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arXiv · 2504.18352

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

Timothy M. Chan·Isaac M. Hair
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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.

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Timothy M. Chan, Isaac M. Hair. 2025-04-25. A Linear Time Algorithm for the Maximum Overlap of Two Convex Polygons Under Translation. https://arxiv.org/abs/2504.18352

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