Graphical House Allocation

Hadi Hosseini, Justin Payan, Rik Sengupta, Rohit Vaish, Vignesh Viswanathan

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


The classical house allocation problem involves assigning n houses (or items) to n agents according to their preferences. A key criteria 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 the envy value 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 broadly, we contribute several structural and computational results for various classes of graphs, including NP-hardness results for disjoint unions of paths, cycles, stars, or cliques; we also obtain fixed-parameter tractable (and, in some cases, polynomial-time) algorithms for paths, cycles, stars, cliques, and their disjoint unions. Additionally, a conceptual contribution of our work is the formulation of a structural property for disconnected graphs that we call separability which results in efficient parameterized algorithms for finding optimal allocations.

Original languageEnglish (US)
Pages (from-to)161-169
Number of pages9
JournalProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
StatePublished - 2023
Event22nd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023 - London, United Kingdom
Duration: May 29 2023Jun 2 2023

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering

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