Polygon area decomposition for multiple-robot workspace division

A new polygon decomposition problem, the anchored area partition problem, which has applications to a multiple-robot terrain-covering problem is presented. This problem concerns dividing a given polygon P into n polygonal pieces, each of a specified area and each containing a certain point (site) on its boundary or in its interior. First the algorithm for the case when P is convex and contains no holes is presented. 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 input polygon IP is assumed to have been divided into a set of p convex pieces (p = 1 when P is convex), which can be done in O(vp log log vp) time, where vp is the number of vertices of p and p = O(vp), using algorithms presented elsewhere in the literature. Assuming this convex decomposition, the running time of the algorithm presented here is O(pn(2) + vn), where v is the sum of the number of vertices of the convex pieces.