License:
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.48
URN: urn:nbn:de:0030-drops-154816
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15481/
Chen, Jianer ;
Huang, Qin ;
Kanj, Iyad ;
Li, Qian ;
Xia, Ge
Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time
Abstract
We present streaming algorithms for the graph k-matching problem in both the insert-only and dynamic models. Our algorithms, while keeping the space complexity matching the best known upper bound, have optimal or near-optimal update time, significantly improving on previous results. More specifically, for the insert-only streaming model, we present a one-pass randomized algorithm that runs in optimal ?(k²) space and has optimal ?(1) update time, and that, w.h.p. (with high probability), computes a maximum weighted k-matching of a weighted graph. Previously, the best upper bound on the update time was ?(log k), which was achieved by a deterministic streaming algorithm that however only works for unweighted graphs [Stefan Fafianie and Stefan Kratsch, 2014]. For the dynamic streaming model, we present a one-pass randomized algorithm that, w.h.p., computes a maximum weighted k-matching of a weighted graph in Õ(Wk²) space and with Õ(1) update time, where W is the number of distinct edge weights. Again the update time of our algorithm improves the previous best upper bound Õ(k²) [Rajesh Chitnis et al., 2016]. Moreover, we prove that in the dynamic streaming model, any randomized streaming algorithm for the problem requires k²⋅ Ω(W(log W+1)) bits of space. Hence, both the space and update-time complexities achieved by our algorithm in the dynamic model are near-optimal. A streaming approximation algorithm for k-matching is also presented, whose space complexity matches the best known upper bound with a significantly improved update time.
BibTeX - Entry
@InProceedings{chen_et_al:LIPIcs.ISAAC.2021.48,
author = {Chen, Jianer and Huang, Qin and Kanj, Iyad and Li, Qian and Xia, Ge},
title = {{Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {48:1--48:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-214-3},
ISSN = {1868-8969},
year = {2021},
volume = {212},
editor = {Ahn, Hee-Kap and Sadakane, Kunihiko},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15481},
URN = {urn:nbn:de:0030-drops-154816},
doi = {10.4230/LIPIcs.ISAAC.2021.48},
annote = {Keywords: streaming algorithms, matching, parameterized algorithms, lower bounds}
}
Keywords: |
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streaming algorithms, matching, parameterized algorithms, lower bounds |
Collection: |
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32nd International Symposium on Algorithms and Computation (ISAAC 2021) |
Issue Date: |
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2021 |
Date of publication: |
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30.11.2021 |