Speeding Up Constrained k-Means Through 2-Means

08/13/2018

∙

by   Qilong Feng, et al.

∙

0

∙

share

For the constrained 2-means problem, we present a O(dn+d(1ϵ)^O(1ϵ) n) time algorithm. It generates a collection U of approximate center pairs (c_1, c_2) such that one of pairs in U can induce a (1+ϵ)-approximation for the problem. The existing approximation scheme for the constrained 2-means problem takes O((1ϵ)^O(1ϵ)dn) time, and the existing approximation scheme for the constrained k-means problem takes O((kϵ)^O(kϵ)dn) time. Using the method developed in this paper, we point out that every existing approximating scheme for the constrained k-means so far with time C(k, n, d, ϵ) can be transformed to a new approximation scheme with time complexity C(k, n, d, ϵ)/ k^Ω(1ϵ).