Algorithmica

, Volume 78, Issue 1, pp 147–165

# Approximating the Maximum Overlap of Polygons under Translation

Article

## Abstract

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.

### Keywords

Approximation algorithms Computational geometry Polygon overlap

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