k-Median Clustering Under Discrete Fréchet and Hausdorff Distances

Authors Abhinandan Nath, Erin Taylor



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Abhinandan Nath
  • Mentor Graphics, Fremont, CA, USA
Erin Taylor
  • Duke University, Durham, NC, USA

Acknowledgements

The authors would like to thank Pankaj K. Agarwal, Kamesh Munagala, and anonymous reviewers for helpful discussions and feedback.

Cite As Get BibTex

Abhinandan Nath and Erin Taylor. k-Median Clustering Under Discrete Fréchet and Hausdorff Distances. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SoCG.2020.58

Abstract

We give the first near-linear time (1+ε)-approximation algorithm for k-median clustering of polygonal trajectories under the discrete Fréchet distance, and the first polynomial time (1+ε)-approximation algorithm for k-median clustering of finite point sets under the Hausdorff distance, provided the cluster centers, ambient dimension, and k are bounded by a constant. The main technique is a general framework for solving clustering problems where the cluster centers are restricted to come from a simpler metric space. We precisely characterize conditions on the simpler metric space of the cluster centers that allow faster (1+ε)-approximations for the k-median problem. We also show that the k-median problem under Hausdorff distance is NP-Hard.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Clustering
  • k-median
  • trajectories
  • point sets
  • discrete Fréchet distance
  • Hausdorff distance

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