k-Median Clustering Under Discrete Fréchet and Hausdorff Distances

Authors Abhinandan Nath, Erin Taylor

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Author Details

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


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

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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)


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
  • Clustering
  • k-median
  • trajectories
  • point sets
  • discrete Fréchet distance
  • Hausdorff distance


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