Algorithms for Fair Partitioning of Convex Polygons

Abstract

In this paper we study the problem of partitioning a convex polygon $P$ with $n$ vertices into $m$ polygons of equal area and perimeter and give efficient algorithms for $m = 2$ and for the more general case when $m$ is a power of 2. While it was known such a partition exists, no algorithmic results were published so far. Our algorithm for $m = 2$ is optimal and runs in $O(n)$ time, while the algorithm for $m = 2^k$, where $k \ge 2$ is an integer, runs in $O(n (2n)^{k-1})$ time. The algorithms have been implemented and tested on randomly generated convex polygons.

Daescu’s research has been partially supported by NSF award CNS1035460.