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arXiv · 2109.14610

A Unifying Framework for Characterizing and Computing Width Measures

Eduard Eiben·Robert Ganian·Thekla Hamm·Lars Jaffke·O-Joung Kwon
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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 compute every possible F-branchwidth, providing a unifying framework that can efficiently obtain near-optimal tree-decompositions, k-expressions, as well as optimal mim-width decompositions.

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Eduard Eiben, Robert Ganian, Thekla Hamm, Lars Jaffke, O-Joung Kwon. 2021-09-28. A Unifying Framework for Characterizing and Computing Width Measures. https://arxiv.org/abs/2109.14610

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