, Volume 78, Issue 1, pp 147–165

Approximating the Maximum Overlap of Polygons under Translation


DOI: 10.1007/s00453-016-0152-9

Cite this article as:
Har-Peled, S. & Roy, S. Algorithmica (2017) 78: 147. doi:10.1007/s00453-016-0152-9


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 

Funding information

Funder NameGrant NumberFunding Note
National Science Foundation
  • CCF-0915984

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of IllinoisUrbanaUSA

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