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Computing Twin-Width Parameterized by the Feedback Edge Number

Authors Jakub Balabán , Robert Ganian , Mathis Rocton

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LIPIcs.STACS.2024.7.pdf
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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • twin-width
  • parameterized complexity
  • kernelization
  • feedback edge number

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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.

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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) https://doi.org/10.4230/LIPIcs.STACS.2024.7

Author Details

Jakub Balabán
  • Faculty of Informatics, Masaryk University, Brno, Czech Republic
Robert Ganian
  • Algorithms and Complexity Group, TU Wien, Austria
Mathis Rocton
  • Algorithms and Complexity Group, TU Wien, Austria

Funding

  • Ganian, Robert: Robert Ganian acknowledges support by the FWF and WWTF Science Funds (FWF project Y1329 and WWTF project ICT22-029).
  • Rocton, Mathis: Mathis Rocton acknowledges support by the European Union’s Horizon 2020 research and innovation COFUND programme (LogiCS@TUWien, grant agreement No 101034440), and the FWF Science Fund (FWF project Y1329).

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