Graphical House Allocation
Hadi Hosseini, Justin Payan, Rik Sengupta, Rohit Vaish, Vignesh, Viswanathan

TL;DR
This paper studies a generalized graph-based house allocation problem aiming to minimize envy among agents connected in a social network, providing structural insights and algorithms for various graph classes.
Contribution
It introduces a novel graph-based fairness model for house allocation, analyzes its complexity, and develops algorithms for specific graph classes.
Findings
NP-hardness for disjoint unions of paths, cycles, stars, or cliques
Fixed-parameter tractable algorithms for paths, cycles, stars, cliques
Polynomial-time algorithms for some graph classes
Abstract
The classical house allocation problem involves assigning houses (or items) to agents according to their preferences. A key criterion in such problems is satisfying some fairness constraints such as envy-freeness. We consider a generalization of this problem wherein the agents are placed along the vertices of a graph (corresponding to a social network), and each agent can only experience envy towards its neighbors. Our goal is to minimize the aggregate envy among the agents as a natural fairness objective, i.e., the sum of all pairwise envy values over all edges in a social graph. When agents have identical and evenly-spaced valuations, our problem reduces to the well-studied problem of linear arrangements. For identical valuations with possibly uneven spacing, we show a number of deep and surprising ways in which our setting is a departure from this classical problem. More…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications
