Distant Representatives for Rectangles in the Plane

Authors Therese Biedl , Anna Lubiw, Anurag Murty Naredla, Peter Dominik Ralbovsky, Graeme Stroud

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Author Details

Therese Biedl
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada
Anna Lubiw
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada
Anurag Murty Naredla
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada
Peter Dominik Ralbovsky
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada
Graeme Stroud
  • David R. Cheriton School of Computer Science, University of Waterloo, Canada


We thank Jeffrey Shallit for help with continued fractions, and we thank anonymous reviewers for their helpful comments.

Cite AsGet BibTex

Therese Biedl, Anna Lubiw, Anurag Murty Naredla, Peter Dominik Ralbovsky, and Graeme Stroud. Distant Representatives for Rectangles in the Plane. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


The input to the distant representatives problem is a set of n objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are axis-aligned rectangles, we give polynomial time constant-factor approximation algorithms for the L₁, L₂, and L_∞ distance measures. We also prove lower bounds on the approximation factors that can be achieved in polynomial time (unless P = NP).

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Distant representatives
  • blocker shapes
  • matching
  • approximation algorithm
  • APX-hardness


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