Censor-Hillel, Keren; Dory, Michal; Korhonen, JanneIST Austria; Leitersdorf, Dean
We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include: A (2+ϵ)-approximation for all-pairs shortest paths in O(log2n/ϵ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model. A (1+ϵ)-approximation for multi-source shortest paths from O(n−−√) sources in O(log2n/ϵ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in O~(n1/6) rounds.
Open access funding provided by Institute of Science and Technology (IST Austria). We thank Mohsen Ghaffari, Michael Elkin and Merav Parter for fruitful discussions. This project has received funding from the European Union’s Horizon 2020 Research And Innovation Program under Grant Agreement No. 755839.
Censor-Hillel K, Dory M, Korhonen J, Leitersdorf D. Fast approximate shortest paths in the congested clique. Distributed Computing. 2020. doi:10.1007/s00446-020-00380-5
Censor-Hillel, K., Dory, M., Korhonen, J., & Leitersdorf, D. (2020). Fast approximate shortest paths in the congested clique. Distributed Computing. Springer Nature. https://doi.org/10.1007/s00446-020-00380-5
Censor-Hillel, Keren, Michal Dory, Janne Korhonen, and Dean Leitersdorf. “Fast Approximate Shortest Paths in the Congested Clique.” Distributed Computing. Springer Nature, 2020. https://doi.org/10.1007/s00446-020-00380-5.
K. Censor-Hillel, M. Dory, J. Korhonen, and D. Leitersdorf, “Fast approximate shortest paths in the congested clique,” Distributed Computing. Springer Nature, 2020.
Censor-Hillel K, Dory M, Korhonen J, Leitersdorf D. 2020. Fast approximate shortest paths in the congested clique. Distributed Computing.
Censor-Hillel, Keren, et al. “Fast Approximate Shortest Paths in the Congested Clique.” Distributed Computing, Springer Nature, 2020, doi:10.1007/s00446-020-00380-5.
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