We consider the fixed-size polygon placement problem: Given a set of n points and a simple polygon P with a bounded number of vertices in the plane, find a placement of P without allowing the rotation of it so that the number of points covered by it is maximized.
We transform this problem to the maximum stabbing point problem which may be considered as the dual of it. We present an O(n) space, O($n^2$) time algorithm for the fixed-size polygon placement problem using its dual one. We also extend the algorithm with the same complexities to find all of such placements.
