Abstract
Twin-width is a structural width parameter and matrix invariant introduced by Bonnet et al. [FOCS 2020], that has been gaining attention due to its various fields of applications. In this paper, inspired by the SAT approach of Schidler and Szeider [ALENEX 2022], we provide a new SAT encoding for computing twin-width. The encoding aims to encode the contraction sequence as a binary tree. The asymptotic size of the formula under our encoding is smaller than in the state-of-the-art relative encoding of Schidler and Szeider. We also conduct an experimental study, comparing the performance of the new encoding and the relative encoding.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
PACE stands for Parameterized Algorithms and Computational Experiments; the challenge is dedicated to bringing the gap between theoretical and practical parameterized algorithms. The official website of the challenge is https://pacechallenge.org/2023/.
- 2.
- 3.
All instances are available at https://pacechallenge.org/2023/.
References
Balabán, J., Hliněný, P.: Twin-width is linear in the Poset width. In: Golovach, P.A., Zehavi, M. (eds.) 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), vol. 214, pp. 6:1–6:13. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl (2021). https://doi.org/10.4230/LIPIcs.IPEC.2021.6
Bergé, P., Bonnet, É., Déprés, H.: Deciding twin-width at most 4 is np-complete. In: Bojanczyk, M., Merelli, E., Woodruff, D.P. (eds.) 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, 4–8 July 2022, Paris. LIPIcs, vol. 229, pp. 18:1–18:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPIcs.ICALP.2022.18
Bonnet, E., Déprés, H.: Twin-width can be exponential in treewidth. J. Comb. Theory Ser. B 161(C), 1–14 (2023). https://doi.org/10.1016/j.jctb.2023.01.003
Bonnet, É., Geniet, C., Kim, E.J., Thomassé, S., Watrigant, R.: Twin-width II: small classes. In: Marx, D. (ed.) Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Virtual Conference, 10–13 January 2021, pp. 1977–1996. SIAM (2021). https://doi.org/10.1137/1.9781611976465.118
Bonnet, É., Geniet, C., Kim, E.J., Thomassé, S., Watrigant, R.: Twin-width III: max independent set, min dominating set, and coloring. In: Bansal, N., Merelli, E., Worrell, J. (eds.) 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, 12–16 July 2021, Glasgow (Virtual Conference). LIPIcs, vol. 198, pp. 35:1–35:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.ICALP.2021.35
Bonnet, E., Kim, E.J., Reinald, A., Thomassé, S., Watrigant, R.: Twin-width and polynomial kernels. In: Golovach, P.A., Zehavi, M. (eds.) 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), vol. 214, pp. 10:1–10:16. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, Dagstuhl (2021). https://doi.org/10.4230/LIPIcs.IPEC.2021.10
Bonnet, É., Kim, E.J., Thomassé, S., Watrigant, R.: Twin-width I: tractable FO model checking. J. ACM 69(1), 3:1–3:46 (2022). https://doi.org/10.1145/3486655
Ganian, R., Pokrývka, F., Schidler, A., Simonov, K., Szeider, S.: Weighted model counting with twin-width. In: Meel, K.S., Strichman, O. (eds.) 25th International Conference on Theory and Applications of Satisfiability Testing, SAT 2022, 2–5 August 2022, Haifa. LIPIcs, vol. 236, pp. 15:1–15:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPIcs.SAT.2022.15
Guillemot, S., Marx, D.: Finding small patterns in permutations in linear time. In: Chekuri, C. (ed.) Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, 5–7 January 2014, pp. 82–101. SIAM (2014). https://doi.org/10.1137/1.9781611973402.7
Jacob, H., Pilipczuk, M.: Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs. In: Bekos, M.A., Kaufmann, M. (eds.) Graph-Theoretic Concepts in Computer Science. WG 2022. LNCS, vol. 13453, pp. 287–299. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15914-5_21
Král, D., Lamaison, A.: Planar graph with twin-width seven. arXiv preprint arXiv:2209.11537 (2022)
Král’, D., Lamaison, A.: Planar graph with twin-width seven. Eur. J. Combinator. 103749 (2023). https://doi.org/10.1016/j.ejc.2023.103749
Marques-Silva, J., Lynce, I.: Towards robust CNF encodings of cardinality constraints. In: Bessiere, C. (ed.) Principles and Practice of Constraint Programming. CP 2007. LNCS, vol. 4741, pp. 483–497. Springer, Cham (2007). https://doi.org/10.1007/978-3-540-74970-7_35
Schidler, A., Szeider, S.: A SAT approach to twin-width. In: Phillips, C.A., Speckmann, B. (eds.) Proceedings of the Symposium on Algorithm Engineering and Experiments, ALENEX 2022, Alexandria, 9–10 January 2022, pp. 67–77. SIAM (2022). https://doi.org/10.1137/1.9781611977042.6
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Horev, Y. et al. (2024). A Contraction Tree SAT Encoding for Computing Twin-Width. In: Yang, DN., Xie, X., Tseng, V.S., Pei, J., Huang, JW., Lin, J.CW. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2024. Lecture Notes in Computer Science(), vol 14646. Springer, Singapore. https://doi.org/10.1007/978-981-97-2253-2_35
Download citation
DOI: https://doi.org/10.1007/978-981-97-2253-2_35
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-97-2252-5
Online ISBN: 978-981-97-2253-2
eBook Packages: Computer ScienceComputer Science (R0)