Mim-Width is paraNP-complete

January 10, 2025 · The Ethereal · 🏛 International Colloquium on Automata, Languages and Programming

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Authors Benjamin Bergougnoux, Édouard Bonnet, Julien Duron arXiv ID 2501.05638 Category cs.CC: Computational Complexity Cross-listed cs.DM, cs.DS, math.CO Citations 3 Venue International Colloquium on Automata, Languages and Programming Last Checked 2 months ago
Abstract
We show that it is NP-hard to distinguish graphs of linear mim-width at most 1211 from graphs of sim-width at least 1216. This implies that Mim-Width, Sim-Width, One-Sided Mim-Width, and their linear counterparts are all paraNP-complete, i.e., NP-complete to compute even when upper bounded by a constant.
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