Polygon Area Decomposition for Multiple-Robot Workspace Division

We present a new polygon decomposition problem, the anchored area partition problem, which has applications to a multiple-robot terrain-covering problem. This problem concerns dividing a given polygon P into n polygonal pieces, each of a speciied area and each containing a certain point (site) on its boundary. We rst present the algorithm for the case when P is convex and contains no holes. Then the generalized version that handles nonconvex and nonsimply connected polygons is presented. The algorithm uses sweep-line and divide-and-conquer techniques to construct the polygon partition. The algorithm assumes the input polygon P has been divided into a set of p convex pieces (p = 1 when P is convex) and runs in time O(pn 2 + vn), where v is the sum of the number of vertices of the convex pieces.