A Complete Landscape of EFX Allocations on Graphs: Goods, Chores and Mixed Manna
Bo Li, Minming Li, Tianze Wei, Zekai Wu, Yu Zhou

TL;DR
This paper provides a comprehensive analysis of envy-free up to any item (EFX) allocations on graphs, covering goods, chores, and mixed manna, with new results on existence, computation, and complexity under various valuation assumptions.
Contribution
It generalizes previous work by considering arbitrary items and valuations, establishing existence and computational complexity results for different EFX notions across goods, chores, and mixed manna.
Findings
Existence of EFX allocations varies by item type and valuation assumptions.
Polynomial-time algorithms are provided for certain EFX notions and settings.
Determining the existence of some EFX allocations is NP-complete.
Abstract
We study envy-free up to any item (EFX) allocations on simple graphs where vertices and edges represent agents and items respectively. An agent (vertex) is only interested in items (edges) that are incident to her and all other items always have zero marginal value to her. Christodoulou et al. [EC, 2023] first proposed this setting and studied the case of goods where every item has non-negative marginal values to every agent. In this work, we significantly generalize this setting and provide a complete set of results by considering the allocation of arbitrary items that can be goods, chores, or mixed manna under doubly monotone valuations with a mild assumption. For goods, we complement the results by Christodoulou et al. [EC, 2023] by considering another weaker notion of EFX in the literature and showing that an orientation -- a special allocation where each edge must be allocated to…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems
