The Complexity of Envy-Free Graph Cutting
Abstract
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be assigned a connected piece of this graph, and the fairness notion considered is the classical envy freeness. The problem is NP-complete, and we analyze its complexity with respect to two natural complexity measures: the number of agents and the number of edges in the graph. While the problem remains NP-hard even for instances with 2 agents, we provide a dichotomy characterizing the complexity of the problem when the number of agents is constant based on structural properties of the graph. For the latter case, we design a polynomial-time algorithm when the graph has a constant number of edges.
Keywords
Cite
@article{arxiv.2312.07043,
title = {The Complexity of Envy-Free Graph Cutting},
author = {Argyrios Deligkas and Eduard Eiben and Robert Ganian and Thekla Hamm and Sebastian Ordyniak},
journal= {arXiv preprint arXiv:2312.07043},
year = {2023}
}
Comments
Short version appeared at IJCAI 2022