Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
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3694906.3743322.pdf
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664.37 KB
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Author(s)
Ghaffari, Mohsen
Koo, Jaehyun
Date Issued
July 16, 2025
Publisher
ACM|37th ACM Symposium on Parallelism in Algorithms and Architectures
Citation
Mohsen Ghaffari and Jaehyun Koo. 2025. Parallel Batch-Dynamic Algorithms for Spanners, and Extensions. In Proceedings of the 37th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA '25). Association for Computing Machinery, New York, NY, USA, 299–313.
Version
Final published version
Abstract
This paper presents the first parallel batch-dynamic algorithms for computing spanners and sparsifiers. Our algorithms process any batch of edge insertions and deletions in an n-node undirected graph, in poly(log n) depth and using amortized work near-linear in the batch size. Our concrete results are as follows:
• Our base algorithm maintains a spanner with (2k -1) stretch and Õ(n1+1/k) edges, for any k ≥ 1.
• Our first extension maintains a sparse spanner with only O(n) edges, and Õ(log n) stretch.
• Our second extension maintains a t-bundle of spanners --- i.e., t spanners, each of which is the spanner of the graph remaining after removing the previous ones---and allows us to maintain cut/spectral sparsifiers with Õ(n) edges.
Description
SPAA ’25, Portland, OR, USA
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-NoDerivatives
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DOI of Published Version
https://doi.org/10.1145/3694906.3743322
