3 Search Results for "Huang, Hongyao"

Document
DOI: 10.4230/LIPIcs.WADS.2025.38
Clustering Point Sets Revisited

Authors: Md. Billal Hossain and Benjamin Raichel

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In the sets clustering problem one is given a collection of point sets 𝒫 = {P_1,… P_m} in ℝ^d, where for any set of k centers in ℝ^d, each P_i is assigned to its nearest center as determine by some local cost functions. The goal is then to select a set of k centers to minimize some global cost function of the corresponding local assignment costs. Specifically, we consider either summing or taking the maximum cost over all P_i, where for each P_i the cost of assigning it to a center c is either max_{p ∈ P_i} ‖c-p‖, ∑_{p ∈ P_i} ‖c-p‖, or ∑_{p ∈ P_i} ‖c-p‖². Different combinations of the global and local cost functions naturally generalize the k-center, k-median, and k-means clustering problems. In this paper, we improve the prior results for the natural generalization of k-center, give the first result for the natural generalization of k-means, and give results for generalizations of k-median and k-center which differ from those previously studied.
Cite as

Md. Billal Hossain and Benjamin Raichel. Clustering Point Sets Revisited. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hossain_et_al:LIPIcs.WADS.2025.38,
  author =	{Hossain, Md. Billal and Raichel, Benjamin},
  title =	{{Clustering Point Sets Revisited}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.38},
  URN =		{urn:nbn:de:0030-drops-242693},
  doi =		{10.4230/LIPIcs.WADS.2025.38},
  annote =	{Keywords: Clustering, k-center, k-median, k-means}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.10
Clustering with Faulty Centers

Authors: Kyle Fox, Hongyao Huang, and Benjamin Raichel

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
In this paper we introduce and formally study the problem of k-clustering with faulty centers. Specifically, we study the faulty versions of k-center, k-median, and k-means clustering, where centers have some probability of not existing, as opposed to prior work where clients had some probability of not existing. For all three problems we provide fixed parameter tractable algorithms, in the parameters k, d, and ε, that (1+ε)-approximate the minimum expected cost solutions for points in d dimensional Euclidean space. For Faulty k-center we additionally provide a 5-approximation for general metrics. Significantly, all of our algorithms have a small dependence on n. Specifically, our Faulty k-center algorithms have only linear dependence on n, while for our algorithms for Faulty k-median and Faulty k-means the dependence is still only n^(1 + o(1)).
Cite as

Kyle Fox, Hongyao Huang, and Benjamin Raichel. Clustering with Faulty Centers. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fox_et_al:LIPIcs.ISAAC.2022.10,
  author =	{Fox, Kyle and Huang, Hongyao and Raichel, Benjamin},
  title =	{{Clustering with Faulty Centers}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.10},
  URN =		{urn:nbn:de:0030-drops-172950},
  doi =		{10.4230/LIPIcs.ISAAC.2022.10},
  annote =	{Keywords: clustering, approximation, probabilistic input, uncertain input}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.6
Clustering with Neighborhoods

Authors: Hongyao Huang, Georgiy Klimenko, and Benjamin Raichel

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

Abstract
In the standard planar k-center clustering problem, one is given a set P of n points in the plane, and the goal is to select k center points, so as to minimize the maximum distance over points in P to their nearest center. Here we initiate the systematic study of the clustering with neighborhoods problem, which generalizes the k-center problem to allow the covered objects to be a set of general disjoint convex objects C rather than just a point set P. For this problem we first show that there is a PTAS for approximating the number of centers. Specifically, if r_opt is the optimal radius for k centers, then in n^O(1/ε²) time we can produce a set of (1+ε)k centers with radius ≤ r_opt. If instead one considers the standard goal of approximating the optimal clustering radius, while keeping k as a hard constraint, we show that the radius cannot be approximated within any factor in polynomial time unless P = NP, even when C is a set of line segments. When C is a set of unit disks we show the problem is hard to approximate within a factor of (√{13}-√3)(2-√3) ≈ 6.99. This hardness result complements our main result, where we show that when the objects are disks, of possibly differing radii, there is a (5+2√3)≈ 8.46 approximation algorithm. Additionally, for unit disks we give an O(n log k)+(k/ε)^O(k) time (1+ε)-approximation to the optimal radius, that is, an FPTAS for constant k whose running time depends only linearly on n. Finally, we show that the one dimensional version of the problem, even when intersections are allowed, can be solved exactly in O(n log n) time.
Cite as

Hongyao Huang, Georgiy Klimenko, and Benjamin Raichel. Clustering with Neighborhoods. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{huang_et_al:LIPIcs.ISAAC.2021.6,
  author =	{Huang, Hongyao and Klimenko, Georgiy and Raichel, Benjamin},
  title =	{{Clustering with Neighborhoods}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{6:1--6:17},
  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/entities/document/10.4230/LIPIcs.ISAAC.2021.6},
  URN =		{urn:nbn:de:0030-drops-154398},
  doi =		{10.4230/LIPIcs.ISAAC.2021.6},
  annote =	{Keywords: Clustering, Approximation, Hardness}
}
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