Document Open Access Logo

On the Complexity of Minimising the Moving Distance for Dispersing Objects

Authors Nicolás Honorato-Droguett , Kazuhiro Kurita , Tesshu Hanaka , Hirotaka Ono

PDF

File

Thumbnail PDF
PDF
LIPIcs.WADS.2025.36.pdf
  • Filesize: 1.11 MB
  • 14 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
Keywords
  • Intersection graphs
  • Optimisation
  • Graph modification

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an O(n log n)-time algorithm that minimises the total moving distance to disperse unit intervals. This algorithm is applied to render a given unit interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. We next show that GGED becomes strongly NP-hard when rendering a weighted interval graph (i) edgeless, (ii) acyclic and (iii) k-clique-free. Lastly, we prove that minimising the maximum moving distance for rendering a unit disk graph edgeless is strongly NP-hard over the L₁ and L₂ distances.

Cite As Get BibTex

Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. On the Complexity of Minimising the Moving Distance for Dispersing Objects. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.36

Author Details

Nicolás Honorato-Droguett
  • Nagoya University, Japan
Kazuhiro Kurita
  • Nagoya University, Japan
Tesshu Hanaka
  • Kyushu University, Fukuoka, Japan
Hirotaka Ono
  • Nagoya University, Japan

Funding

  • Kurita, Kazuhiro: This work is partially supported by JSPS KAKENHI Grant Numbers JP21K17812, JP22H03549, and JST ACT-X Grant Number JPMJAX2105.
  • Hanaka, Tesshu: This work is partially supported by JSPS KAKENHI Grant Numbers JP21K17707, JP23H04388, JST CRONOS Grant Number JPMJCS24K2.
  • Ono, Hirotaka: This work is partially supported by JSPS KAKENHI Grant Numbers JP20H05967, JP21K19765, JP22H00513, JST CRONOS Grant Number JPMJCS24K2.

References

  1. Stephen P. Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004. URL: https://doi.org/10.1017/cbo9780511804441.
  2. Pablo Burzyn, Flavia Bonomo, and Guillermo Durán. NP-completeness results for edge modification problems. Discrete Applied Mathematics, 154(13):1824-1844, 2006. URL: https://doi.org/10.1016/j.dam.2006.03.031.
  3. Fan R. K. Chung and David Mumford. Chordal Completions of Planar Graphs. J. Comb. Theory Ser. B, 62(1):96-106, 1994. URL: https://doi.org/10.1006/jctb.1994.1056.
  4. Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, 3rd Edition. MIT Press, 2009. Google Scholar
  5. Christophe Crespelle, Pål Grønås Drange, Fedor V. Fomin, and Petr A. Golovach. A survey of parameterized algorithms and the complexity of edge modification. Computer Science Review, 48:100556, 2023. URL: https://doi.org/10.1016/j.cosrev.2023.100556.
  6. Mark de Berg, Sándor Kisfaludi-Bak, and Gerhard J. Woeginger. The complexity of dominating set in geometric intersection graphs. Theoretical Computer Science, 769:18-31, 2019. URL: https://doi.org/10.1016/j.tcs.2018.10.007.
  7. Reinhard Diestel. Graph Theory, 5th Edition. Graduate texts in mathematics. Springer, Berlin, Germany, 2017. URL: https://doi.org/10.1007/978-3-662-53622-3.
  8. Pål Grønås Drange. Parameterized Graph Modification Algorithms. PhD thesis, The University of Bergen, 2015. URL: https://bora.uib.no/bora-xmlui/handle/1956/10774.
  9. Jirí Fiala, Jan Kratochvíl, and Andrzej Proskurowski. Systems of distant representatives. Discrete Applied Mathematics, 145(2):306-316, 2005. URL: https://doi.org/10.1016/j.dam.2004.02.018.
  10. Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Kernelization for spreading points. In ESA 2023, volume 274 of LIPIcs, pages 48:1-48:16, 2023. URL: https://doi.org/10.4230/LIPICS.ESA.2023.48.
  11. Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Parameterized geometric graph modification with disk scaling. In ITCS 2025, volume 325 of LIPIcs, pages 51:1-51:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. URL: https://doi.org/10.4230/LIPICS.ITCS.2025.51.
  12. Fedor V. Fomin, Saket Saurabh, and Neeldhara Misra. Graph modification problems: A modern perspective. In Frontiers in Algorithmics, pages 3-6. Springer International Publishing, 2015. URL: https://doi.org/10.1007/978-3-319-19647-3_1.
  13. M. R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979. Google Scholar
  14. Marc Hellmuth, Manuela Geiß, and Peter F. Stadler. Complexity of modification problems for reciprocal best match graphs. Theoretical Computer Science, 809:384-393, 2020. URL: https://doi.org/10.1016/j.tcs.2019.12.033.
  15. Hung P. Hoang, Stefan Lendl, and Lasse Wulf. Assistance and interdiction problems on interval graphs. Discrete Applied Mathematics, 340:153-170, 2023. URL: https://doi.org/10.1016/j.dam.2023.06.046.
  16. Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. Algorithms for optimally shifting intervals under intersection graph models. In IJTCS-FAW 2024, volume 14752, pages 66-78. Springer, 2024. URL: https://doi.org/10.1007/978-981-97-7752-5_5.
  17. Nicolás Honorato-Droguett, Kazuhiro Kurita, Tesshu Hanaka, and Hirotaka Ono. On the complexity of minimising the moving distance for dispersing objects, 2025. URL: https://doi.org/10.48550/arXiv.2502.12903.
  18. Donald E. Knuth and Arvind Raghunathan. The problem of compatible representatives. SIAM Journal on Discrete Mathematics, 5(3):422-427, 1992. URL: https://doi.org/10.1137/0405033.
  19. John M. Lewis and Mihalis Yannakakis. The node-deletion problem for hereditary properties is NP-Complete. Journal of Computer and System Sciences, 20(2):219-230, 1980. URL: https://doi.org/10.1016/0022-0000(80)90060-4.
  20. Heng Li and Richard Durbin. Fast and accurate short read alignment with burrows–wheeler transform. Bioinformatics, 25(14):1754-1760, 2009. URL: https://doi.org/10.1093/bioinformatics/btp324.
  21. David Lichtenstein. Planar formulae and their uses. SIAM Journal on Computing, 11(2):329-343, 1982. URL: https://doi.org/10.1137/0211025.
  22. Terry A. McKee and F. R. McMorris. Topics in Intersection Graph Theory. Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, 1999. URL: https://doi.org/10.1137/1.9780898719802.
  23. Fahad Panolan, Saket Saurabh, and Meirav Zehavi. Contraction decomposition in unit disk graphs and algorithmic applications in parameterized complexity. ACM Trans. Algorithms, 20(2):15, 2024. URL: https://doi.org/10.1145/3648594.
  24. Franco P. Preparata and Michael Ian Shamos. Computational Geometry - An Introduction. Texts and Monographs in Computer Science. Springer, 1985. URL: https://doi.org/10.1007/978-1-4612-1098-6.
  25. R. Sritharan. Graph modification problem for some classes of graphs. Journal of Discrete Algorithms, 38-41:32-37, 2016. URL: https://doi.org/10.1016/j.jda.2016.06.003.
  26. Craig A. Tovey. A simplified NP-complete satisfiability problem. Discrete Applied Mathematics, 8(1):85-89, 1984. URL: https://doi.org/10.1016/0166-218x(84)90081-7.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact