Equal-area locus-based convex polygon decomposition

This paper presents an algorithm for convex polygon decomposition around a given set of locations. Given an n-vertex convex polygon P and a set X of k points positioned arbitrarily inside P, the task is to divide P into k equal area convex parts, each containing exactly one point of X. The problem is motivated by a terrain covering task for a swarm of autonomous mobile robots. The algorithm runs in time O(kn + k(2) log k).