Document Open Access Logo

Pathfinding in Self-Deleting Graphs

Authors Michal Dvořák , Dušan Knop , Michal Opler , Jan Pokorný , Ondřej Suchý , Krisztina Szilágyi

PDF

File

Thumbnail PDF
PDF
LIPIcs.ISAAC.2025.28.pdf
  • Filesize: 0.86 MB
  • 15 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized complexity
  • self-deleting graphs
  • pathfinding

Metrics

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

Abstract

In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we study self-deleting graphs, introduced by Carmesin et al. [Sarah Carmesin et al., 2023], which consist of a graph G = (V, E) and a function f: V → 2^E, where f(v) is the set of edges that will be deleted after visiting the vertex v. In the (Shortest) Self-Deleting s-t-path problem we are given a self-deleting graph and its vertices s and t, and we are asked to find a (shortest) path from s to t, such that it does not traverse an edge in f(v) after visiting v for any vertex v.
We prove that Self-Deleting s-t-path is NP-hard even if the given graph is outerplanar, bipartite, has maximum degree 3, bandwidth 2 and |f(v)| ≤ 1 for each vertex v. We show that Shortest Self-Deleting s-t-path is W[1]-complete parameterized by the length of the sought path and that Self-Deleting s-t-path is W[1]-complete parameterized by the vertex cover number, feedback vertex set number and treedepth. We also show that the problem becomes FPT when we parameterize by the maximum size of f(v) and several structural parameters. Lastly, we show that the problem does not admit a polynomial kernel even for parameterization by the vertex cover number and the maximum size of f(v) combined already on 2-outerplanar graphs.

Cite As Get BibTex

Michal Dvořák, Dušan Knop, Michal Opler, Jan Pokorný, Ondřej Suchý, and Krisztina Szilágyi. Pathfinding in Self-Deleting Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.28

Author Details

Michal Dvořák
  • Czech Technical University, Prague, Czech Republic
Dušan Knop
  • Czech Technical University, Prague, Czech Republic
Michal Opler
  • Czech Technical University, Prague, Czech Republic
Jan Pokorný
  • Czech Technical University, Prague, Czech Republic
Ondřej Suchý
  • Czech Technical University, Prague, Czech Republic
Krisztina Szilágyi
  • Czech Technical University, Prague, Czech Republic

Funding

This work was co-funded by the European Union under the project Robotics and advanced industrial production (reg. no. CZ.02.01.01/00/22_008/0004590). Michal Dvořák and Jan Pokorný acknowledge the support of Grant Agency of the Czech Technical University in Prague, grant No. SGS23/205/OHK3/3T/18.

References

  1. Noga Alon, Raphael Yuster, and Uri Zwick. Color-coding. Journal of the Association for Computing Machinery, 42(4):844-856, July 1995. URL: https://doi.org/10.1145/210332.210337.
  2. J. Añez, T. De La Barra, and B. Pérez. Dual graph representation of transport networks. Transportation Research Part B: Methodological, 30(3):209-216, 1996. URL: https://doi.org/10.1016/0191-2615(95)00024-0.
  3. Hans L. Bodlaender, Bart M. P. Jansen, and Stefan Kratsch. Kernel bounds for path and cycle problems. Theoretical Computer Science, 511:117-136, 2013. URL: https://doi.org/10.1016/J.TCS.2012.09.006.
  4. Liming Cai and David W. Juedes. Subexponential parameterized algorithms collapse the W-hierarchy. In Fernando Orejas, Paul G. Spirakis, and Jan van Leeuwen, editors, Automata, Languages and Programming, 28th International Colloquium, ICALP 2001, Crete, Greece, July 8-12, 2001, Proceedings, volume 2076 of Lecture Notes in Computer Science, pages 273-284. Springer, 2001. URL: https://doi.org/10.1007/3-540-48224-5_23.
  5. Sarah Carmesin, David Woller, David Parker, Miroslav Kulich, and Masoumeh Mansouri. The Hamiltonian cycle and travelling salesperson problems with traversal-dependent edge deletion. Journal of Computer Science, 74:102156, 2023. URL: https://doi.org/10.1016/J.JOCS.2023.102156.
  6. Raffaele Cerulli, Francesca Guerriero, Edoardo Scalzo, and Carmine Sorgente. Shortest paths with exclusive-disjunction arc pairs conflicts. Computers & Operations Research, 152:106158, 2023. URL: https://doi.org/10.1016/J.COR.2023.106158.
  7. Jianer Chen, Xiuzhen Huang, Iyad A. Kanj, and Ge Xia. Linear FPT reductions and computational lower bounds. In László Babai, editor, Proceedings of the 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, June 13-16, 2004, pages 212-221. ACM, 2004. URL: https://doi.org/10.1145/1007352.1007391.
  8. Jianer Chen, Xiuzhen Huang, Iyad A. Kanj, and Ge Xia. Strong computational lower bounds via parameterized complexity. Journal of Computer and System Sciences, 72(8):1346-1367, 2006. URL: https://doi.org/10.1016/J.JCSS.2006.04.007.
  9. Ting Chen, Ming-Yang Kao, Matthew Tepel, John Rush, and George M. Church. A dynamic programming approach to de novo peptide sequencing via tandem mass spectrometry. Journal of Computational Biology, 8(3):325-337, 2001. URL: https://doi.org/10.1089/10665270152530872.
  10. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. Google Scholar
  11. Reinhard Diestel. Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics. Springer, 2012. Google Scholar
  12. Michal Dvořák, Dušan Knop, Michal Opler, Jan Pokorný, Ondřej Suchý, and Krisztina Szilágyi. Density of traceable graphs, 2025. URL: https://arxiv.org/abs/2506.22269.
  13. Harold N. Gabow, Shachindra N. Maheswari, and Leon J. Osterweil. On two problems in the generation of program test paths. IEEE Transactions on Software Engineering, 2(3):227-231, 1976. URL: https://doi.org/10.1109/TSE.1976.233819.
  14. Russell Impagliazzo and Ramamohan Paturi. On the complexity of k-SAT. Journal of Computer and System Sciences, 62(2):367-375, 2001. URL: https://doi.org/10.1006/JCSS.2000.1727.
  15. Russell Impagliazzo, Ramamohan Paturi, and Francis Zane. Which problems have strongly exponential complexity? Journal of Computer and System Sciences, 63(4):512-530, 2001. URL: https://doi.org/10.1006/JCSS.2001.1774.
  16. Ronald F. Kirby and Renfrey B. Potts. The minimum route problem for networks with turn penalties and prohibitions. Transportation Research, 3(3):397-408, 1969. URL: https://doi.org/10.1016/S0041-1647(69)80022-5.
  17. Petr Kolman and Ondřej Pangrác. On the complexity of paths avoiding forbidden pairs. Discrete Applied Mathematics, 157(13):2871-2876, 2009. URL: https://doi.org/10.1016/J.DAM.2009.03.018.
  18. Jakub Kováč. Complexity of the path avoiding forbidden pairs problem revisited. Discrete Applied Mathematics, 161(10):1506-1512, 2013. URL: https://doi.org/10.1016/j.dam.2012.12.022.
  19. K. Krause, R. Smith, and M. Goodwin. Optimal software test planning through automated network analysis. In Proceedings of the IEEE Symposium on Computer Software Reliability, pages 18-22, 1973. Google Scholar
  20. Stefan Szeider. Finding paths in graphs avoiding forbidden transitions. Discrete Applied Mathematics, 126(2):261-273, 2003. URL: https://doi.org/10.1016/S0166-218X(02)00251-2.
  21. Piotr Wojciechowski, K. Subramani, and Alvaro Velasquez. Reachability in choice networks. Discrete Optimization, 48:100761, 2023. URL: https://doi.org/10.1016/j.disopt.2023.100761.
  22. Piotr Wojciechowski, M. Williamson, and K. Subramani. On the analysis of optimization problems in arc-dependent networks. Discrete Optimization, 45:100729, 2022. URL: https://doi.org/10.1016/j.disopt.2022.100729.
  23. Huanhuan Wu, James Cheng, Yiping Ke, Silu Huang, Yuzhen Huang, and Hejun Wu. Efficient algorithms for temporal path computation. IEEE Transactions on Knowledge and Data Engineering, 28(11):2927-2942, 2016. URL: https://doi.org/10.1109/TKDE.2016.2594065.
  24. Hananya Yinnone. On paths avoiding forbidden pairs of vertices in a graph. Discrete Applied Mathematics, 74(1):85-92, 1997. URL: https://doi.org/10.1016/S0166-218X(96)00017-0.
  25. Athanasios K. Ziliaskopoulos and Hani S. Mahmassani. A note on least time path computation considering delays and prohibitions for intersection movements. Transportation Research Part B: Methodological, 30(5):359-367, 1996. URL: https://doi.org/10.1016/0191-2615(96)00001-X.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

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