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Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time

Authors Jianer Chen, Qin Huang, Iyad Kanj, Qian Li, Ge Xia

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Author Details

Jianer Chen
  • Department of Computer Science & Engineering, Texas A&M University, College Station, TX, USA
Qin Huang
  • Department of Computer Science & Engineering, Texas A&M University, College Station, TX, USA
Iyad Kanj
  • School of Computing, DePaul University, Chicago, IL, USA
Qian Li
  • Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China
Ge Xia
  • Department of Computer Science, Lafayette College, Easton, PA, USA

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Jianer Chen, Qin Huang, Iyad Kanj, Qian Li, and Ge Xia. Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ISAAC.2021.48

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 𝒪(k²) space and has optimal 𝒪(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 𝒪(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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • streaming algorithms
  • matching
  • parameterized algorithms
  • lower bounds

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