On parameterized approximation algorithms for balanced clustering
Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the pr...
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| Published in: | Journal of combinatorial optimization Vol. 45; no. 1; p. 49 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
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Springer US
01.01.2023
Springer Nature B.V |
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| ISSN: | 1382-6905, 1573-2886 |
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| Abstract | Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the problems of balanced
k
-means and
k
-median are W[2]-hard if parameterized by
k
, implying that the existences of FPT(
k
)-time exact algorithms for these problems are unlikely. In this paper, we give FPT(
k
)-time
(
9
+
ϵ
)
-approximation and
(
3
+
ϵ
)
-approximation algorithms for balanced
k
-means and
k
-median respectively, improving upon the previous best approximation ratios of
86.9
+
ϵ
and
7.2
+
ϵ
obtained in the same time. Our main technical contribution and the crucial step in getting the improved ratios is a different random sampling method for selecting opened facilities. |
|---|---|
| AbstractList | Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the problems of balanced
k
-means and
k
-median are W[2]-hard if parameterized by
k
, implying that the existences of FPT(
k
)-time exact algorithms for these problems are unlikely. In this paper, we give FPT(
k
)-time
(
9
+
ϵ
)
-approximation and
(
3
+
ϵ
)
-approximation algorithms for balanced
k
-means and
k
-median respectively, improving upon the previous best approximation ratios of
86.9
+
ϵ
and
7.2
+
ϵ
obtained in the same time. Our main technical contribution and the crucial step in getting the improved ratios is a different random sampling method for selecting opened facilities. Balanced clustering is a frequently encountered problem in applications requiring balanced class distributions, which generalizes the standard clustering problem in that the number of clients connected to each facility is constrained by the given lower and upper bounds. It was known that both the problems of balanced k-means and k-median are W[2]-hard if parameterized by k, implying that the existences of FPT(k)-time exact algorithms for these problems are unlikely. In this paper, we give FPT(k)-time (9+ϵ)-approximation and (3+ϵ)-approximation algorithms for balanced k-means and k-median respectively, improving upon the previous best approximation ratios of 86.9+ϵ and 7.2+ϵ obtained in the same time. Our main technical contribution and the crucial step in getting the improved ratios is a different random sampling method for selecting opened facilities. |
| ArticleNumber | 49 |
| Author | Kong, Xiangyan Feng, Qilong Zhang, Zhen |
| Author_xml | – sequence: 1 givenname: Xiangyan surname: Kong fullname: Kong, Xiangyan organization: School of Computer Science and Engineering, Central South University – sequence: 2 givenname: Zhen orcidid: 0000-0002-2974-5781 surname: Zhang fullname: Zhang, Zhen email: csuzz@foxmail.com organization: School of Frontier Crossover Studies, Hunan University of Technology and Business – sequence: 3 givenname: Qilong surname: Feng fullname: Feng, Qilong organization: School of Computer Science and Engineering, Central South University |
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| Cites_doi | 10.1006/jagm.1998.0993 10.1145/2981561 10.1109/JIOT.2018.2842766 10.1145/2983633 10.1016/j.ejor.2017.04.054 10.1016/j.ins.2018.10.058 10.1007/s11081-020-09503-0 10.1137/1.9781611974331.ch56 10.1007/s11432-021-3411-7 10.24963/ijcai.2019/414 10.1049/iet-wss.2015.0069 10.1137/070699007 10.1137/18M1171321 10.1016/j.ins.2018.11.030 10.1145/2835776.2835829 10.1007/978-3-030-58150-3_51 10.1016/j.tcs.2020.07.022 10.1137/130938645 10.1145/3519935.3520011 |
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| References_xml | – reference: SiavoshiSKavianYSSharifHLoad-balanced energy efficient clustering protocol for wireless sensor networksIET Wirel Sens Syst201663677310.1049/iet-wss.2015.0069 – reference: DingHFaster balanced clusterings in high dimensionTheor Comput Sci20208422840415616310.1016/j.tcs.2020.07.0221455.68274 – reference: QiLWangRHuCLiSHeQXuXTime-aware distributed service recommendation with privacy-preservationInf Sci201948035436410.1016/j.ins.2018.11.030 – reference: Wu X, Shi F, Guo Y, Zhang Z, Huang J, Wang J (2022) An approximation algorithm for lower-bounded k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-median with constant factor. Sci China Inf Sci 65(4):140601:1–140601:9 – reference: Manurangsi P, Raghavendra P (2017) A birthday repetition theorem and complexity of approximating dense CSPs. In: Proceedings of 44th international colloquium on automata, languages, and programming (ICALP), pp 78:1–78:15 – reference: XuXDuZChenXCaiCConfidence consensus-based model for large-scale group decision making: a novel approach to managing non-cooperative behaviorsInf Sci201947741042710.1016/j.ins.2018.10.058 – reference: Lin W, He Z, Xiao M (2019) Balanced clustering: A uniform model and fast algorithm. 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