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arXiv · 2606.07238

No, Cake Cutting Really is a Piece of Cake

Stephen Arndt·Benjamin Moseley·Sungjin Im·Kirk Pruhs
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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.

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Stephen Arndt, Benjamin Moseley, Sungjin Im, Kirk Pruhs. 2026-06-05. No, Cake Cutting Really is a Piece of Cake. https://arxiv.org/abs/2606.07238

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