Fair Division of Land

As the world becomes more crowded, we need methods for fair division of land. The starting point of my research is the classic challenge of Fair cake-cutting. My goal is to generalize this framework in various ways in order to make it more applicable to division of land.

Online demos

Publications and working papers

  1. "Waste Makes Haste - Bounded Time Protocols for Envy-Free Cake Cutting with Free Disposal": Erel Segal-Halevi, Avinatan Hassidim, Yonatan Aumann.      ACM Transactions on Algorithms 2016, 12:1–32. Preliminary versions: AAMAS 2015 and arXiv 2016. → Presentation
  2. "Fair and Square - Cake-Cutting in Two Dimensions": Erel Segal-Halevi, Shmuel Nitzan, Avinatan Hassidim, Yonatan Aumann.      Journal of Mathematical Economics 2017, 70:1–28. “The paper is now a full treatise on the subject, with enough material to fill three or four regular length articles” (–an anonymous reviewer). Preliminary versions: EuroCG 2016 (4 pages) and arXiv 2016 (54 pages). → Live demo → Presentation
  3. "Fairly Dividing a Cake after Some Parts were Burnt in the Oven": Erel Segal-Halevi.      AAMAS 2018 and arXiv 2018. → Presentation
  4. "Fair Division of Land (Ph.D. Thesis)": Erel Segal-Halevi (supervised by Yonatan Aumann and Avinatan Hassidim).      Submitted version. → Presentation
  5. "Monotonicity and Competitive Equilibrium in Cake-cutting": Erel Segal-Halevi, Balázs Sziklai.      Economic Theory 2018, 68(2):363–401. Preliminary version: arXiv 2018. → Presentation
  6. "Redividing the Cake": Erel Segal-Halevi.      IJCAI 2018 and arXiv 2018. → Presentation
  7. "Resource-monotonicity and Population-monotonicity in Connected Cake-cutting": Erel Segal-Halevi, Balázs Sziklai.      Mathematical Social Sciences 2018, 95:19–30. Preliminary version: arXiv 2017.
  8. "Counting Blanks in Polygonal Arrangements (Previously called "Cutting a Cake without Harming the Toppings").": Arseniy Akopyan, Erel Segal-Halevi.      SIAM Journal on Discrete Mathematics 2018, 32(3):2242–-2257 and arXiv 2018.
  9. "Fair Cake-cutting among Families": Erel Segal-Halevi, Shmuel Nitzan.      Social Choice and Welfare 2019, 53(4):709–740 and arXiv 2019. → Presentation
  10. "Cake-Cutting with Different Entitlements -- How Many Cuts are Needed?": Erel Segal-Halevi.      Journal of Mathematical Analysis 2019, 123382 and arXiv 2019.
  11. "Fair and Efficient Division among Families": Sophie Bade and Erel Segal-Halevi.      arXiv 2019.
  12. "Fair Cake Cutting in Practice": Maria Kyropoulou and Josue Ortega and Erel Segal-Halevi.      EC 2019 and arXiv 2019.
  13. "Envy-Free Division of Land": Erel Segal-Halevi, Shmuel Nitzan, Avinatan Hassidim, Yonatan Aumann.      Mathematics of Operations Research 2020, 45(3):896–922 and arXiv 2019 (42 pages). Preliminary version: AAAI 2015 (8 pages). → Presentation
  14. "Fractionally balanced hypergraphs and rainbow KKM theorems": Ron Aharoni, Eli Berger, Joseph Briggs, Erel Segal-Halevi, Shira Zerbib.      arXiv 2020. → Presentation
  15. "How to Cut a Cake Fairly - A Generalization to Groups": Erel Segal-Halevi, Warut Suksompong.      American Mathematical Monthly 2021, 128:79–83 and arXiv 2020 (5 pages).
  16. "Mind the Gap - Cake Cutting With Separation": Edith Elkind, Erel Segal-Halevi, Warut Suksompong.      AAAI 2021 and arXiv 2020. → Presentation
  17. "Fair Multi-Cake Cutting (Previously called "Fair Division of an Archipelago")": Erel Segal-Halevi.      Discrete Applied Mathematics 2021, 291:15–35 and arXiv 2020 (32 pages).
  18. "Keep Your Distance - Land Division With Separation": Edith Elkind, Erel Segal-Halevi, Warut Suksompong.      IJCAI 2021 distinguished paper award and arXiv 2021. → Presentation
  19. "Graphical Cake Cutting via Maximin Share": Edith Elkind, Erel Segal-Halevi, Warut Suksompong.      IJCAJ 2021 and arXiv 2021. → Presentation
  20. "Fair Cake-Cutting Algorithms with Real Land-Value Data‏": Itay Shtechman and Rica Gonen and Erel Segal-Halevi.      JAAMAS 2021, 35:39. There is also a 2-page extended abstract.