The Query Complexity of Cake Cutting

Authors: Simina Branzei, Noam Nisan

NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical 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 ϵ-envy-free allocations with contiguous pieces, we also give an upper bound of O(n/ϵ) and lower bound of Ω(log(1/ϵ)) queries for any number n 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.
Researcher Affiliation Academia Simina Brânzei Purdue University, USA simina.branzei@gmail.com Noam Nisan Hebrew University of Jerusalem, Israel noam@cs.huji.ac.il
Pseudocode No The paper describes procedures in text, such as 'Equitable Protocol: Player 1 slides a knife continuously across the cake, from 0 to 1.', but does not include any formally structured pseudocode or algorithm blocks.
Open Source Code No The paper is theoretical and does not mention releasing any source code for its methodology. The checklist confirms N/A for code and data reproduction.
Open Datasets No The paper is theoretical and does not involve empirical studies with datasets, training, or public data availability. The checklist confirms N/A for experiments.
Dataset Splits No The paper is theoretical and does not involve empirical studies with dataset splits for training, validation, or testing. The checklist confirms N/A for experiments.
Hardware Specification No The paper is theoretical and does not describe running experiments, therefore no hardware specifications are mentioned. The checklist confirms N/A for experiments.
Software Dependencies No The paper is theoretical and does not describe running experiments, therefore no software dependencies with version numbers are mentioned. The checklist confirms N/A for experiments.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or training settings. The checklist confirms N/A for experiments.