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Let $k \geq 2$ be a constant. Given any $k$ convex polygons in the plane witha total of $n$ vertices, we present an $O(n\log^{2k-3}n)$ time algorithm thatfinds a translation of each of the polygons such that the area of intersectionof the $k$ polygons is maximized. Given one such placement, we also give an$O(n)$ time algorithm which computes the set of all translations of thepolygons which achieve this maximum.

Maximum Overlap Area of Several Convex Polygons Under Translations