Offset-Polygon Annulus Placement Problems

In this paper we address several variants of the polygon annulus placement problem: given an input polygon P and a set S of points, find an optimal placement of P that maximizes the number of points in S that fall in a certain annulus region defined by P and some offset distance ffi ? 0. We address the following variants of the problem: placement of a convex polygon as well as a simple polygon; placement by translation only, or by a translation and a rotation; off-line and on-line versions of the corresponding decision problems; and decision as well as optimization versions of the problems. We present efficient algorithms in each case