4 Search Results for "Huang, Qin"


Document
Matroid-Constrained Maximum Vertex Cover: Approximate Kernels and Streaming Algorithms

Authors: Chien-Chung Huang and François Sellier

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)


Abstract
Given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid, with the objective of maximizing the total weight of covered edges. This problem is a generalization of the much studied max k-vertex cover problem, where the matroid is the simple uniform matroid, and it is also a special case of maximizing a monotone submodular function under a matroid constraint. In this work, we give a Fixed Parameter Tractable Approximation Scheme (FPT-AS) when the given matroid is a partition matroid, a laminar matroid, or a transversal matroid. Precisely, if k is the rank of the matroid, we obtain (1 - ε) approximation using (1/(ε))^{O(k)}n^{O(1)} time for partition and laminar matroids and using (1/(ε)+k)^{O(k)}n^{O(1)} time for transversal matroids. This extends a result of Manurangsi for uniform matroids [Pasin Manurangsi, 2018]. We also show that these ideas can be applied in the context of (single-pass) streaming algorithms. Our FPT-AS introduces a new technique based on matroid union, which may be of independent interest in extremal combinatorics.

Cite as

Chien-Chung Huang and François Sellier. Matroid-Constrained Maximum Vertex Cover: Approximate Kernels and Streaming Algorithms. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{huang_et_al:LIPIcs.SWAT.2022.27,
  author =	{Huang, Chien-Chung and Sellier, Fran\c{c}ois},
  title =	{{Matroid-Constrained Maximum Vertex Cover: Approximate Kernels and Streaming Algorithms}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.27},
  URN =		{urn:nbn:de:0030-drops-161874},
  doi =		{10.4230/LIPIcs.SWAT.2022.27},
  annote =	{Keywords: Maximum vertex cover, matroid, approximate kernel, streaming}
}
Document
Near-Optimal Algorithms for Point-Line Covering Problems

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

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)


Abstract
We study fundamental point-line covering problems in computational geometry, in which the input is a set S of points in the plane. The first is the Rich Lines problem, which asks for the set of all lines that each covers at least λ points from S, for a given integer parameter λ ≥ 2; this problem subsumes the 3-Points-on-Line problem and the Exact Fitting problem, which - the latter - asks for a line containing the maximum number of points. The second is the NP-hard problem Line Cover, which asks for a set of k lines that cover the points of S, for a given parameter k ∈ ℕ. Both problems have been extensively studied. In particular, the Rich Lines problem is a fundamental problem whose solution serves as a building block for several algorithms in computational geometry. For Rich Lines and Exact Fitting, we present a randomized Monte Carlo algorithm that achieves a lower running time than that of Guibas et al.’s algorithm [Computational Geometry 1996], for a wide range of the parameter λ. We derive lower-bound results showing that, for λ = Ω(√{n log n}), the upper bound on the running time of this randomized algorithm matches the lower bound that we derive on the time complexity of Rich Lines in the algebraic computation trees model. For Line Cover, we present two kernelization algorithms: a randomized Monte Carlo algorithm and a deterministic algorithm. Both algorithms improve the running time of existing kernelization algorithms for Line Cover. We derive lower-bound results showing that the running time of the randomized algorithm we present comes close to the lower bound we derive on the time complexity of kernelization algorithms for Line Cover in the algebraic computation trees model.

Cite as

Jianer Chen, Qin Huang, Iyad Kanj, and Ge Xia. Near-Optimal Algorithms for Point-Line Covering Problems. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chen_et_al:LIPIcs.STACS.2022.21,
  author =	{Chen, Jianer and Huang, Qin and Kanj, Iyad and Xia, Ge},
  title =	{{Near-Optimal Algorithms for Point-Line Covering Problems}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{21:1--21:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.21},
  URN =		{urn:nbn:de:0030-drops-158312},
  doi =		{10.4230/LIPIcs.STACS.2022.21},
  annote =	{Keywords: line cover, rich lines, exact fitting, kernelization, randomized algorithms, complexity lower bounds, algebraic computation trees}
}
Document
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
Communication Complexity of Approximate Matching in Distributed Graphs

Authors: Zengfeng Huang, Bozidar Radunovic, Milan Vojnovic, and Qin Zhang

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)


Abstract
In this paper we consider the communication complexity of approximation algorithms for maximum matching in a graph in the message-passing model of distributed computation. The input graph consists of n vertices and edges partitioned over a set of k sites. The output is an \alpha-approximate maximum matching in the input graph which has to be reported by one of the sites. We show a lower bound on the communication complexity of \Omega(\alpha^2 k n) and show that it is tight up to poly-logarithmic factors. This lower bound also applies to other combinatorial problems on graphs in the message-passing computation model, including max-flow and graph sparsification.

Cite as

Zengfeng Huang, Bozidar Radunovic, Milan Vojnovic, and Qin Zhang. Communication Complexity of Approximate Matching in Distributed Graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 460-473, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{huang_et_al:LIPIcs.STACS.2015.460,
  author =	{Huang, Zengfeng and Radunovic, Bozidar and Vojnovic, Milan and Zhang, Qin},
  title =	{{Communication Complexity of Approximate Matching in Distributed Graphs}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{460--473},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.460},
  URN =		{urn:nbn:de:0030-drops-49348},
  doi =		{10.4230/LIPIcs.STACS.2015.460},
  annote =	{Keywords: approximate maximum matching, distributed computation, communication complexity}
}
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