No, Cake Cutting Really is a Piece of Cake

Abstract

We design and analyze a deterministic cake cutting algorithm that achieves proportional fairness using a linear number of cuts. The best previous upper bound on the number of cuts for a deterministic algorithm was $O(n\log n)$, which was obtained by a natural divide-and-conquer algorithm due to Even and Paz. It has long been conjectured that $O(n\log n)$ cuts was optimal for a deterministic algorithm.