A Unifying Framework for Characterizing and Computing Width Measures

Authors Eduard Eiben , Robert Ganian , Thekla Hamm , Lars Jaffke , O-joung Kwon



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Author Details

Eduard Eiben
  • Department of Computer Science, Royal Holloway, University of London, Egham, UK
Robert Ganian
  • Algorithms and Complexity Group, TU Wien, Austria
Thekla Hamm
  • Algorithms and Complexity Group, TU Wien, Austria
Lars Jaffke
  • Department of Informatics, University of Bergen, Norway
O-joung Kwon
  • Department of Mathematics, Incheon National University, South Korea
  • Discrete Mathematics Group, Institute for Basic Science, Daejeon, South Korea

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Eduard Eiben, Robert Ganian, Thekla Hamm, Lars Jaffke, and O-joung Kwon. A Unifying Framework for Characterizing and Computing Width Measures. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 63:1-63:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITCS.2022.63

Abstract

Algorithms for computing or approximating optimal decompositions for decompositional parameters such as treewidth or clique-width have so far traditionally been tailored to specific width parameters. Moreover, for mim-width, no efficient algorithms for computing good decompositions were known, even under highly restrictive parameterizations. In this work we identify ℱ-branchwidth as a class of generic decompositional parameters that can capture mim-width, treewidth, clique-width as well as other measures. We show that while there is an infinite number of ℱ-branchwidth parameters, only a handful of these are asymptotically distinct. We then develop fixed-parameter and kernelization algorithms (under several structural parameterizations) that can approximate every possible ℱ-branchwidth, providing a unifying parameterized framework that can efficiently obtain near-optimal tree-decompositions, k-expressions, as well as optimal mim-width decompositions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • branchwidth
  • parameterized algorithms
  • mim-width
  • treewidth
  • clique-width

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