Clustering under perturbation stability in near-linear time

Journal Article

We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is α-stable if the underlying optimal clustering continues to remain optimal even when all pairwise distances are arbitrarily perturbed by a factor of at most α. Our main contribution is in presenting efficient exact algorithms for α-stable clustering instances whose running times depend near-linearly on the size of the data set when α ≥ 2 + √3. For k-center and k-means problems, our algorithms also achieve polynomial dependence on the number of clusters, k, when α ≥ 2 + √3 + ε for any constant ε > 0 in any fixed dimension. For k-median, our algorithms have polynomial dependence on k for α > 5 in any fixed dimension; and for α ≥ 2 + √3 in two dimensions. Our algorithms are simple, and only require applying techniques such as local search or dynamic programming to a suitably modified metric space, combined with careful choice of data structures.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Chang, HC; Munagala, K; Taylor, E; Welzl, E

Published Date

  • December 1, 2020

Published In

Volume / Issue

  • 182 /

International Standard Serial Number (ISSN)

  • 1868-8969

Digital Object Identifier (DOI)

  • 10.4230/LIPIcs.FSTTCS.2020.8

Citation Source

  • Scopus