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 an
(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 suggest that for polygons that are "close" to being convex, the problem
can be solved (approximately), in near linear time