Document Open Access Logo

A Simple Dynamic Spanner via APSP

Authors Rasmus Kyng , Simon Meierhans , Gernot Zöcklein

PDF HTML 5

Files

Thumbnail PDF
PDF
LIPIcs.ICALP.2025.111.pdf
  • Filesize: 0.78 MB
  • 11 pages
HTML5 Logo HTML (experimental)
LIPIcs.ICALP.2025.111.html

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Theory of computation → Sparsification and spanners
Keywords
  • Dynamic graph algorithms
  • Spanner
  • Dynamic Greedy Spanner

Metrics

Abstract

We give a simple algorithm for maintaining a n^{o(1)}-approximate spanner H of a graph G with n vertices as G receives edge updates by reduction to the dynamic All-Pairs Shortest Paths (APSP) problem. Given an initially empty graph G, our algorithm processes m insertions and n deletions in total time m^{1 + o(1)} and maintains an initially empty spanner H with total recourse n^{1 + o(1)}. When the number of insertions is much larger than the number of deletions, this notably yields recourse sub-linear in the total number of updates. 
Our simple algorithm can be extended to maintain a δ ≥ ω(1)-approximate spanner with n^{1+o(1)} edges throughout a sequence of m insertions and D deletions with amortized update time n^{o(1)} and total recourse n^{1 + o(1)} + n^{o(1)} ⋅ D via batching.

Cite As Get BibTex

Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein. A Simple Dynamic Spanner via APSP. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 111:1-111:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.111

Author Details

Rasmus Kyng
  • ETH Zurich, Switzerland
Simon Meierhans
  • ETH Zurich, Switzerland
Gernot Zöcklein
  • ETH Zurich, Switzerland

Funding

  • Kyng, Rasmus: The research leading to these results has received funding from grant no. 200021 204787 and from the starting grant "A New Paradigm for Flow and Cut Algorithms" (no. TMSGI2_218022) of the Swiss National Science Foundation.
  • Meierhans, Simon: The research leading to these results has received funding from grant no. 200021 204787 of the Swiss National Science Foundation. Simon Meierhans is supported by a Google PhD Fellowship.

Acknowledgements

The authors are very grateful for feedback from Maximilian Probst Gutenberg and Pratyai Mazumder on a draft of this article that improved the presentation.

References

  1. Ingo Althöfer, Gautam Das, David Dobkin, Deborah Joseph, and José Soares. On sparse spanners of weighted graphs. Discrete & Computational Geometry, 9(1):81-100, 1993. URL: https://doi.org/10.1007/BF02189308.
  2. Surender Baswana, Sumeet Khurana, and Soumojit Sarkar. Fully dynamic randomized algorithms for graph spanners. ACM Trans. Algorithms, 8(4), 2012. URL: https://doi.org/10.1145/2344422.2344425.
  3. Aaron Bernstein, Jan van den Brand, Maximilian Probst Gutenberg, Danupon Nanongkai, Thatchaphol Saranurak, Aaron Sidford, and He Sun. Fully-Dynamic Graph Sparsifiers Against an Adaptive Adversary. In Mikołaj Bojańczyk, Emanuela Merelli, and David P. Woodruff, editors, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022), volume 229 of Leibniz International Proceedings in Informatics (LIPIcs), pages 20:1-20:20, Dagstuhl, Germany, 2022. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.20.
  4. Sayan Bhattacharya, Thatchaphol Saranurak, and Pattara Sukprasert. Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary. In Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman, editors, 30th Annual European Symposium on Algorithms (ESA 2022), volume 244 of Leibniz International Proceedings in Informatics (LIPIcs), pages 17:1-17:19, Dagstuhl, Germany, 2022. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.ESA.2022.17.
  5. J. Brand, L. Chen, R. Kyng, Y. P. Liu, R. Peng, M. Gutenberg, S. Sachdeva, and A. Sidford. A deterministic almost-linear time algorithm for minimum-cost flow. In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 503-514, Los Alamitos, CA, USA, November 2023. IEEE Computer Society. URL: https://doi.org/10.1109/FOCS57990.2023.00037.
  6. Li Chen, Rasmus Kyng, Yang P. Liu, Simon Meierhans, and Maximilian Probst Gutenberg. Almost-linear time algorithms for incremental graphs: Cycle detection, sccs, s-t shortest path, and minimum-cost flow. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, pages 1165-1173, New York, NY, USA, 2024. Association for Computing Machinery. URL: https://doi.org/10.1145/3618260.3649745.
  7. Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva. Maximum flow and minimum-cost flow in almost-linear time. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 612-623, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00064.
  8. Julia Chuzhoy and Merav Parter. Fully dynamic algorithms for graph spanners via low-diameter router decomposition. In Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 785-823, 2025. URL: https://doi.org/10.1137/1.9781611978322.23.
  9. Julia Chuzhoy and Ruimin Zhang. A new deterministic algorithm for fully dynamic all-pairs shortest paths. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, pages 1159-1172, New York, NY, USA, 2023. Association for Computing Machinery. URL: https://doi.org/10.1145/3564246.3585196.
  10. Sebastian Forster and Gramoz Goranci. Dynamic low-stretch trees via dynamic low-diameter decompositions. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, pages 377-388, New York, NY, USA, 2019. Association for Computing Machinery. URL: https://doi.org/10.1145/3313276.3316381.
  11. Bernhard Haeupler, Yaowei Long, and Thatchaphol Saranurak. Dynamic deterministic constant-approximate distance oracles with n^ε worst-case update time, 2024. URL: https://doi.org/10.48550/arXiv.2402.18541.
  12. Rasmus Kyng, Simon Meierhans, and Maximilian Probst Gutenberg. A dynamic shortest paths toolbox: Low-congestion vertex sparsifiers and their applications. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, pages 1174-1183, New York, NY, USA, 2024. Association for Computing Machinery. URL: https://doi.org/10.1145/3618260.3649767.
  13. Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein. Bootstrapping dynamic apsp via sparsification, 2024. URL: https://doi.org/10.48550/arXiv.2408.11375.
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