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arXiv · 2110.06146

A SAT Approach to Twin-Width

André Schidler·Stefan Szeider
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Abstract

The graph invariant twin-width was recently introduced by Bonnet, Kim, Thomass\'e, and Watrigan. Problems expressible in first-order logic, which includes many prominent NP-hard problems, are tractable on graphs of bounded twin-width if a certificate for the twin-width bound is provided as an input. Computing such a certificate, however, is an intrinsic problem, for which no nontrivial algorithm is known. In this paper, we propose the first practical approach for computing the twin-width of graphs together with the corresponding certificate. We propose efficient SAT-encodings that rely on a characterization of twin-width based on elimination sequences. This allows us to determine the twin-width of many famous graphs with previously unknown twin-width. We utilize our encodings to identify the smallest graphs for a given twin-width bound $d \in \{1,\dots,4\}$.

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André Schidler, Stefan Szeider. 2021-10-12. A SAT Approach to Twin-Width. https://arxiv.org/abs/2110.06146

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