8 Search Results for "Galby, Esther"


Document
Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs

Authors: Esther Galby, Andrea Munaro, and Shizhou Yang

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)


Abstract
We investigate a relaxation of the notion of treewidth-fragility, namely tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for independent packing problems on fractionally tree-independence-number-fragile graph classes. Our approach unifies and extends several known polynomial-time approximation schemes on seemingly unrelated graph classes, such as classes of intersection graphs of fat objects in a fixed dimension or proper minor-closed classes. We also study the related notion of layered tree-independence number, a relaxation of layered treewidth.

Cite as

Esther Galby, Andrea Munaro, and Shizhou Yang. Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 34:1-34:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{galby_et_al:LIPIcs.SoCG.2023.34,
  author =	{Galby, Esther and Munaro, Andrea and Yang, Shizhou},
  title =	{{Polynomial-Time Approximation Schemes for Independent Packing Problems on Fractionally Tree-Independence-Number-Fragile Graphs}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.34},
  URN =		{urn:nbn:de:0030-drops-178840},
  doi =		{10.4230/LIPIcs.SoCG.2023.34},
  annote =	{Keywords: Independent packings, intersection graphs, polynomial-time approximation schemes, tree-independence number}
}
Document
Domination and Cut Problems on Chordal Graphs with Bounded Leafage

Authors: Esther Galby, Dániel Marx, Philipp Schepper, Roohani Sharma, and Prafullkumar Tale

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)


Abstract
The leafage of a chordal graph G is the minimum integer 𝓁 such that G can be realized as an intersection graph of subtrees of a tree with 𝓁 leaves. We consider structural parameterization by the leafage of classical domination and cut problems on chordal graphs. Fomin, Golovach, and Raymond [ESA 2018, Algorithmica 2020] proved, among other things, that Dominating Set on chordal graphs admits an algorithm running in time 2^𝒪(𝓁²) ⋅ n^𝒪(1). We present a conceptually much simpler algorithm that runs in time 2^𝒪(𝓁) ⋅ n^𝒪(1). We extend our approach to obtain similar results for Connected Dominating Set and Steiner Tree. We then consider the two classical cut problems MultiCut with Undeletable Terminals and Multiway Cut with Undeletable Terminals. We prove that the former is W[1]-hard when parameterized by the leafage and complement this result by presenting a simple n^𝒪(𝓁)-time algorithm. To our surprise, we find that Multiway Cut with Undeletable Terminals on chordal graphs can be solved, in contrast, in n^O(1)-time.

Cite as

Esther Galby, Dániel Marx, Philipp Schepper, Roohani Sharma, and Prafullkumar Tale. Domination and Cut Problems on Chordal Graphs with Bounded Leafage. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 14:1-14:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{galby_et_al:LIPIcs.IPEC.2022.14,
  author =	{Galby, Esther and Marx, D\'{a}niel and Schepper, Philipp and Sharma, Roohani and Tale, Prafullkumar},
  title =	{{Domination and Cut Problems on Chordal Graphs with Bounded Leafage}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{14:1--14:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.14},
  URN =		{urn:nbn:de:0030-drops-173704},
  doi =		{10.4230/LIPIcs.IPEC.2022.14},
  annote =	{Keywords: Chordal Graphs, Leafage, FPT Algorithms, Dominating Set, MultiCut with Undeletable Terminals, Multiway Cut with Undeletable Terminals}
}
Document
Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters

Authors: Esther Galby, Liana Khazaliya, Fionn Mc Inerney, Roohani Sharma, and Prafullkumar Tale

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


Abstract
For a graph G, a subset S ⊆ V(G) is called a resolving set if for any two vertices u,v ∈ V(G), there exists a vertex w ∈ S such that d(w,u) ≠ d(w,v). The Metric Dimension problem takes as input a graph G and a positive integer k, and asks whether there exists a resolving set of size at most k. This problem was introduced in the 1970s and is known to be NP-hard [GT 61 in Garey and Johnson’s book]. In the realm of parameterized complexity, Hartung and Nichterlein [CCC 2013] proved that the problem is W[2]-hard when parameterized by the natural parameter k. They also observed that it is FPT when parameterized by the vertex cover number and asked about its complexity under smaller parameters, in particular the feedback vertex set number. We answer this question by proving that Metric Dimension is W[1]-hard when parameterized by the feedback vertex set number. This also improves the result of Bonnet and Purohit [IPEC 2019] which states that the problem is W[1]-hard parameterized by the treewidth. Regarding the parameterization by the vertex cover number, we prove that Metric Dimension does not admit a polynomial kernel under this parameterization unless NP ⊆ coNP/poly. We observe that a similar result holds when the parameter is the distance to clique. On the positive side, we show that Metric Dimension is FPT when parameterized by either the distance to cluster or the distance to co-cluster, both of which are smaller parameters than the vertex cover number.

Cite as

Esther Galby, Liana Khazaliya, Fionn Mc Inerney, Roohani Sharma, and Prafullkumar Tale. Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 51:1-51:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{galby_et_al:LIPIcs.MFCS.2022.51,
  author =	{Galby, Esther and Khazaliya, Liana and Mc Inerney, Fionn and Sharma, Roohani and Tale, Prafullkumar},
  title =	{{Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{51:1--51:15},
  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.2022.51},
  URN =		{urn:nbn:de:0030-drops-168496},
  doi =		{10.4230/LIPIcs.MFCS.2022.51},
  annote =	{Keywords: Metric Dimension, Parameterized Complexity, Feedback Vertex Set}
}
Document
Blocking Dominating Sets for H-Free Graphs via Edge Contractions

Authors: Esther Galby, Paloma T. Lima, and Bernard Ries

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)


Abstract
In this paper, we consider the following problem: given a connected graph G, can we reduce the domination number of G by one by using only one edge contraction? We show that the problem is NP-hard when restricted to {P_6,P_4+P_2}-free graphs and that it is coNP-hard when restricted to subcubic claw-free graphs and 2P_3-free graphs. As a consequence, we are able to establish a complexity dichotomy for the problem on H-free graphs when H is connected.

Cite as

Esther Galby, Paloma T. Lima, and Bernard Ries. Blocking Dominating Sets for H-Free Graphs via Edge Contractions. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 21:1-21:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


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@InProceedings{galby_et_al:LIPIcs.ISAAC.2019.21,
  author =	{Galby, Esther and Lima, Paloma T. and Ries, Bernard},
  title =	{{Blocking Dominating Sets for H-Free Graphs via Edge Contractions}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{21:1--21:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.21},
  URN =		{urn:nbn:de:0030-drops-115171},
  doi =		{10.4230/LIPIcs.ISAAC.2019.21},
  annote =	{Keywords: domination number, blocker problem, H-free graphs}
}
Document
Reducing the Domination Number of Graphs via Edge Contractions

Authors: Esther Galby, Paloma T. Lima, and Bernard Ries

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
In this paper, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k >= 0? We show that for k <= 2, the problem is coNP-hard. We further prove that for k=1, the problem is W[1]-hard parameterized by the size of a minimum dominating set plus the mim-width of the input graph, and that it remains NP-hard when restricted to P_9-free graphs, bipartite graphs and {C_3,...,C_{l}}-free graphs for any l >= 3. Finally, we show that for any k >= 1, the problem is polynomial-time solvable for P_5-free graphs and that it can be solved in FPT-time and XP-time when parameterized by tree-width and mim-width, respectively.

Cite as

Esther Galby, Paloma T. Lima, and Bernard Ries. Reducing the Domination Number of Graphs via Edge Contractions. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{galby_et_al:LIPIcs.MFCS.2019.41,
  author =	{Galby, Esther and Lima, Paloma T. and Ries, Bernard},
  title =	{{Reducing the Domination Number of Graphs via Edge Contractions}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{41:1--41:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.41},
  URN =		{urn:nbn:de:0030-drops-109856},
  doi =		{10.4230/LIPIcs.MFCS.2019.41},
  annote =	{Keywords: domination number, blocker problem, graph classes}
}
Document
A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs

Authors: Lars Jaffke and Paloma T. Lima

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
A b-coloring of a graph G is a proper coloring of its vertices such that each color class contains a vertex that has at least one neighbor in all the other color classes. The b-Coloring problem asks whether a graph G has a b-coloring with k colors. The b-chromatic number of a graph G, denoted by chi_b(G), is the maximum number k such that G admits a b-coloring with k colors. We consider the complexity of the b-Coloring problem, whenever the value of k is close to one of two upper bounds on chi_b(G): The maximum degree Delta(G) plus one, and the m-degree, denoted by m(G), which is defined as the maximum number i such that G has i vertices of degree at least i-1. We obtain a dichotomy result for all fixed k in N when k is close to one of the two above mentioned upper bounds. Concretely, we show that if k in {Delta(G) + 1 - p, m(G) - p}, the problem is polynomial-time solvable whenever p in {0, 1} and, even when k = 3, it is NP-complete whenever p >= 2. We furthermore consider parameterizations of the b-Coloring problem that involve the maximum degree Delta(G) of the input graph G and give two FPT-algorithms. First, we show that deciding whether a graph G has a b-coloring with m(G) colors is FPT parameterized by Delta(G). Second, we show that b-Coloring{} is FPT parameterized by Delta(G) + l_k(G), where l_k(G) denotes the number of vertices of degree at least k.

Cite as

Lars Jaffke and Paloma T. Lima. A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 34:1-34:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{jaffke_et_al:LIPIcs.MFCS.2019.34,
  author =	{Jaffke, Lars and Lima, Paloma T.},
  title =	{{A Complexity Dichotomy for Critical Values of the b-Chromatic Number of Graphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{34:1--34:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.34},
  URN =		{urn:nbn:de:0030-drops-109784},
  doi =		{10.4230/LIPIcs.MFCS.2019.34},
  annote =	{Keywords: b-Coloring, b-Chromatic Number}
}
Document
The Power Word Problem

Authors: Markus Lohrey and Armin Weiß

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
In this work we introduce a new succinct variant of the word problem in a finitely generated group G, which we call the power word problem: the input word may contain powers p^x, where p is a finite word over generators of G and x is a binary encoded integer. The power word problem is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over G). The main result of the paper states that the power word problem for a finitely generated free group F is AC^0-Turing-reducible to the word problem for F. Moreover, the following hardness result is shown: For a wreath product G Wr Z, where G is either free of rank at least two or finite non-solvable, the power word problem is complete for coNP. This contrasts with the situation where G is abelian: then the power word problem is shown to be in TC^0.

Cite as

Markus Lohrey and Armin Weiß. The Power Word Problem. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2019.43,
  author =	{Lohrey, Markus and Wei{\ss}, Armin},
  title =	{{The Power Word Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.43},
  URN =		{urn:nbn:de:0030-drops-109871},
  doi =		{10.4230/LIPIcs.MFCS.2019.43},
  annote =	{Keywords: word problem, compressed word problem, free groups}
}
Document
On Matrix Powering in Low Dimensions

Authors: Esther Galby, Joël Ouaknine, and James Worrell

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)


Abstract
We investigate the Matrix Powering Positivity Problem, PosMatPow: given an m X m square integer matrix M, a linear function f: Z^{m X m} -> Z with integer coefficients, and a positive integer n (encoded in binary), determine whether f(M^n) \geq 0. We show that for fixed dimensions m of 2 and 3, this problem is decidable in polynomial time.

Cite as

Esther Galby, Joël Ouaknine, and James Worrell. On Matrix Powering in Low Dimensions. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 329-340, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{galby_et_al:LIPIcs.STACS.2015.329,
  author =	{Galby, Esther and Ouaknine, Jo\"{e}l and Worrell, James},
  title =	{{On Matrix Powering in Low Dimensions}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{329--340},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.329},
  URN =		{urn:nbn:de:0030-drops-49240},
  doi =		{10.4230/LIPIcs.STACS.2015.329},
  annote =	{Keywords: matrix powering, complexity, Baker's theorem}
}
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