The Query Complexity of Cake Cutting

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Simina Branzei, Noam Nisan


We consider the query complexity of cake cutting in the standard query model and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing contiguous envy-free allocations among $n=3$ players and for computing perfect and equitable allocations with minimum number of cuts between $n=2$ players. For $\epsilon$-envy-free allocations with contiguous pieces, we also give an upper bound of $O(n/\epsilon)$ and lower bound of $\Omega(\log(1/\epsilon))$ queries for any number $n \geq 3$ of players.We also formalize moving knife procedures and show that a large subclass of this family, which captures all the known moving knife procedures, can be simulated efficiently with arbitrarily small error in the Robertson-Webb query model.