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Connectivity Oracles for Predictable Vertex Failures

Authors Bingbing Hu, Evangelos Kosinas, Adam Polak

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Author Details

Bingbing Hu
  • Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
  • University of California San Diego, CA, USA
Evangelos Kosinas
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria
Adam Polak
  • Bocconi University, Milan, Italy

Acknowledgements

Part of this work was done when Evangelos Kosinas was at University of Ioannina and Adam Polak was at Max Planck Institute of Informatics.

Cite AsGet BibTex

Bingbing Hu, Evangelos Kosinas, and Adam Polak. Connectivity Oracles for Predictable Vertex Failures. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 72:1-72:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.72

Abstract

The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Data structures
  • graph connectivity
  • algorithms with predictions

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References

  1. Amir Abboud and Virginia Vassilevska Williams. Popular conjectures imply strong lower bounds for dynamic problems. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS, pages 434-443. IEEE Computer Society, 2014. URL: https://doi.org/10.1109/FOCS.2014.53.
  2. Surender Baswana, Shreejit Ray Chaudhury, Keerti Choudhary, and Shahbaz Khan. Dynamic DFS in undirected graphs: Breaking the o(m) barrier. SIAM J. Comput., 48(4):1335-1363, 2019. URL: https://doi.org/10.1137/17M114306X.
  3. Michael A. Bender and Martin Farach-Colton. The level ancestor problem simplified. Theor. Comput. Sci., 321(1):5-12, 2004. URL: https://doi.org/10.1016/j.tcs.2003.05.002.
  4. Timothy M. Chan, Kasper Green Larsen, and Mihai Puatracscu. Orthogonal range searching on the ram, revisited. In Ferran Hurtado and Marc J. van Kreveld, editors, Proceedings of the 27th ACM Symposium on Computational Geometry, Paris, France, June 13-15, 2011, pages 1-10. ACM, 2011. URL: https://doi.org/10.1145/1998196.1998198.
  5. Timothy M. Chan, Mihai Puatracscu, and Liam Roditty. Dynamic connectivity: Connecting to networks and geometry. SIAM J. Comput., 40(2):333-349, 2011. URL: https://doi.org/10.1137/090751670.
  6. Michal Dory and Merav Parter. Fault-tolerant labeling and compact routing schemes. In PODC '21: ACM Symposium on Principles of Distributed Computing, pages 445-455. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467929.
  7. Ran Duan. New data structures for subgraph connectivity. In Automata, Languages and Programming, 37th International Colloquium, ICALP, volume 6198 of Lecture Notes in Computer Science, pages 201-212. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-14165-2_18.
  8. Ran Duan and Seth Pettie. Connectivity oracles for failure prone graphs. In Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, pages 465-474. ACM, 2010. URL: https://doi.org/10.1145/1806689.1806754.
  9. Ran Duan and Seth Pettie. Connectivity oracles for graphs subject to vertex failures. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, pages 490-509. SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974782.31.
  10. Ran Duan and Seth Pettie. Connectivity oracles for graphs subject to vertex failures. SIAM J. Comput., 49(6):1363-1396, 2020. URL: https://doi.org/10.1137/17M1146610.
  11. Ran Duan and Le Zhang. Faster randomized worst-case update time for dynamic subgraph connectivity. In Algorithms and Data Structures - 15th International Symposium, WADS, volume 10389 of Lecture Notes in Computer Science, pages 337-348. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-62127-2_29.
  12. Paolo Ferragina and Giorgio Vinciguerra. Learned data structures. In Recent Trends in Learning From Data - Tutorials from the INNS Big Data and Deep Learning Conference (INNSBDDL 2019), volume 896 of Studies in Computational Intelligence, pages 5-41. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-43883-8_2.
  13. Daniele Frigioni and Giuseppe F. Italiano. Dynamically switching vertices in planar graphs. Algorithmica, 28(1):76-103, 2000. URL: https://doi.org/10.1007/S004530010032.
  14. Monika Henzinger, Sebastian Krinninger, Danupon Nanongkai, and Thatchaphol Saranurak. Unifying and strengthening hardness for dynamic problems via the online matrix-vector multiplication conjecture. In Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, pages 21-30. ACM, 2015. URL: https://doi.org/10.1145/2746539.2746609.
  15. Monika Henzinger and Stefan Neumann. Incremental and fully dynamic subgraph connectivity for emergency planning. In 24th Annual European Symposium on Algorithms, ESA 2016, volume 57 of LIPIcs, pages 48:1-48:11. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. URL: https://doi.org/10.4230/LIPICS.ESA.2016.48.
  16. Monika Henzinger, Barna Saha, Martin P. Seybold, and Christopher Ye. On the complexity of algorithms with predictions for dynamic graph problems. In 15th Innovations in Theoretical Computer Science Conference, ITCS 2024, volume 287 of LIPIcs, pages 62:1-62:25. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPICS.ITCS.2024.62.
  17. Taisuke Izumi, Yuval Emek, Tadashi Wadayama, and Toshimitsu Masuzawa. Deterministic fault-tolerant connectivity labeling scheme. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC, pages 190-199. ACM, 2023. URL: https://doi.org/10.1145/3583668.3594584.
  18. Ce Jin and Yinzhan Xu. Tight dynamic problem lower bounds from generalized BMM and omv. In STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, pages 1515-1528. ACM, 2022. URL: https://doi.org/10.1145/3519935.3520036.
  19. Bruce M. Kapron, Valerie King, and Ben Mountjoy. Dynamic graph connectivity in polylogarithmic worst case time. In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, pages 1131-1142. SIAM, 2013. URL: https://doi.org/10.1137/1.9781611973105.81.
  20. Tsvi Kopelowitz, Seth Pettie, and Ely Porat. Higher lower bounds from the 3SUM conjecture. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, pages 1272-1287. SIAM, 2016. URL: https://doi.org/10.1137/1.9781611974331.ch89.
  21. Evangelos Kosinas. Connectivity queries under vertex failures: Not optimal, but practical. In 31st Annual European Symposium on Algorithms, ESA 2023, volume 274 of LIPIcs, pages 75:1-75:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.ESA.2023.75.
  22. Tim Kraska, Alex Beutel, Ed H. Chi, Jeffrey Dean, and Neoklis Polyzotis. The case for learned index structures. In Proceedings of the 2018 International Conference on Management of Data, SIGMOD Conference 2018, pages 489-504. ACM, 2018. URL: https://doi.org/10.1145/3183713.3196909.
  23. Honghao Lin, Tian Luo, and David P. Woodruff. Learning augmented binary search trees. In International Conference on Machine Learning, ICML 2022, volume 162 of Proceedings of Machine Learning Research, pages 13431-13440. PMLR, 2022. URL: https://proceedings.mlr.press/v162/lin22f.html.
  24. Alexander Lindermayr and Nicole Megow. Algorithms with predictions. https://algorithms-with-predictions.github.io, 2022. Accessed 8 September 2023.
  25. Quanquan C. Liu and Vaidehi Srinivas. The predicted-updates dynamic model: Offline, incremental, and decremental to fully dynamic transformations. In The Thirty Seventh Annual Conference on Learning Theory, COLT 2024, Proceedings of Machine Learning Research. PMLR, 2024. Google Scholar
  26. Yaowei Long and Thatchaphol Saranurak. Near-optimal deterministic vertex-failure connectivity oracles. In 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, pages 1002-1010. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00098.
  27. Yaowei Long and Yunfan Wang. Better decremental and fully dynamic sensitivity oracles for subgraph connectivity. In 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024, LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. Google Scholar
  28. Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. In Tim Roughgarden, editor, Beyond the Worst-Case Analysis of Algorithms, pages 646-662. Cambridge University Press, 2020. URL: https://doi.org/10.1017/9781108637435.037.
  29. Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. Commun. ACM, 65(7):33-35, 2022. URL: https://doi.org/10.1145/3528087.
  30. Merav Parter and Asaf Petruschka. Õptimal dual vertex failure connectivity labels. In 36th International Symposium on Distributed Computing, DISC, volume 246 of LIPIcs, pages 32:1-32:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.DISC.2022.32.
  31. Merav Parter, Asaf Petruschka, and Seth Pettie. Connectivity labeling and routing with multiple vertex failures. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, pages 823-834. ACM, 2024. URL: https://doi.org/10.1145/3618260.3649729.
  32. Mihai Pătraşcu and Mikkel Thorup. Planning for fast connectivity updates. In 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2007), pages 263-271. IEEE Computer Society, 2007. URL: https://doi.org/10.1109/FOCS.2007.54.
  33. David Peleg. Informative labeling schemes for graphs. Theor. Comput. Sci., 340(3):577-593, 2005. URL: https://doi.org/10.1016/J.TCS.2005.03.015.
  34. Michal Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz, Szymon Torunczyk, and Alexandre Vigny. Algorithms and data structures for first-order logic with connectivity under vertex failures. In 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, volume 229 of LIPIcs, pages 102:1-102:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.102.
  35. Jan van den Brand, Sebastian Forster, Yasamin Nazari, and Adam Polak. On dynamic graph algorithms with predictions. In Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3534-3557. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.126.
  36. Jan van den Brand and Thatchaphol Saranurak. Sensitive distance and reachability oracles for large batch updates. In 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS, pages 424-435. IEEE Computer Society, 2019. URL: https://doi.org/10.1109/FOCS.2019.00034.
  37. Virginia Vassilevska Williams and Yinzhan Xu. Monochromatic triangles, triangle listing and APSP. In 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, pages 786-797. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00078.
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