, Volume 78, Issue 1, pp 147–165 | Cite as

Approximating the Maximum Overlap of Polygons under Translation

  • Sariel Har-Peled
  • Subhro RoyEmail author


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 \((1-\varepsilon )\)-approximation algorithm, for finding the translation of \(Q\), which maximizes its area of overlap with \(P\). Our algorithm runs in \(O\left( {c n}\right) \) time, where c is a constant that depends only on k and \(\varepsilon \). This suggests that for polygons that are “close” to being convex, the problem can be solved (approximately), in near linear time.


Approximation algorithms Computational geometry Polygon overlap 



The authors would like to thank the anonymous referees for their insightful comments. In particular, the improved construction of Lemma 12 was suggested by an anonymous referee.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of IllinoisUrbanaUSA

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