On parameterized approximation algorithms for balanced clustering

Xiangyan Kong, Zhen Zhang () and Qilong Feng
Additional contact information
Xiangyan Kong: Central South University
Zhen Zhang: Hunan University of Technology and Business
Qilong Feng: Central South University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 50, 14 pages

Abstract: 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 $$(9+\epsilon )$$ ( 9 + ϵ ) -approximation and $$(3+\epsilon )$$ ( 3 + ϵ ) -approximation algorithms for balanced k-means and k-median respectively, improving upon the previous best approximation ratios of $$86.9+\epsilon $$ 86.9 + ϵ and $$7.2+\epsilon $$ 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.

Keywords: Approximation algorithm; Parameterized algorithm; Clustering (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-022-00980-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00980-w

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-022-00980-w

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().