Maximin Fairness with Mixed Divisible and Indivisible Goods
Authors: Xiaohui Bei, Shengxin Liu, Xinhang Lu, Hongao Wang5167-5175
AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study fair resource allocation when the resources contain a mixture of divisible and indivisible goods, focusing on the well-studied fairness notion of maximin share fairness (MMS). With only indivisible goods, a full MMS allocation may not exist, but a constant multiplicative approximate allocation always does. We analyze how the MMS approximation guarantee would be affected when the resources to be allocated also contain divisible goods. In particular, we show that the worst-case MMS approximation guarantee with mixed goods is no worse than that with only indivisible goods. However, there exist problem instances to which adding some divisible resources would strictly decrease the MMS approximation ratios of the instances. On the algorithmic front, we propose a constructive algorithm that will always produce an α-MMS allocation for any number of agents, where α takes values between 1/2 and 1 and is a monotonically increasing function determined by how agents value the divisible goods relative to their MMS values. |
| Researcher Affiliation | Academia | 1 Nanyang Technological University, Singapore 2 Harbin Institute of Technology, Shenzhen, China |
| Pseudocode | Yes | Algorithm 1: MIXED-MMS-HOMOGENEOUS( N, M ˆC ) Algorithm 2: The Mixed MMS Algorithm |
| Open Source Code | No | The paper does not provide any statements about releasing code or links to a code repository for the described methodology. |
| Open Datasets | No | The paper is theoretical and focuses on algorithm design and theoretical analysis of fair division. It does not involve experimental evaluation on datasets, and therefore no dataset access information is provided. |
| Dataset Splits | No | The paper is theoretical and does not describe any experiments that would use training, validation, or test splits. Therefore, no information on dataset splits is provided. |
| Hardware Specification | No | The paper describes theoretical algorithms and analysis, not empirical experiments. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper describes theoretical algorithms and analysis, not empirical experiments. It refers to specific solvers like 'CPLEX 12.4' in a general discussion of computational aspects (e.g., 'When goods are indivisible, Woeginger (1997) showed a polynomial-time approximation scheme (PTAS) to approximately compute the MMS value of an agent.'), but not as a dependency for their own experimental setup. |
| Experiment Setup | No | The paper is theoretical and focuses on algorithm design and analysis. It does not describe empirical experiments, and thus no experimental setup details, hyperparameters, or training configurations are provided. |