Parallel Dynamic Maximal Matching
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3626183.3659982.pdf
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1.06 MB
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Author(s)
Ghaffari, Mohsen
Trygub, Anton
Date Issued
June 17, 2024
Publisher
ACM|Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures
Citation
Ghaffari, Mohsen and Trygub, Anton. 2024. "Parallel Dynamic Maximal Matching."
Version
Final published version
Abstract
We present the first (randomized) parallel dynamic algorithm for maximal matching, which can process an arbitrary number of updates simultaneously. Given a batch of edge deletion or insertion updates to the graph, our parallel algorithm adjusts the maximal matching to these updates in poly(łog n) depth and using poly(łog n) amortized work per update. That is, the amortized work for processing a batch of k updates is k poly(łog n), while all this work is done in poly(łog n) depth, with high probability. This can be seen as a parallel counterpart of the sequential dynamic algorithms for constant-approximate and maximal matching [Onak and Rubinfeld STOC'10; Baswana, Gupta, and Sen FOCS'11; and Solomon FOCS'16]. Our algorithm readily generalizes to maximal matching in hypergraphs of rank r---where each hyperedge has at most r endpoints---with a poly(r) increase in work, while retaining the poly(łog n) depth.
Description
SPAA ’24, June 17–21, 2024, Nantes, France
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3626183.3659982
