Document Open Access Logo

Incremental Approximate Single-Source Shortest Paths with Predictions

Authors Samuel McCauley, Benjamin Moseley , Aidin Niaparast, Helia Niaparast, Shikha Singh

PDF

File

Thumbnail PDF
PDF
LIPIcs.ICALP.2025.117.pdf
  • Filesize: 0.78 MB
  • 20 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
Keywords
  • Algorithms with Predictions
  • Shortest Paths
  • Approximation Algorithms
  • Dynamic Graph Algorithms

Metrics

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

Abstract

The algorithms-with-predictions framework has been used extensively to develop online algorithms with improved beyond-worst-case competitive ratios. Recently, there is growing interest in leveraging predictions for designing data structures with improved beyond-worst-case running times. In this paper, we study the fundamental data structure problem of maintaining approximate shortest paths in incremental graphs in the algorithms-with-predictions model. Given a sequence σ of edges that are inserted one at a time, the goal is to maintain approximate shortest paths from the source to each vertex in the graph at each time step. Before any edges arrive, the data structure is given a prediction of the online edge sequence σ̂ which is used to "warm start" its state. 
As our main result, we design a learned algorithm that maintains (1+ε)-approximate single-source shortest paths, which runs in Õ(m η log W/ε) time, where W is the weight of the heaviest edge and η is the prediction error. We show these techniques immediately extend to the all-pairs shortest-path setting as well. Our algorithms are consistent (performing nearly as fast as the offline algorithm) when predictions are nearly perfect, have a smooth degradation in performance with respect to the prediction error and, in the worst case, match the best offline algorithm up to logarithmic factors. That is, the algorithms are "ideal" in the algorithms-with-predictions model.
As a building block, we study the offline incremental approximate single-source shortest-path (SSSP) problem. In the offline incremental SSSP problem, the edge sequence σ is known a priori and the goal is to construct a data structure that can efficiently return the length of the shortest paths in the intermediate graph G_t consisting of the first t edges, for all t. Note that the offline incremental problem is defined in the worst-case setting (without predictions) and is of independent interest.

Cite As Get BibTex

Samuel McCauley, Benjamin Moseley, Aidin Niaparast, Helia Niaparast, and Shikha Singh. Incremental Approximate Single-Source Shortest Paths with Predictions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 117:1-117:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.117

Author Details

Samuel McCauley
  • Williams College, Williamstown, MA, USA
Benjamin Moseley
  • Carnegie Mellon University, Pittsburgh, PA, USA
Aidin Niaparast
  • Carnegie Mellon University, Pittsburgh, PA, USA
Helia Niaparast
  • Carnegie Mellon University, Pittsburgh, PA,USA
Shikha Singh
  • Williams College, Williamstown, MA, USA

Funding

  • McCauley, Samuel: Supported in part by NSF CCF-2103813.
  • Moseley, Benjamin: Supported in part by Google Research Award, an Infor Research Award, a Carnegie Bosch Junior Faculty Chair, NSF grants CCF-2121744 and CCF-1845146.
  • Niaparast, Aidin: Supported in part by the Air Force Office of Scientific Research under award number FA9550-23-1-0031 and NSF award CCF-1845146.
  • Niaparast, Helia: Supported in part by NSF CCF-1845146.
  • Singh, Shikha: Supported in part by NSF CCF-1947789.

References

  1. Xingjian Bai and Christian Coester. Sorting with predictions. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL: https://openreview.net/forum?id=Qv7rWR9JWa.
  2. Ziyad Benomar and Christian Coester. Learning-augmented priority queues. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL: https://openreview.net/forum?id=1ATLLgvURu.
  3. Ioana O. Bercea, Jakob Bæk Tejs Houen, and Rasmus Pagh. Daisy Bloom Filters. In Hans L. Bodlaender, editor, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024), volume 294 of Leibniz International Proceedings in Informatics (LIPIcs), pages 9:1-9:19, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.SWAT.2024.9.
  4. Aaron Bernstein. Fully dynamic (2+ ε) approximate all-pairs shortest paths with fast query and close to linear update time. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science, pages 693-702. IEEE, 2009. URL: https://doi.org/10.1109/FOCS.2009.16.
  5. Aaron Bernstein. Maintaining shortest paths under deletions in weighted directed graphs. SIAM Journal on Computing, 45(2):548-574, 2016. URL: https://doi.org/10.1137/130938670.
  6. Aaron Bernstein, Maximilian Probst Gutenberg, and Thatchaphol Saranurak. Deterministic decremental SSSP and approximate min-cost flow in almost-linear time. In 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Denver, CO, USA, February 7-10, 2022, pages 1000-1008. IEEE, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00100.
  7. Aaron Bernstein, Maximilian Probst Gutenberg, and Christian Wulff-Nilsen. Near-optimal decremental SSSP in dense weighted digraphs. In Sandy Irani, editor, 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, November 16-19, 2020, pages 1112-1122. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00107.
  8. Aditya Bhaskara, Sreenivas Gollapudi, Kostas Kollias, and Kamesh Munagala. Adaptive probing policies for shortest path routing. Advances in Neural Information Processing Systems (NeurIPS), 33:8682-8692, 2020. Google Scholar
  9. Shiri Chechik and Tianyi Zhang. Incremental single source shortest paths in sparse digraphs. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 2463-2477. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.146.
  10. Jingbang Chen and Li Chen. On the power of learning-augmented BSTs. arXiv preprint arXiv:2211.09251, 2022. URL: https://doi.org/10.48550/arXiv.2211.09251.
  11. Yifan Dai, Yien Xu, Aishwarya Ganesan, Ramnatthan Alagappan, Brian Kroth, Andrea Arpaci-Dusseau, and Remzi Arpaci-Dusseau. From WiscKey to Bourbon: A learned index for log-structured merge trees. In 14th USENIX Symposium on Operating Systems Design and Implementation (OSDI), pages 155-171, 2020. URL: https://www.usenix.org/conference/osdi20/presentation/dai.
  12. Sami Davies, Benjamin Moseley, Sergei Vassilvitskii, and Yuyan Wang. Predictive flows for faster ford-fulkerson. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett, editors, Proc. of the 40th International Conference on Machine Learning (ICML), volume 202 of Proceedings of Machine Learning Research, pages 7231-7248. PMLR, 23-29 July 2023. URL: https://proceedings.mlr.press/v202/davies23b.html.
  13. Jialin Ding, Umar Farooq Minhas, Jia Yu, Chi Wang, Jaeyoung Do, Yinan Li, Hantian Zhang, Badrish Chandramouli, Johannes Gehrke, Donald Kossmann, et al. ALEX: an updatable adaptive learned index. In Proc. 46th Annual ACM International Conference on Management of Data (SIGMOD), pages 969-984, 2020. Google Scholar
  14. Michael Dinitz, Sungjin Im, Thomas Lavastida, Benjamin Moseley, Aidin Niaparast, and Sergei Vassilvitskii. Binary search with distributional predictions. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors, Advances in Neural Information Processing Systems, volume 37, pages 90456-90472. Curran Associates, Inc., 2024. URL: https://proceedings.neurips.cc/paper_files/paper/2024/file/a4b293979b8b521e9222d30c40246911-Paper-Conference.pdf.
  15. Michael Dinitz, Sungjin Im, Thomas Lavastida, Benjamin Moseley, and Sergei Vassilvitskii. Faster matchings via learned duals. In Marc'Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan, editors, Proc. 34th Conference on Advances in Neural Information Processing Systems (NeurIPS), pages 10393-10406, 2021. URL: https://proceedings.neurips.cc/paper/2021/hash/5616060fb8ae85d93f334e7267307664-Abstract.html.
  16. Elbert Du, Franklyn Wang, and Michael Mitzenmacher. Putting the “learning” into learning-augmented algorithms for frequency estimation. In Proc. 38th Annual International Conference on Machine Learning (ICML), pages 2860-2869. PMLR, 2021. URL: http://proceedings.mlr.press/v139/du21d.html.
  17. Adam Górkiewicz and Adam Karczmarz. On incremental approximate shortest paths in directed graphs. CoRR, abs/2502.10348, 2025. URL: https://doi.org/10.48550/arXiv.2502.10348.
  18. Maximilian Probst Gutenberg and Christian Wulff-Nilsen. Deterministic algorithms for decremental approximate shortest paths: Faster and simpler. In Shuchi Chawla, editor, Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 2522-2541. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.154.
  19. Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. Sublinear-time decremental algorithms for single-source reachability and shortest paths on directed graphs. In Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pages 674-683, 2014. URL: https://doi.org/10.1145/2591796.2591869.
  20. Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. Improved algorithms for decremental single-source reachability on directed graphs. In Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I 42, pages 725-736. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-47672-7_59.
  21. Monika Henzinger, Sebastian Krinninger, and Danupon Nanongkai. Dynamic approximate all-pairs shortest paths: Breaking the o(mn) barrier and derandomization. SIAM J. Comput., 45(3):947-1006, 2016. URL: https://doi.org/10.1137/140957299.
  22. Monika Henzinger, Barna Saha, Martin P. Seybold, and Christopher Ye. On the complexity of algorithms with predictions for dynamic graph problems. In Venkatesan Guruswami, editor, 15th Innovations in Theoretical Computer Science Conference, ITCS 2024, January 30 to February 2, 2024, Berkeley, CA, USA, 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.
  23. Monika Rauch Henzinger and Valerie King. Fully dynamic biconnectivity and transitive closure. In Proceedings of IEEE 36th Annual Foundations of Computer Science, pages 664-672. IEEE, 1995. URL: https://doi.org/10.1109/SFCS.1995.492668.
  24. Chen-Yu Hsu, Piotr Indyk, Dina Katabi, and Ali Vakilian. Learning-based frequency estimation algorithms. In Proc. 7th Annual International Conference on Learning Representations (ICLR), 2019. Google Scholar
  25. Piotr Indyk, Frederik Mallmann-Trenn, Slobodan Mitrovic, and Ronitt Rubinfeld. Online page migration with ML advice. In Gustau Camps-Valls, Francisco J. R. Ruiz, and Isabel Valera, editors, International Conference on Artificial Intelligence and Statistics, (AISTATS), volume 151 of Proceedings of Machine Learning Research, pages 1655-1670. PMLR, 2022. URL: https://proceedings.mlr.press/v151/indyk22a.html.
  26. Zhihao Jiang, Debmalya Panigrahi, and Kevin Sun. Online algorithms for weighted paging with predictions. In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, 47th International Colloquium on Automata, Languages, and Programming, (ICALP), volume 168 of LIPIcs, pages 69:1-69:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.69.
  27. Tim Kraska, Alex Beutel, Ed H. Chi, Jeffrey Dean, and Neoklis Polyzotis. The case for learned index structures. In Gautam Das, Christopher M. Jermaine, and Philip A. Bernstein, editors, Proc. 44th Annual International Conference on Management of Data, (SIGMOD), pages 489-504. ACM, 2018. URL: https://doi.org/10.1145/3183713.3196909.
  28. Rasmus Kyng, Simon Meierhans, and Maximilian Probst Gutenberg. Incremental sssp for sparse digraphs beyond the hopset barrier. In Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 3452-3481. SIAM, 2022. URL: https://doi.org/10.1137/1.9781611977073.137.
  29. Silvio Lattanzi, Ola Svensson, and Sergei Vassilvitskii. Speeding up bellman ford via minimum violation permutations. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett, editors, International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pages 18584-18598. PMLR, 2023. URL: https://proceedings.mlr.press/v202/lattanzi23a.html.
  30. Honghao Lin, Tian Luo, and David Woodruff. Learning augmented binary search trees. In Proc. 35th International Conference on Machine Learning (ICML), pages 13431-13440. PMLR, 2022. URL: https://proceedings.mlr.press/v162/lin22f.html.
  31. Honghao Lin, Tian Luo, and David P. Woodruff. Learning augmented binary search trees. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato, editors, International Conference on Machine Learning, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pages 13431-13440. PMLR, 2022. URL: https://proceedings.mlr.press/v162/lin22f.html.
  32. Quanquan C. Liu and Vaidehi Srinivas. The predicted-updates dynamic model: Offline, incremental, and decremental to fully dynamic transformations. In Shipra Agrawal and Aaron Roth, editors, Proceedings of Thirty Seventh Conference on Learning Theory, volume 247 of Proceedings of Machine Learning Research, pages 3582-3641. PMLR, 30 June-03 July 2024. URL: https://proceedings.mlr.press/v247/liu24c.html.
  33. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. Journal of the ACM (JACM), 68(4):1-25, 2021. URL: https://doi.org/10.1145/3447579.
  34. Aleksander Madry. Faster approximation schemes for fractional multicommodity flow problems via dynamic graph algorithms. In Proceedings of the forty-second ACM symposium on Theory of computing, pages 121-130, 2010. URL: https://doi.org/10.1145/1806689.1806708.
  35. Samuel McCauley, Benjamin Moseley, Aidin Niaparast, Helia Niaparast, and Shikha Singh. Incremental approximate single-source shortest paths with predictions, 2025. URL: https://doi.org/10.48550/arXiv.2502.08125.
  36. Samuel McCauley, Benjamin Moseley, Aidin Niaparast, and Shikha Singh. Online list labeling with predictions. In A. Oh, T. Naumann, A. Globerson, K. Saenko, M. Hardt, and S. Levine, editors, Proc. 36th Conference on Neural Information Processing Systems (NeurIPS), volume 36, pages 60278-60290. Curran Associates, Inc., 2023. Google Scholar
  37. Samuel Mccauley, Benjamin Moseley, Aidin Niaparast, and Shikha Singh. Incremental topological ordering and cycle detection with predictions. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp, editors, Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedings of Machine Learning Research, pages 35240-35254. PMLR, 21-27 July 2024. URL: https://proceedings.mlr.press/v235/mccauley24a.html.
  38. Michael Mitzenmacher. A model for learned bloom filters and optimizing by sandwiching. Proc. 31st Conference on Neural Information Processing Systems (NeurIPS), 31, 2018. Google Scholar
  39. Binghui Peng and Aviad Rubinstein. Fully-dynamic-to-incremental reductions with known deletion order (e.g. sliding window). In Telikepalli Kavitha and Kurt Mehlhorn, editors, 2023 Symposium on Simplicity in Algorithms, SOSA 2023, Florence, Italy, January 23-25, 2023, pages 261-271. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977585.CH24.
  40. Adam Polak and Maksym Zub. Learning-augmented maximum flow. Information Processing Letters, 186:106487, 2024. URL: https://doi.org/10.1016/j.ipl.2024.106487.
  41. Maximilian Probst Gutenberg, Virginia Vassilevska Williams, and Nicole Wein. New algorithms and hardness for incremental single-source shortest paths in directed graphs. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pages 153-166, 2020. URL: https://doi.org/10.1145/3357713.3384236.
  42. Liam Roditty and Uri Zwick. On dynamic shortest paths problems. Algorithmica, 61(2):389-401, 2011. URL: https://doi.org/10.1007/S00453-010-9401-5.
  43. Shinsaku Sakaue and Taihei Oki. Discrete-convex-analysis-based framework for warm-starting algorithms with predictions. In 35th Conference on Neural Information Processing Systems (NeurIPS), 2022. Google Scholar
  44. Yossi Shiloach and Shimon Even. An on-line edge-deletion problem. Journal of the ACM (JACM), 28(1):1-4, 1981. URL: https://doi.org/10.1145/322234.322235.
  45. Vaidehi Srinivas and Avrim Blum. Competitive strategies to use "warm start" algorithms with predictions. In Proceedings of the 2025 ACM-SIAM Symposium on Discrete Algorithms, SODA 2025. SIAM, 2025. URL: https://doi.org/10.1137/1.9781611978322.127.
  46. Kapil Vaidya, Eric Knorr, Michael Mitzenmacher, and Tim Kraska. Partitioned learned bloom filters. In Proc. 9th Annual International Conference on Learning Representations (ICLR), 2021. URL: https://openreview.net/forum?id=6BRLOfrMhW.
  47. Jan van den Brand, Sebastian Forster, Yasamin Nazari, and Adam Polak. On dynamic graph algorithms with predictions. In David P. Woodruff, editor, Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms, SODA 2024, Alexandria, VA, USA, January 7-10, 2024, pages 3534-3557. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977912.126.
  48. Ali Zeynali, Shahin Kamali, and Mohammad Hajiesmaili. Robust learning-augmented dictionaries. In Forty-first International Conference on Machine Learning, 2024. URL: https://openreview.net/forum?id=XyhgssAo5b.
  49. Ali Zeynali, Shahin Kamali, and Mohammad Hajiesmaili. Robust learning-augmented dictionaries. In Forty-first International Conference on Machine Learning, ICML 2024, Vienna, Austria, July 21-27, 2024. OpenReview.net, 2024. URL: https://openreview.net/forum?id=XyhgssAo5b.
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