On the complexity of fair house allocation

Naoyuki Kamiyama, Pasin Manurangsi, Warut Suksompong

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study fairness in house allocation, where m houses are to be allocated among n agents so that every agent receives one house. We show that maximizing the number of envy-free agents is hard to approximate to within a factor of n1−γ for any constant γ>0, and that the exact version is NP-hard even for binary utilities. Moreover, we prove that deciding whether a proportional allocation exists is computationally hard, whereas the corresponding problem for equitability can be solved efficiently.

Original languageEnglish
Pages (from-to)572-577
Number of pages6
JournalOperations Research Letters
Issue number4
Publication statusPublished - Jul 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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