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On the Complexity of Temporal Arborescence Reconfiguration

Authors Riccardo Dondi , Manuel Lafond

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Riccardo Dondi
  • Università degli Studi di Bergamo, Italy
Manuel Lafond
  • Université de Sherbrooke, Canada

Acknowledgements

The authors thank the anonymous reviewers for their comments on the paper. The authors also thank Shun-ichi Maezawa for introducing the problem to the authors.

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Riccardo Dondi and Manuel Lafond. On the Complexity of Temporal Arborescence Reconfiguration. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAND.2024.10

Abstract

We analyze the complexity of Arborescence Reconfiguration on temporal digraphs (Temporal Arborescence Reconfiguration). The problem, given two temporal arborescences in a temporal digraph, asks for the minimum number of arc flips, i.e. arc exchanges, that result in a sequence of temporal arborescences that transforms one into the other. We analyze the complexity of the problem, taking into account also its approximation and parameterized complexity, even in restricted cases. First, we solve an open problem showing that Temporal Arborescence Reconfiguration is NP-hard for two timestamps. Then we show that even if the two temporal arborescences differ only by two arcs, then the problem is not approximable within factor bln|V(D)|, for any constant 0 < b < 1, where V(D) is the set of vertices of the temporal arborescences. Finally, we prove that Temporal Arborescence Reconfiguration is W[1]-hard when parameterized by the number of arc flips needed to transform one temporal arborescence into the other.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph theory
Keywords
  • Arborescence
  • Temporal Graphs
  • Graph Algorithms
  • Parameterized Complexity
  • Approximation Complexity

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References

  1. Eleni C. Akrida, George B. Mertzios, Paul G. Spirakis, and Christoforos L. Raptopoulos. The temporal explorer who returns to the base. J. Comput. Syst. Sci., 120:179-193, 2021. URL: https://doi.org/10.1016/j.jcss.2021.04.001.
  2. Noga Alon, Dana Moshkovitz, and Shmuel Safra. Algorithmic construction of sets for k-restrictions. ACM Trans. Algorithms, 2(2):153-177, 2006. URL: https://doi.org/10.1145/1150334.1150336.
  3. Marco Amoruso, Daniele Anello, Vincenzo Auletta, Raffaele Cerulli, Diodato Ferraioli, and Andrea Raiconi. Contrasting the spread of misinformation in online social networks. J. Artif. Intell. Res., 69:847-879, 2020. URL: https://doi.org/10.1613/JAIR.1.11509.
  4. Daniela Bubboloni, Costanza Catalano, Andrea Marino, and Ana Silva. On computing optimal temporal branchings. In Henning Fernau and Klaus Jansen, editors, Fundamentals of Computation Theory - 24th International Symposium, FCT 2023, Trier, Germany, September 18-21, 2023, Proceedings, volume 14292 of Lecture Notes in Computer Science, pages 103-117. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-43587-4_8.
  5. Irit Dinur and David Steurer. Analytical approach to parallel repetition. In David B. Shmoys, editor, Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 624-633. ACM, 2014. URL: https://doi.org/10.1145/2591796.2591884.
  6. Michael R. Fellows, Danny Hermelin, Frances A. Rosamond, and Stéphane Vialette. On the parameterized complexity of multiple-interval graph problems. Theor. Comput. Sci., 410(1):53-61, 2009. URL: https://doi.org/10.1016/J.TCS.2008.09.065.
  7. Guillaume Fertin, Julien Fradin, and Géraldine Jean. The maximum colorful arborescence problem: How (computationally) hard can it be? Theoretical Computer Science, 852:104-120, 2021. Google Scholar
  8. Ziyun Guang, Matthew Smith-Erb, and Layla Oesper. A weighted distance-based approach for deriving consensus tumor evolutionary trees. Journal Title Here, pages 1-9, 2023. Google Scholar
  9. Petter Holme. Modern temporal network theory: a colloquium. The European Physical Journal B, 88(9):234, 2015. Google Scholar
  10. Petter Holme and Jari Saramäki. A map of approaches to temporal networks. In Temporal Network Theory, pages 1-24. Springer, 2019. Google Scholar
  11. Silu Huang, Ada Wai-Chee Fu, and Ruifeng Liu. Minimum spanning trees in temporal graphs. In Timos K. Sellis, Susan B. Davidson, and Zachary G. Ives, editors, Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, Melbourne, Victoria, Australia, May 31 - June 4, 2015, pages 419-430. ACM, 2015. URL: https://doi.org/10.1145/2723372.2723717.
  12. Takehiro Ito, Erik D. Demaine, Nicholas J. A. Harvey, Christos H. Papadimitriou, Martha Sideri, Ryuhei Uehara, and Yushi Uno. On the complexity of reconfiguration problems. Theor. Comput. Sci., 412(12-14):1054-1065, 2011. URL: https://doi.org/10.1016/J.TCS.2010.12.005.
  13. Takehiro Ito, Yuni Iwamasa, Naoyuki Kamiyama, Yasuaki Kobayashi, Yusuke Kobayashi, Shun-ichi Maezawa, and Akira Suzuki. Reconfiguration of time-respecting arborescences. In Pat Morin and Subhash Suri, editors, Algorithms and Data Structures - 18th International Symposium, WADS 2023, Montreal, QC, Canada, July 31 - August 2, 2023, Proceedings, volume 14079 of Lecture Notes in Computer Science, pages 521-532. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-38906-1_34.
  14. Takehiro Ito, Yuni Iwamasa, Yasuaki Kobayashi, Yu Nakahata, Yota Otachi, and Kunihiro Wasa. Reconfiguring (non-spanning) arborescences. Theor. Comput. Sci., 943:131-141, 2023. URL: https://doi.org/10.1016/J.TCS.2022.12.007.
  15. Naoyuki Kamiyama and Yasushi Kawase. On packing arborescences in temporal networks. Inf. Process. Lett., 115(2):321-325, 2015. URL: https://doi.org/10.1016/J.IPL.2014.10.005.
  16. Richard M. Karp. Reducibility among combinatorial problems. In Raymond E. Miller and James W. Thatcher, editors, Proceedings of a symposium on the Complexity of Computer Computations, held March 20-22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972. URL: https://doi.org/10.1007/978-1-4684-2001-2_9.
  17. David Kempe, Jon M. Kleinberg, and Amit Kumar. Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci., 64(4):820-842, 2002. URL: https://doi.org/10.1006/jcss.2002.1829.
  18. Ning Li and Jennifer C. Hou. Topology control in heterogeneous wireless networks: Problems and solutions. In Proceedings IEEE INFOCOM 2004, The 23rd Annual Joint Conference of the IEEE Computer and Communications Societies, Hong Kong, China, March 7-11, 2004. IEEE, 2004. URL: https://doi.org/10.1109/INFCOM.2004.1354497.
  19. Othon Michail. An introduction to temporal graphs: An algorithmic perspective. Internet Math., 12(4):239-280, 2016. URL: https://doi.org/10.1080/15427951.2016.1177801.
  20. Dana Moshkovitz. The projection games conjecture and the np-hardness of ln n-approximating set-cover. Theory Comput., 11:221-235, 2015. URL: https://doi.org/10.4086/TOC.2015.V011A007.
  21. Naomi Nishimura. Introduction to reconfiguration. Algorithms, 11(4):52, 2018. URL: https://doi.org/10.3390/A11040052.
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