Conclusion
In this paper, we propose the first fully dynamic parallel allpairs shortest path algorithm in the MPC model with a worstcase update rounds of \(O({n^{{2 \over 3} - {\alpha \over 6}}}\log n/\alpha )\). We compare our algorithm with the existing static APSP algorithms in the MPC model, demonstrating the efficiency of our approach
References
Dinitz M, Nazari Y. Massively parallel approximate distance sketches. In: Proceedings of the 23rd International Conference on Principles of Distributed Systems. 2019, 35: 1–35: 17
Abraham I, Chechik S, Krinninger S. Fully dynamic all-pairs shortest paths with worst-case update-time revisited. In: Proceedings of the 28th Annual ACM SIAM Symposium on Discrete Algorithms. 2017, 440–452
Zhu X, Li W, Yang Y, Wang J. Incremental algorithms for the maximum internal spanning tree problem. Science China Information Sciences, 2021, 64(5): 152103
Henzinger M R, King V. Maintaining minimum spanning forests in dynamic graphs. SIAM Journal on Computing, 2001, 31(2): 364–374
Italiano G F, Lattanzi S, Mirrokni V S, Parotsidis N. Dynamic algorithms for the massively parallel computation model. In: Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures. 2019, 49–58
Sao P, Kannan R, Gera P, Vuduc R W. A supernodal all-pairs shortest path algorithm. In: Proceedings of the 25th SIGPLAN Symposium on Principles and Practice of Parallel Programming. 2020, 250–261
Hajiaghayi M, Lattanzi S, Seddighin S, Stein C. MapReduce meets finegrained complexity: MapReduce algorithms for APSP, matrix multiplication, 3-SUM, and beyond. 2019, arXiv preprint arXiv: 1905.01748
Karczmarz A, Sankowski P. A deterministic parallel APSP algorithm and its applications. In: Proceedings of the 32nd Annual ACM-SIAM Symposium on Discrete Algorithms. 2021, 255–272
Cao N, Fineman J T. Parallel exact shortest paths in almost linear work and square root depth. In: Proceedings of 2023 ACM-SIAM Symposium on Discrete Algorithms. 2023, 4354–4372
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61972447 and 61832006).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests The authors declare that they have no competing interests or financial conflicts to disclose.
Additional information
Supporting information The supporting information is available online at journal.hep.com.cn and link.springer.com.
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Wang, C., Hua, QS., Jin, H. et al. Massively parallel algorithms for fully dynamic all-pairs shortest paths. Front. Comput. Sci. 18, 184611 (2024). https://doi.org/10.1007/s11704-024-3452-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11704-024-3452-2