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A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation

Authors Timothy M. Chan , Isaac M. Hair

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Convex polygons
  • shape matching
  • prune-and-search
  • parametric search

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Abstract

Given two convex polygons P and Q with n and m edges, the maximum overlap problem is to find a translation of P that maximizes the area of its intersection with Q. We give the first randomized algorithm for this problem with linear running time. Our result improves the previous two-and-a-half-decades-old algorithm by de Berg, Cheong, Devillers, van Kreveld, and Teillaud (1998), which ran in O((n+m)log(n+m)) time, as well as multiple recent algorithms given for special cases of the problem.

Cite As Get BibTex

Timothy M. Chan and Isaac M. Hair. A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.31

Author Details

Timothy M. Chan
  • Siebel School of Computing and Data Science, University of Illinois at Urbana-Champaign, IL, USA
Isaac M. Hair
  • Department of Computer Science, University of California, Santa Barbara, CA, USA

Funding

  • Chan, Timothy M.: Work supported by NSF Grant CCF-2224271.

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