Approximating the Maximum Overlap of Polygons under Translation

Sariel Har-Peled, Subhro Roy

Research output: Contribution to journalArticlepeer-review


Let P and Q be two simple polygons in the plane of total complexity n, each of which can be decomposed into at most k convex parts. We present a (1 - ε) -approximation algorithm, for finding the translation of Q, which maximizes its area of overlap with P. Our algorithm runs in O(cn) time, where c is a constant that depends only on k and ε. This suggests that for polygons that are “close” to being convex, the problem can be solved (approximately), in near linear time.

Original languageEnglish (US)
Pages (from-to)147-165
Number of pages19
Issue number1
StatePublished - May 1 2017


  • Approximation algorithms
  • Computational geometry
  • Polygon overlap

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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