2 Search Results for "Balabán, Jakub"

Document
DOI: 10.4230/LIPIcs.STACS.2024.7
Computing Twin-Width Parameterized by the Feedback Edge Number

Authors: Jakub Balabán, Robert Ganian, and Mathis Rocton

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

Abstract
The problem of whether and how one can compute the twin-width of a graph - along with an accompanying contraction sequence - lies at the forefront of the area of algorithmic model theory. While significant effort has been aimed at obtaining a fixed-parameter approximation for the problem when parameterized by twin-width, here we approach the question from a different perspective and consider whether one can obtain (near-)optimal contraction sequences under a larger parameterization, notably the feedback edge number k. As our main contributions, under this parameterization we obtain (1) a linear bikernel for the problem of either computing a 2-contraction sequence or determining that none exists and (2) an approximate fixed-parameter algorithm which computes an 𝓁-contraction sequence (for an arbitrary specified 𝓁) or determines that the twin-width of the input graph is at least 𝓁. These algorithmic results rely on newly obtained insights into the structure of optimal contraction sequences, and as a byproduct of these we also slightly tighten the bound on the twin-width of graphs with small feedback edge number.
Cite as

Jakub Balabán, Robert Ganian, and Mathis Rocton. Computing Twin-Width Parameterized by the Feedback Edge Number. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{balaban_et_al:LIPIcs.STACS.2024.7,
  author =	{Balab\'{a}n, Jakub and Ganian, Robert and Rocton, Mathis},
  title =	{{Computing Twin-Width Parameterized by the Feedback Edge Number}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{7:1--7:19},
  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.2024.7},
  URN =		{urn:nbn:de:0030-drops-197170},
  doi =		{10.4230/LIPIcs.STACS.2024.7},
  annote =	{Keywords: twin-width, parameterized complexity, kernelization, feedback edge number}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2021.6
Twin-Width Is Linear in the Poset Width

Authors: Jakub Balabán and Petr Hliněný

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

Abstract
Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced just very recently, in 2020 by Bonnet, Kim, Thomassé and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result, they also claimed that posets of bounded width have bounded twin-width, thus capturing prior result on FO model checking of posets of bounded width in FPT. However, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. We prove that posets of width d have twin-width at most 8d with a direct and elementary argument, and show that this bound is tight up to a constant factor. Specifically, for posets of width 2 we prove that in the worst case their twin-width is also equal 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset.
Cite as

Jakub Balabán and Petr Hliněný. Twin-Width Is Linear in the Poset Width. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balaban_et_al:LIPIcs.IPEC.2021.6,
  author =	{Balab\'{a}n, Jakub and Hlin\v{e}n\'{y}, Petr},
  title =	{{Twin-Width Is Linear in the Poset Width}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{6:1--6:13},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.6},
  URN =		{urn:nbn:de:0030-drops-153895},
  doi =		{10.4230/LIPIcs.IPEC.2021.6},
  annote =	{Keywords: twin-width, digraph, poset, FO model checking, contraction sequence}
}
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