A Bi-Criteria Approximation Algorithm for k-Means

We consider the classical k-means clustering problem in the setting of bi-criteria approximation, in which an algorithm is allowed to output beta*k > k clusters, and must produce a clustering with cost at most alpha times the to the cost of the optimal set of k clusters. We argue that this approach is natural in many settings, for which the exact number of clusters is a priori unknown, or unimportant up to a constant factor. We give new bi-criteria approximation algorithms, based on linear programming and local search, respectively, which attain a guarantee alpha(beta) depending on the number beta*k of clusters that may be opened. Our guarantee alpha(beta) is always at most 9 + epsilon and improves rapidly with beta (for example: alpha(2) < 2.59, and alpha(3) < 1.4). Moreover, our algorithms have only polynomial dependence on the dimension of the input data, and so are applicable in high-dimensional settings.


Editor(s):
Jansen, Klaus
Mathieu, Claire
Rolim, José D.P.
Umans, Chris
Published in:
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016), 14:1--14:20
Year:
2016
Publisher:
Dagstuhl, Germany, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
ISBN:
978-3-95977-018-7
Keywords:
Laboratories:




 Record created 2017-08-03, last modified 2018-03-17


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