Mim-Width is paraNP-complete
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912182349856768 |
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| author | Bergougnoux, Benjamin Bonnet, Édouard Duron, Julien |
| author_facet | Bergougnoux, Benjamin Bonnet, Édouard Duron, Julien |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_05638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mim-Width is paraNP-complete Bergougnoux, Benjamin Bonnet, Édouard Duron, Julien Computational Complexity Discrete Mathematics Data Structures and Algorithms Combinatorics 68Q27 F.2.2 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. |
| title | Mim-Width is paraNP-complete |
| topic | Computational Complexity Discrete Mathematics Data Structures and Algorithms Combinatorics 68Q27 F.2.2 |
| url | https://arxiv.org/abs/2501.05638 |