Fair Division of a Graph into Compact Bundles

Authors: Jayakrishnan Madathil

IJCAI 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We study the computational complexity of fair division of indivisible items in an enriched model: there is an underlying graph on the set of items. And we have to allocate the items (i.e., the vertices of the graph) to a set of agents in such a way that (a) the allocation is fair (for appropriate notions of fairness) and (b) each agent receives a bundle of items (i.e., a subset of vertices) that induces a subgraph with a specific nice structure. This model has previously been studied in the literature with the nice structure being a connected subgraph. In this paper, we propose an alternative for connectivity in fair division. We introduce compact graphs, and look for fair allocations in which each agent receives a compact bundle of items. Through compactness, we attempt to capture the idea that every agent must receive a bundle of closely related items. We prove a host of hardness and tractability results with respect to fairness concepts such as proportionality, envy-freeness and maximin share guarantee.
Researcher Affiliation Academia Jayakrishnan Madathil University of Glasgow, UK jayakrishnan.madathil@glasgow.ac.uk
Pseudocode No The paper describes algorithms and their properties (e.g., dynamic programming, FPT, XP) but does not provide a formal pseudocode block or algorithm listing.
Open Source Code No The paper does not provide any statement or link indicating that the source code for the described methodology is publicly available.
Open Datasets No The paper is theoretical and does not involve empirical evaluation on datasets.
Dataset Splits No The paper is theoretical and does not involve empirical evaluation or data splitting for validation.
Hardware Specification No The paper is theoretical and does not specify any hardware used for experiments.
Software Dependencies No The paper is theoretical and does not specify any software dependencies with version numbers for an implementation.
Experiment Setup No The paper is theoretical and does not describe an experimental setup, hyperparameters, or training configurations.