Algorithms for fair partitioning of convex polygons

In this paper we study the problem of partitioning a convex polygon P of n vertices into m   polygons of equal area and perimeter. We give an algorithm for m=2m=2 that runs in O(n)O(n) time, and an algorithm for m=2km=2k, where k   is an integer, that runs in O((2n)k)O((2n)k) time. These are the first algorithms to solve this problem.