Polygon Area Decomposition for Multiple-Robot Workspace Division

Abstract

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 P 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(v P log log v P ) time, where v P is the number of vertices of P and p = O(v P ), 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.