A constant FPT approximation algorithm for hard-capacitated k-means

Hard-capacitated k -means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and engineering. In HCKM, one is required to partition a given n -point set into k disjoint clusters with known capacity so as to minimize the sum of within-cluster variances. It is known...

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Bibliographic Details
Published in:Optimization and engineering Vol. 21; no. 3; pp. 709 - 722
Main Authors: Xu, Yicheng, Möhring, Rolf H., Xu, Dachuan, Zhang, Yong, Zou, Yifei
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2020
Springer Nature B.V
Subjects:
Algorithms
Approximation
Combinatorial analysis
Control
Engineering
Environmental Management
Financial Engineering
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Research Article
Systems Theory
means clustering
Fixed-parameter tractable
Approximation algorithm
Capacity constraints
ISSN:1389-4420, 1573-2924
Online Access:Get full text
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Summary:Hard-capacitated k -means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and engineering. In HCKM, one is required to partition a given n -point set into k disjoint clusters with known capacity so as to minimize the sum of within-cluster variances. It is known to be at least APX-hard, and most of the work on it has been done from a meta heuristic or bi-criteria approximation perspective. To the best our knowledge, no constant approximation algorithm or existence proof of such an algorithm is known. As our main contribution, we propose an FPT( k ) approximation algorithm with constant performance guarantee for HCKM in this paper.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09503-0