On optimal approximation of orthogonal polygons

In this paper we consider the following problem in computational geometry which has applications in VLSI oorplan design and image processing. Given an orthogonal polygon P (i.e. edges are either vertical or horizontal) with n ver-tices and a positive integer m < n, determine an orthogonal polygon Q with less than or equal to m vertices such that ERROR(P; Q) is minimized, where ERROR(P; Q) is deened as the area of the symmetric diierence of the interiors of the two polygons. We present a polynomial time optimal algorithm to solve this problem for convex orthogonal polygons. Our algorithm is based on a transformation of the polygon approximation problem into a constrained shortest path problem .