2 Search Results for "Chen, Liqian"

Document
DOI: 10.4230/LIPIcs.ISAAC.2021.48
Streaming Algorithms for Graph k-Matching with Optimal or Near-Optimal Update Time

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

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

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.
Cite as

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)

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@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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.48},
  URN =		{urn:nbn:de:0030-drops-154816},
  doi =		{10.4230/LIPIcs.ISAAC.2021.48},
  annote =	{Keywords: streaming algorithms, matching, parameterized algorithms, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.CP.2021.57
Making Rigorous Linear Programming Practical for Program Analysis

Authors: Tengbin Wang, Liqian Chen, Taoqing Chen, Guangsheng Fan, and Ji Wang

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Abstract
Linear programming is a key technique for analysis and verification of numerical properties in programs, neural networks, etc. In particular, in program analysis based on abstract interpretation, many numerical abstract domains (such as Template Constraint Matrix, constraint-only polyhedra, etc.) are designed on top of linear programming. However, most state-of-the-art linear programming solvers use floating-point arithmetic in their implementations, leading to an approximate result that may be unsound. On the other hand, the solvers implemented using exact arithmetic are too costly. To this end, this paper focuses on advancing rigorous linear programming techniques based on floating-point arithmetic for building sound and efficient program analysis. Particularly, as a supplement to existing techniques, we present a novel rigorous linear programming technique based on Fourier-Mozkin elimination. On this basis, we implement a tool, namely, RlpSolver, combining our technique with existing techniques to lift effectiveness of rigorous linear programming in the scene of analysis and verification. Experimental results show that our technique is complementary to existing techniques, and their combination (RlpSolver) can achieve a better trade-off between cost and precision via heuristic rules.
Cite as

Tengbin Wang, Liqian Chen, Taoqing Chen, Guangsheng Fan, and Ji Wang. Making Rigorous Linear Programming Practical for Program Analysis. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 57:1-57:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wang_et_al:LIPIcs.CP.2021.57,
  author =	{Wang, Tengbin and Chen, Liqian and Chen, Taoqing and Fan, Guangsheng and Wang, Ji},
  title =	{{Making Rigorous Linear Programming Practical for Program Analysis}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{57:1--57:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.57},
  URN =		{urn:nbn:de:0030-drops-153486},
  doi =		{10.4230/LIPIcs.CP.2021.57},
  annote =	{Keywords: Linear programming, rigorous linear programming, abstract interpretation, program analysis, Fourier-Mozkin elimination}
}
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