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An $Ω(n \log n)$ Randomized Lower Bound for Cutting a Cake into Proportionally Fair Pieces

Published 20 May 2026 in cs.DS and cs.DM | (2605.21829v1)

Abstract: We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use $Ω(n \log n)$ queries.

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