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Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces

Authors Florestan Brunck , Hsien-Chih Chang , Maarten Löffler , Tim Ophelders , Lena Schlipf

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Fixed parameter tractability
Keywords
  • Curve Arrangements
  • Reconfiguration
  • Curve Arrangements
  • NP-hardness
  • Fixed-Parameter Tractability
  • Puzzle Generation

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Abstract

We study reconfiguration in curve arrangements, where a subset of the crossings are marked as switches which have three possible states, and the goal is to set the switches such that the resulting curve arrangement has few self-intersections, or few faces that are incident to the same curve multiple times (a.k.a. popular faces). Our results are that these problems are NP-hard, but FPT in the number of switches. Minimizing self-intersections is also FPT in the number of non-switchable crossings; for minimizing popular faces this problem remains open. Our results can be applied to generating curved nonograms, a type of logic puzzle that has received some attention lately. Specifically, our results make it possible to efficiently convert expert puzzles into advanced puzzles (or determine that this is impossible).

Cite As Get BibTex

Florestan Brunck, Hsien-Chih Chang, Maarten Löffler, Tim Ophelders, and Lena Schlipf. Reconfiguration in Curve Arrangements to Reduce Self-Intersections and Popular Faces. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.36

Author Details

Florestan Brunck
  • University of Copenhagen, Denmark
Hsien-Chih Chang
  • Dartmouth College, Hanover, NH, USA
Maarten Löffler
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
  • Department of Computer Science, Tulane University, New Orleans, LA, USA
Tim Ophelders
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Lena Schlipf
  • AI Center, Department of Computer Science, University of Tübingen, Germany

Funding

  • Ophelders, Tim: Partially supported by the Dutch Research Council (NWO) under project no. VI.Veni.212.260.

References

  1. Kees Batenburg and Walter Kosters. On the difficulty of nonograms. ICGA journal, 35:195-205, December 2012. URL: https://doi.org/10.3233/ICG-2012-35402.
  2. David Callan. A combinatorial survey of identities for the double factorial. https://arxiv.org/abs/0906.1317, 2009.
  3. Yen-Chi Chen and Shun-Shii Lin. A fast nonogram solver that won the TAAI 2017 and ICGA 2018 tournaments. ICGA Journal, 41(1):2-14, 2019. URL: https://doi.org/10.3233/ICG-190097.
  4. Phoebe de Nooijer. Resolving popular faces in curve arrangements. Master’s thesis, Utrecht University, 2022. URL: https://studenttheses.uu.nl/handle/20.500.12932/494.
  5. Phoebe de Nooijer, Soeren Nickel, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. Removing popular faces in curve arrangements. In Proc. 31st International Symposium on Graph Drawing, 2023. Google Scholar
  6. Phoebe de Nooijer, Soeren Terziadis, Alexandra Weinberger, Zuzana Masárová, Tamara Mchedlidze, Maarten Löffler, and Günter Rote. Removing popular faces in curve arrangements. Journal of Graph Algorithms and Applications, 28(2):47-82, November 2024. URL: https://doi.org/10.7155/jgaa.v28i2.2988.
  7. Cole A. Giller. A family of links and the Conway calculus. Transactions of the American Mathematical Society, 270(1):75-109, 1982. Google Scholar
  8. Jim Hoste. The Arf invariant of a totally proper link. Topology and its Applications, 18(2–3):163-177, 1984. Google Scholar
  9. Vaughan F. R. Jones. On knot invariants related to some statistical mechanical models. Pacific journal of mathematics, 137(2):311-334, 1989. Google Scholar
  10. Louis H. Kauffman. State models and the Jones polynomial. Topology, 26(3):395-407, 1987. Google Scholar
  11. Louis H. Kauffman. Gauss codes, quantum groups and ribbon Hopf algebras. Reviews in Mathematical Physics, 5(4):735-773, 1993. Google Scholar
  12. Maarten Löffler, Günter Rote, Soeren Terziadis, and Alexandra Weinberger. On solving simple curved nonograms. In Proc. 36th International Workshop on Combinatorial Algorithms (IWOCA 2025), 2025. Google Scholar
  13. Neil Robertson and Paul D. Seymour. Disjoint paths—a survey. SIAM Journal on Algebraic Discrete Methods, 6(2):300-305, 1985. URL: https://doi.org/10.1137/0606030.
  14. Alexander Schrijver. On the uniqueness of kernels. Journal of Combinatorial Theory, Series B, 55(1):146-160, May 1992. URL: https://doi.org/10.1016/0095-8956(92)90038-Y.
  15. Nobuhisa Ueda and Tadaaki Nagao. NP-completeness results for NONOGRAM via parsimonious reductions. Technical Report TR96-0008, Department of Computer Science, Tokyo Institute of Technology, 1996. CiteSeerX 10.1.1.57.5277, URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.5277.
  16. Mees van de Kerkhof, Tim de Jong, Raphael Parment, Maarten Löffler, Amir Vaxman, and Marc J. van Kreveld. Design and automated generation of Japanese picture puzzles. Comput. Graph. Forum, 38(2):343-353, 2019. URL: https://doi.org/10.1111/cgf.13642.
  17. Jan van Rijn. Playing games: The complexity of Klondike, Mahjong, nonograms and animal chess. Master’s thesis, Leiden Institute of Advanced Computer Science, Leiden University, 2012. Google Scholar
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