18 Search Results for "Kanté, Mamadou Moustapha"

Volume

LIPIcs, Volume 289

41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

STACS 2024, March 12-14, 2024, Clermont-Ferrand, France

Editors: Olaf Beyersdorff, Mamadou Moustapha Kanté, Orna Kupferman, and Daniel Lokshtanov

Volume

LIPIcs, Volume 254

40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

STACS 2023, March 7-9, 2023, Hamburg, Germany

Editors: Petra Berenbrink, Patricia Bouyer, Anuj Dawar, and Mamadou Moustapha Kanté

Document
DOI: 10.4230/LIPIcs.SEA.2024.23
Engineering A* Search for the Flip Distance of Plane Triangulations

Authors: Philip Mayer and Petra Mutzel

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The flip distance for two triangulations of a point set is defined as the smallest number of edge flips needed to transform one triangulation into another, where an edge flip is the act of replacing an edge of a triangulation by a different edge such that the result remains a triangulation. We adapt and engineer a sophisticated A* search algorithm acting on the so-called flip graph. In particular, we prove that previously proposed lower bounds for the flip distance form consistent heuristics for A* and show that they can be computed efficiently using dynamic algorithms. As an alternative approach, we present an integer linear program (ILP) for the flip distance problem. We experimentally evaluate our approaches on a new real-world benchmark data set based on an application in geodesy, namely sea surface reconstruction. Our evaluation reveals that A* search consistently outperforms our ILP formulation as well as a naive baseline, which is bidirectional breadth-first search. In particular, the runtime of our approach improves upon the baseline by more than two orders of magnitude. Furthermore, our A* search successfully solves most of the considered sea surface instances with up to 41 points. This is a substantial improvement compared to the baseline, which struggles with subsets of the real-world data of size 25. Lastly, to allow the consideration of global sea level data, we developed a decomposition-based heuristic for the flip distance. In our experiments it yields optimal flip distance values for most of the considered sea level data and it can be applied to large data sets due to its fast runtime.
Cite as

Philip Mayer and Petra Mutzel. Engineering A* Search for the Flip Distance of Plane Triangulations. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mayer_et_al:LIPIcs.SEA.2024.23,
  author =	{Mayer, Philip and Mutzel, Petra},
  title =	{{Engineering A* Search for the Flip Distance of Plane Triangulations}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.23},
  URN =		{urn:nbn:de:0030-drops-203887},
  doi =		{10.4230/LIPIcs.SEA.2024.23},
  annote =	{Keywords: Computational Geometry, Triangulations, Flip Distance, A-star Search, Integer Linear Programming}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.16
NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials

Authors: Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
An s-sparse polynomial has at most s monomials with nonzero coefficients. The Equivalence Testing problem for sparse polynomials (ETsparse) asks to decide if a given polynomial f is equivalent to (i.e., in the orbit of) some s-sparse polynomial. In other words, given f ∈ 𝔽[𝐱] and s ∈ ℕ, ETsparse asks to check if there exist A ∈ GL(|𝐱|, 𝔽) and 𝐛 ∈ 𝔽^|𝐱| such that f(A𝐱 + 𝐛) is s-sparse. We show that ETsparse is NP-hard over any field 𝔽, if f is given in the sparse representation, i.e., as a list of nonzero coefficients and exponent vectors. This answers a question posed by Gupta, Saha and Thankey (SODA 2023) and also, more explicitly, by Baraskar, Dewan and Saha (STACS 2024). The result implies that the Minimum Circuit Size Problem (MCSP) is NP-hard for a dense subclass of depth-3 arithmetic circuits if the input is given in sparse representation. We also show that approximating the smallest s₀ such that a given s-sparse polynomial f is in the orbit of some s₀-sparse polynomial to within a factor of s^{1/3 - ε} is NP-hard for any ε > 0; observe that s-factor approximation is trivial as the input is s-sparse. Finally, we show that for any constant σ ≥ 6, checking if a polynomial (given in sparse representation) is in the orbit of some support-σ polynomial is NP-hard. Support of a polynomial f is the maximum number of variables present in any monomial of f. These results are obtained via direct reductions from the 3-SAT problem.
Cite as

Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha. NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baraskar_et_al:LIPIcs.ICALP.2024.16,
  author =	{Baraskar, Omkar and Dewan, Agrim and Saha, Chandan and Sinha, Pulkit},
  title =	{{NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.16},
  URN =		{urn:nbn:de:0030-drops-201598},
  doi =		{10.4230/LIPIcs.ICALP.2024.16},
  annote =	{Keywords: Equivalence testing, MCSP, sparse polynomials, 3SAT}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.29
A Tight Monte-Carlo Algorithm for Steiner Tree Parameterized by Clique-Width

Authors: Narek Bojikian and Stefan Kratsch

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Given a graph G = (V,E), a set T ⊆ V, and an integer b, the Steiner Tree problem asks whether G has a connected subgraph H with at most b vertices that spans all of T. This work presents a 3^k⋅ n^𝒪(1) time one-sided Monte-Carlo algorithm for solving Steiner Tree when additionally a clique-expression of width k is provided. Known lower bounds for less expressive parameters imply that this dependence on the clique-width of G is optimal assuming the Strong Exponential-Time Hypothesis (SETH). Indeed our work establishes that the parameter dependence of Steiner Tree is the same for any graph parameter between cutwidth and clique-width, assuming SETH. Our work contributes to the program of determining the exact parameterized complexity of fundamental hard problems relative to structural graph parameters such as treewidth, which was initiated by Lokshtanov et al. [SODA 2011 & TALG 2018] and which by now has seen a plethora of results. Since the cut-and-count framework of Cygan et al. [FOCS 2011 & TALG 2022], connectivity problems have played a key role in this program as they pose many challenges for developing tight upper and lower bounds. Recently, Hegerfeld and Kratsch [ESA 2023] gave the first application of the cut-and-count technique to problems parameterized by clique-width and obtained tight bounds for Connected Dominating Set and Connected Vertex Cover, leaving open the complexity of other benchmark connectivity problems such as Steiner Tree and Feedback Vertex Set. Our algorithm for Steiner Tree does not follow the cut-and-count technique and instead works with the connectivity patterns of partial solutions. As a first technical contribution we identify a special family of so-called complete patterns that has strong (existential) representation properties, and using these at least one solution will be preserved. Furthermore, there is a family of 3^k basis patterns that (parity) represents the complete patterns, i.e., it has the same number of solutions modulo two. Our main technical contribution, a new technique called "isolating a representative," allows us to leverage both forms of representation (existential and parity). Both complete patterns and isolation of a representative will likely be applicable to other (connectivity) problems.
Cite as

Narek Bojikian and Stefan Kratsch. A Tight Monte-Carlo Algorithm for Steiner Tree Parameterized by Clique-Width. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bojikian_et_al:LIPIcs.ICALP.2024.29,
  author =	{Bojikian, Narek and Kratsch, Stefan},
  title =	{{A Tight Monte-Carlo Algorithm for Steiner Tree Parameterized by Clique-Width}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.29},
  URN =		{urn:nbn:de:0030-drops-201728},
  doi =		{10.4230/LIPIcs.ICALP.2024.29},
  annote =	{Keywords: Parameterized complexity, Steiner tree, clique-width}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.78
Isomorphism for Tournaments of Small Twin Width

Authors: Martin Grohe and Daniel Neuen

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We prove that isomorphism of tournaments of twin width at most k can be decided in time k^O(log k) n^O(1). This implies that the isomorphism problem for classes of tournaments of bounded or moderately growing twin width is in polynomial time. By comparison, there are classes of undirected graphs of bounded twin width that are isomorphism complete, that is, the isomorphism problem for the classes is as hard as the general graph isomorphism problem. Twin width is a graph parameter that has been introduced only recently (Bonnet et al., FOCS 2020), but has received a lot of attention in structural graph theory since then. On directed graphs, it is functionally smaller than clique width. We prove that on tournaments (but not on general directed graphs) it is also functionally smaller than directed tree width (and thus, the same also holds for cut width and directed path width). Hence, our result implies that tournament isomorphism testing is also fixed-parameter tractable when parameterized by any of these parameters. Our isomorphism algorithm heavily employs group-theoretic techniques. This seems to be necessary: as a second main result, we show that the combinatorial Weisfeiler-Leman algorithm does not decide isomorphism of tournaments of twin width at most 35 if its dimension is o(n). (Throughout this abstract, n is the order of the input graphs.)
Cite as

Martin Grohe and Daniel Neuen. Isomorphism for Tournaments of Small Twin Width. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grohe_et_al:LIPIcs.ICALP.2024.78,
  author =	{Grohe, Martin and Neuen, Daniel},
  title =	{{Isomorphism for Tournaments of Small Twin Width}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{78:1--78:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.78},
  URN =		{urn:nbn:de:0030-drops-202216},
  doi =		{10.4230/LIPIcs.ICALP.2024.78},
  annote =	{Keywords: tournament isomorphism, twin width, fixed-parameter tractability, Weisfeiler-Leman algorithm}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.STACS.2024
LIPIcs, Volume 289, STACS 2024, Complete Volume

Authors: Olaf Beyersdorff, Mamadou Moustapha Kanté, Orna Kupferman, and Daniel Lokshtanov

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
LIPIcs, Volume 289, STACS 2024, Complete Volume
Cite as

41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 1-1048, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{beyersdorff_et_al:LIPIcs.STACS.2024,
  title =	{{LIPIcs, Volume 289, STACS 2024, Complete Volume}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{1--1048},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024},
  URN =		{urn:nbn:de:0030-drops-197098},
  doi =		{10.4230/LIPIcs.STACS.2024},
  annote =	{Keywords: LIPIcs, Volume 289, STACS 2024, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.STACS.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Olaf Beyersdorff, Mamadou Moustapha Kanté, Orna Kupferman, and Daniel Lokshtanov

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{beyersdorff_et_al:LIPIcs.STACS.2024.0,
  author =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.0},
  URN =		{urn:nbn:de:0030-drops-197108},
  doi =		{10.4230/LIPIcs.STACS.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.18
Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth

Authors: Benjamin Bergougnoux, Vera Chekan, Robert Ganian, Mamadou Moustapha Kanté, Matthias Mnich, Sang-il Oum, Michał Pilipczuk, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming uses space that is exponential in the decomposition’s width, and there are good reasons to believe that this is necessary. However, it has been shown that in graphs of low treedepth it is possible to design algorithms which achieve polynomial space complexity without requiring worse time complexity than their counterparts working on tree decompositions of bounded width. Here, treedepth is a graph parameter that, intuitively speaking, takes into account both the depth and the width of a tree decomposition of the graph, rather than the width alone. Motivated by the above, we consider graphs that admit clique expressions with bounded depth and label count, or equivalently, graphs of low shrubdepth. Here, shrubdepth is a bounded-depth analogue of cliquewidth, in the same way as treedepth is a bounded-depth analogue of treewidth. We show that also in this setting, bounding the depth of the decomposition is a deciding factor for improving the space complexity. More precisely, we prove that on n-vertex graphs equipped with a tree-model (a decomposition notion underlying shrubdepth) of depth d and using k labels, - Independent Set can be solved in time 2^𝒪(dk) ⋅ n^𝒪(1) using 𝒪(dk²log n) space; - Max Cut can be solved in time n^𝒪(dk) using 𝒪(dk log n) space; and - Dominating Set can be solved in time 2^𝒪(dk) ⋅ n^𝒪(1) using n^𝒪(1) space via a randomized algorithm. We also establish a lower bound, conditional on a certain assumption about the complexity of Longest Common Subsequence, which shows that at least in the case of Independent Set the exponent of the parametric factor in the time complexity has to grow with d if one wishes to keep the space complexity polynomial.
Cite as

Benjamin Bergougnoux, Vera Chekan, Robert Ganian, Mamadou Moustapha Kanté, Matthias Mnich, Sang-il Oum, Michał Pilipczuk, and Erik Jan van Leeuwen. Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bergougnoux_et_al:LIPIcs.ESA.2023.18,
  author =	{Bergougnoux, Benjamin and Chekan, Vera and Ganian, Robert and Kant\'{e}, Mamadou Moustapha and Mnich, Matthias and Oum, Sang-il and Pilipczuk, Micha{\l} and van Leeuwen, Erik Jan},
  title =	{{Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.18},
  URN =		{urn:nbn:de:0030-drops-186710},
  doi =		{10.4230/LIPIcs.ESA.2023.18},
  annote =	{Keywords: Parameterized complexity, shrubdepth, space complexity, algebraic methods}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.STACS.2023
LIPIcs, Volume 254, STACS 2023, Complete Volume

Authors: Petra Berenbrink, Patricia Bouyer, Anuj Dawar, and Mamadou Moustapha Kanté

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
LIPIcs, Volume 254, STACS 2023, Complete Volume
Cite as

40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 1-1026, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{berenbrink_et_al:LIPIcs.STACS.2023,
  title =	{{LIPIcs, Volume 254, STACS 2023, Complete Volume}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{1--1026},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023},
  URN =		{urn:nbn:de:0030-drops-176515},
  doi =		{10.4230/LIPIcs.STACS.2023},
  annote =	{Keywords: LIPIcs, Volume 254, STACS 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.STACS.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Petra Berenbrink, Patricia Bouyer, Anuj Dawar, and Mamadou Moustapha Kanté

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 0:i-0:xxii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berenbrink_et_al:LIPIcs.STACS.2023.0,
  author =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{0:i--0:xxii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.0},
  URN =		{urn:nbn:de:0030-drops-176525},
  doi =		{10.4230/LIPIcs.STACS.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.11
Tight Lower Bounds for Problems Parameterized by Rank-Width

Authors: Benjamin Bergougnoux, Tuukka Korhonen, and Jesper Nederlof

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
We show that there is no 2^o(k²) n^O(1) time algorithm for Independent Set on n-vertex graphs with rank-width k, unless the Exponential Time Hypothesis (ETH) fails. Our lower bound matches the 2^O(k²) n^O(1) time algorithm given by Bui-Xuan, Telle, and Vatshelle [Discret. Appl. Math., 2010] and it answers the open question of Bergougnoux and Kanté [SIAM J. Discret. Math., 2021]. We also show that the known 2^O(k²) n^O(1) time algorithms for Weighted Dominating Set, Maximum Induced Matching and Feedback Vertex Set parameterized by rank-width k are optimal assuming ETH. Our results are the first tight ETH lower bounds parameterized by rank-width that do not follow directly from lower bounds for n-vertex graphs.
Cite as

Benjamin Bergougnoux, Tuukka Korhonen, and Jesper Nederlof. Tight Lower Bounds for Problems Parameterized by Rank-Width. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bergougnoux_et_al:LIPIcs.STACS.2023.11,
  author =	{Bergougnoux, Benjamin and Korhonen, Tuukka and Nederlof, Jesper},
  title =	{{Tight Lower Bounds for Problems Parameterized by Rank-Width}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.11},
  URN =		{urn:nbn:de:0030-drops-176636},
  doi =		{10.4230/LIPIcs.STACS.2023.11},
  annote =	{Keywords: rank-width, exponential time hypothesis, Boolean-width, parameterized algorithms, independent set, dominating set, maximum induced matching, feedback vertex set}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.40
Obstructions for Matroids of Path-Width at most k and Graphs of Linear Rank-Width at most k

Authors: Mamadou Moustapha Kanté, Eun Jung Kim, O-joung Kwon, and Sang-il Oum

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Every minor-closed class of matroids of bounded branch-width can be characterized by a minimal list of excluded minors, but unlike graphs, this list could be infinite in general. However, for each fixed finite field F, the list contains only finitely many F-representable matroids, due to the well-quasi-ordering of F-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)]. But this proof is non-constructive and does not provide any algorithm for computing these F-representable excluded minors in general. We consider the class of matroids of path-width at most k for fixed k. We prove that for a finite field F, every F-representable excluded minor for the class of matroids of path-width at most k has at most 2^{|𝔽|^{O(k²)}} elements. We can therefore compute, for any integer k and a fixed finite field F, the set of F-representable excluded minors for the class of matroids of path-width k, and this gives as a corollary a polynomial-time algorithm for checking whether the path-width of an F-represented matroid is at most k. We also prove that every excluded pivot-minor for the class of graphs having linear rank-width at most k has at most 2^{2^{O(k²)}} vertices, which also results in a similar algorithmic consequence for linear rank-width of graphs.
Cite as

Mamadou Moustapha Kanté, Eun Jung Kim, O-joung Kwon, and Sang-il Oum. Obstructions for Matroids of Path-Width at most k and Graphs of Linear Rank-Width at most k. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 40:1-40:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kante_et_al:LIPIcs.STACS.2022.40,
  author =	{Kant\'{e}, Mamadou Moustapha and Kim, Eun Jung and Kwon, O-joung and Oum, Sang-il},
  title =	{{Obstructions for Matroids of Path-Width at most k and Graphs of Linear Rank-Width at most k}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{40:1--40:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.40},
  URN =		{urn:nbn:de:0030-drops-158507},
  doi =		{10.4230/LIPIcs.STACS.2022.40},
  annote =	{Keywords: path-width, matroid, linear rank-width, graph, forbidden minor, vertex-minor, pivot-minor}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.64
A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth

Authors: Mamadou Moustapha Kanté, Christophe Paul, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels (represented by a graph) that is contaminated by some infectious substance and we are looking for a search strategy that, at each step, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneously occupied by searchers. It was proved that the minimum number of searchers required for a successful cleaning strategy is equal to the pathwidth of the graph plus one. Two desired characteristics for a cleaning strategy is to be monotone (no recontamination occurs) and connected (clean territories always remain connected). Under these two demands, the number of searchers is equivalent to a variant of pathwidth called connected pathwidth. We prove that connected pathwidth is fixed parameter tractable, in particular we design a 2^O(k²)⋅n time algorithm that checks whether the connected pathwidth of G is at most k. This resolves an open question by [Dereniowski, Osula, and Rzążewski, Finding small-width connected path-decompositions in polynomial time. Theor. Comput. Sci., 794:85–100, 2019]. For our algorithm, we enrich the typical sequence technique that is able to deal with the connectivity demand. Typical sequences have been introduced in [Bodlaender and Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358–402, 1996] for the design of linear parameterized algorithms for treewidth and pathwidth. While this technique has been later applied to other parameters, none of its advancements was able to deal with the connectivity demand, as it is a "global" demand that concerns an unbounded number of parts of the graph of unbounded size. The proposed extension is based on an encoding of the connectivity property that is quite versatile and may be adapted so to deliver linear parameterized algorithms for the connected variants of other width parameters as well. An immediate consequence of our result is a 2^O(k²)⋅n time algorithm for the monotone and connected version of the edge search number.
Cite as

Mamadou Moustapha Kanté, Christophe Paul, and Dimitrios M. Thilikos. A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kante_et_al:LIPIcs.ESA.2020.64,
  author =	{Kant\'{e}, Mamadou Moustapha and Paul, Christophe and Thilikos, Dimitrios M.},
  title =	{{A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.64},
  URN =		{urn:nbn:de:0030-drops-129307},
  doi =		{10.4230/LIPIcs.ESA.2020.64},
  annote =	{Keywords: Graph decompositions, Parameterized algorithms, Typical sequences, Pathwidth, Graph searching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.17
More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity Constraints

Authors: Benjamin Bergougnoux and Mamadou Moustapha Kanté

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. For all these problems, we obtain 2^O(k)* n^O(1), 2^O(k log(k))* n^O(1), 2^O(k^2) * n^O(1) and n^O(k) time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of the parameters and match asymptotically also the running time of the best algorithms for basic NP-hard problems such as Vertex Cover and Dominating Set. Our framework is based on the d-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013]. The results we obtain highlight the importance and the generalizing power of this equivalence relation on width measures. We also prove that this equivalence relation could be useful for Max Cut: a W[1]-hard problem parameterized by clique-width. For this latter problem, we obtain n^O(k), n^O(k) and n^(2^O(k)) time algorithm parameterized by clique-width, Q-rank-width and rank-width.
Cite as

Benjamin Bergougnoux and Mamadou Moustapha Kanté. More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity Constraints. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bergougnoux_et_al:LIPIcs.ESA.2019.17,
  author =	{Bergougnoux, Benjamin and Kant\'{e}, Mamadou Moustapha},
  title =	{{More Applications of the d-Neighbor Equivalence: Connectivity and Acyclicity Constraints}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.17},
  URN =		{urn:nbn:de:0030-drops-111383},
  doi =		{10.4230/LIPIcs.ESA.2019.17},
  annote =	{Keywords: connectivity problem, feedback vertex set, d-neighbor equivalence, \{sigma,rho\}-domination, clique-width, rank-width, mim-width}
}
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