(G)\V(Q). Knots are important graph structures, because they characterize the existence of deadlocks in a classical distributed computation model, the so-called OR-model. Deadlock detection is correlated with the recognition of knot-free graphs as well as deadlock resolution is closely related to the Knot-Free Vertex Deletion (KFVD) problem, which consists of determining whether an input graph G has a subset S subseteq V(G) of size at most k such that G[V\S] contains no knot. Because of natural applications in deadlock resolution, KFVD is closely related to Directed Feedback Vertex Set. In this paper we focus on graph width measure parameterizations for KFVD. First, we show that: (i) KFVD parameterized by the size of the solution k is W[1]-hard even when p, the length of a longest directed path of the input graph, as well as kappa, its Kenny-width, are bounded by constants, and we remark that KFVD is para-NP-hard even considering many directed width measures as parameters, but in FPT when parameterized by clique-width; (ii) KFVD can be solved in time 2^{O(tw)} x n, but assuming ETH it cannot be solved in 2^{o(tw)} x n^{O(1)}, where tw is the treewidth of the underlying undirected graph. Finally, since the size of a minimum directed feedback vertex set (dfv) is an upper bound for the size of a minimum knot-free vertex deletion set, we investigate parameterization by dfv and we show that (iii) KFVD can be solved in FPT-time parameterized by either dfv+kappa or dfv+p. Results of (iii) cannot be improved when replacing dfv by k due to (i).
Cite as

Stéphane Bessy, Marin Bougeret, Alan D. A. Carneiro, Fábio Protti, and Uéverton S. Souza. Width Parameterizations for Knot-Free Vertex Deletion on Digraphs. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bessy_et_al:LIPIcs.IPEC.2019.2,
  author =	{Bessy, St\'{e}phane and Bougeret, Marin and Carneiro, Alan D. A. and Protti, F\'{a}bio and Souza, U\'{e}verton S.},
  title =	{{Width Parameterizations for Knot-Free Vertex Deletion on Digraphs}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{2:1--2:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.2},
  URN =		{urn:nbn:de:0030-drops-114631},
  doi =		{10.4230/LIPIcs.IPEC.2019.2},
  annote =	{Keywords: Knot, deadlock, width measure, FPT, W\lbrack1\rbrack-hard, directed feedback vertex set}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2019.12
Computing the Largest Bond of a Graph

Authors: Gabriel L. Duarte, Daniel Lokshtanov, Lehilton L. C. Pedrosa, Rafael C. S. Schouery, and Uéverton S. Souza

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
A bond of a graph G is an inclusion-wise minimal disconnecting set of G, i.e., bonds are cut-sets that determine cuts [S,V\S] of G such that G[S] and G[V\S] are both connected. Given s,t in V(G), an st-bond of G is a bond whose removal disconnects s and t. Contrasting with the large number of studies related to maximum cuts, there are very few results regarding the largest bond of general graphs. In this paper, we aim to reduce this gap on the complexity of computing the largest bond and the largest st-bond of a graph. Although cuts and bonds are similar, we remark that computing the largest bond of a graph tends to be harder than computing its maximum cut. We show that Largest Bond remains NP-hard even for planar bipartite graphs, and it does not admit a constant-factor approximation algorithm, unless P = NP. We also show that Largest Bond and Largest st-Bond on graphs of clique-width w cannot be solved in time f(w) x n^{o(w)} unless the Exponential Time Hypothesis fails, but they can be solved in time f(w) x n^{O(w)}. In addition, we show that both problems are fixed-parameter tractable when parameterized by the size of the solution, but they do not admit polynomial kernels unless NP subseteq coNP/poly.
Cite as

Gabriel L. Duarte, Daniel Lokshtanov, Lehilton L. C. Pedrosa, Rafael C. S. Schouery, and Uéverton S. Souza. Computing the Largest Bond of a Graph. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{duarte_et_al:LIPIcs.IPEC.2019.12,
  author =	{Duarte, Gabriel L. and Lokshtanov, Daniel and Pedrosa, Lehilton L. C. and Schouery, Rafael C. S. and Souza, U\'{e}verton S.},
  title =	{{Computing the Largest Bond of a Graph}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.12},
  URN =		{urn:nbn:de:0030-drops-114732},
  doi =		{10.4230/LIPIcs.IPEC.2019.12},
  annote =	{Keywords: bond, cut, maximum cut, connected cut, FPT, treewidth, clique-width}
}

Souza, Uéverton dos Santos

Document
DOI: 10.4230/LIPIcs.MFCS.2020.82
Hitting Forbidden Induced Subgraphs on Bounded Treewidth Graphs

Authors: Ignasi Sau and Uéverton dos Santos Souza

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
For a fixed graph H, the H-IS-Deletion problem asks, given a graph G, for the minimum size of a set S ⊆ V(G) such that G⧵ S does not contain H as an induced subgraph. Motivated by previous work about hitting (topological) minors and subgraphs on bounded treewidth graphs, we are interested in determining, for a fixed graph H, the smallest function f_H(t) such that H-IS-Deletion can be solved in time f_H(t) ⋅ n^{𝒪(1)} assuming the Exponential Time Hypothesis (ETH), where t and n denote the treewidth and the number of vertices of the input graph, respectively. We show that f_H(t) = 2^{𝒪(t^{h-2})} for every graph H on h ≥ 3 vertices, and that f_H(t) = 2^{𝒪(t)} if H is a clique or an independent set. We present a number of lower bounds by generalizing a reduction of Cygan et al. [MFCS 2014] for the subgraph version. In particular, we show that when H deviates slightly from a clique, the function f_H(t) suffers a sharp jump: if H is obtained from a clique of size h by removing one edge, then f_H(t) = 2^{Θ(t^{h-2})}. We also show that f_H(t) = 2^{Ω(t^{h})} when H = K_{h,h}, and this reduction answers an open question of Mi. Pilipczuk [MFCS 2011] about the function f_{C₄}(t) for the subgraph version. Motivated by Cygan et al. [MFCS 2014], we also consider the colorful variant of the problem, where each vertex of G is colored with some color from V(H) and we require to hit only induced copies of H with matching colors. In this case, we determine, under the ETH, the function f_H(t) for every connected graph H on h vertices: if h ≤ 2 the problem can be solved in polynomial time; if h ≥ 3, f_H(t) = 2^{Θ(t)} if H is a clique, and f_H(t) = 2^{Θ(t^{h-2})} otherwise.
Cite as

Ignasi Sau and Uéverton dos Santos Souza. Hitting Forbidden Induced Subgraphs on Bounded Treewidth Graphs. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 82:1-82:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sau_et_al:LIPIcs.MFCS.2020.82,
  author =	{Sau, Ignasi and Souza, U\'{e}verton dos Santos},
  title =	{{Hitting Forbidden Induced Subgraphs on Bounded Treewidth Graphs}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{82:1--82:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.82},
  URN =		{urn:nbn:de:0030-drops-127511},
  doi =		{10.4230/LIPIcs.MFCS.2020.82},
  annote =	{Keywords: parameterized complexity, induced subgraphs, treewidth, hitting subgraphs, dynamic programming, lower bound, Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.34
On the Parameterized Complexity of Grid Contraction

Authors: Saket Saurabh, Uéverton dos Santos Souza, and Prafullkumar Tale

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

Abstract
For a family of graphs 𝒢, the 𝒢-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists F ⊆ E(G) of size at most k such that G/F belongs to 𝒢. Here, G/F is the graph obtained from G by contracting all the edges in F. In this article, we initiate the study of Grid Contraction from the parameterized complexity point of view. We present a fixed parameter tractable algorithm, running in time c^k ⋅ |V(G)|^{{O}(1)}, for this problem. We complement this result by proving that unless ETH fails, there is no algorithm for Grid Contraction with running time c^{o(k)} ⋅ |V(G)|^{{O}(1)}. We also present a polynomial kernel for this problem.
Cite as

Saket Saurabh, Uéverton dos Santos Souza, and Prafullkumar Tale. On the Parameterized Complexity of Grid Contraction. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{saurabh_et_al:LIPIcs.SWAT.2020.34,
  author =	{Saurabh, Saket and Souza, U\'{e}verton dos Santos and Tale, Prafullkumar},
  title =	{{On the Parameterized Complexity of Grid Contraction}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.34},
  URN =		{urn:nbn:de:0030-drops-122810},
  doi =		{10.4230/LIPIcs.SWAT.2020.34},
  annote =	{Keywords: Grid Contraction, FPT, Kernelization, Lower Bound}
}
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