On the Pursuit of EFX for Chores: Non-existence and Approximations

Authors: Vasilis Christoforidis, Christodoulos Santorinaios

IJCAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We resolve this question by providing a negative answer for the latter, presenting a simple construction that admits no EFX solutions for allocating six items to three agents equipped with superadditive cost functions, thus proving a separation result between goods and bads. In fact, we uncover a deeper insight, showing that the instance has unbounded approximation ratio. Moreover, we show that deciding whether an EFX allocation exists is NP-complete. On the positive side, we establish the existence of EFX allocations under general monotone cost functions when the number of items is at most n+2. We then shift our attention to additive cost functions. We employ a general framework in order to improve the approximation guarantees in the well-studied case of three additive agents, and provide several conditional approximation bounds that leverage ordinal information.
Researcher Affiliation Academia Vasilis Christoforidis1,2 and Christodoulos Santorinaios1,3 1Archimedes / Athena RC 2Aristotle University of Thessaloniki 3Athens University of Economics and Business
Pseudocode Yes Algorithm 1 Top trading envy cycle elimination algorithm, Algorithm 2 Chore approximation framework, Algorithm 3 Top n 1 disagreement
Open Source Code No The paper does not provide concrete access to source code for the methodology described in this paper.
Open Datasets No The paper is theoretical and does not conduct experiments on datasets, thus no information on publicly available datasets is provided.
Dataset Splits No The paper is theoretical and does not describe empirical experiments with data splits.
Hardware Specification No The paper is theoretical and does not describe any experiments that would require specific hardware, thus no hardware specifications are provided.
Software Dependencies No The paper does not provide specific ancillary software details with version numbers that would be needed to replicate experiments.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or training configurations.