EFX: A Simpler Approach and an (Almost) Optimal Guarantee via Rainbow Cycle Number
Published Online:21 Oct 2024https://doi.org/10.1287/opre.2023.0433
References
- (2024) Breaking the 3/4 barrier for approximate maximin share. Proc. 2024 ACM-SIAM Sympos. Discrete Algorithms (SODA) (SIAM, Philadelphia), 74–91.Google Scholar
- (2022) An EF2X allocation protocol for restricted additive valuations. Proc. Thirty-First Internat. Joint Conf. Artificial Intelligence, IJCAI 2022 (ijcai.org), 17–23.Google Scholar
- (2023) Simplification and improvement of MMS approximation. Proc. Thirty-Second Internat. Joint Conf. Artificial Intelligence, IJCAI 2023 (AAAI Press, Palo Alto, CA).Google Scholar
- (2021) Divisible subdivisions. J. Graph Theory 98(4):623–629.Crossref, Google Scholar
- (2016) The Probabilistic Method, 4th ed. (John Wiley & Sons, Hoboken, NJ).Google Scholar
- (2020) Multiple birds with one stone: Beating 1/2 for EFX and GMMS via envy cycle elimination. Theoret. Comput. Sci. 841:94–109.Crossref, Google Scholar
- (2017) Approximation algorithms for computing maximim share allocations. ACM Trans. Algorithms 13(4):1–28.Google Scholar
- (2015) Fair assignment of indivisible objects under ordinal preferences. Artificial Intelligence 227:71–92.Crossref, Google Scholar
- (2021) Achieving proportionality up to the maximin item with indivisible goods. Thirty-Fifth AAAI Conf. Artificial Intelligence, AAAI 2021 (AAAI Press, Palo Alto, CA), 5143–5150.Google Scholar
- (2017) Approximation algorithms for maximin fair division. Daskalakis C, Babaioff M, Moulin H, eds. Proc. 2017 ACM Conf. Econom. Comput., EC ’17 (ACM, New York), 647–664.Google Scholar
- (2018) Finding fair and efficient allocations. Tardos E, Elkind E, Vohra R, eds. Proc. 2018 ACM Conf. Econom. Comput. (ACM, New York), 557–574.Google Scholar
- (2022) Fixed-point cycles and EFX allocations. Szeider S, Ganian R, Silva A, eds. 47th Internat. Sympos. Mathematical Foundations Comput. Science, MFCS, LIPIcs, vol. 241, 17:1–17:13.Google Scholar
- (2022) (Almost full) EFX exists for four agents (and beyond). Proc. 36th Conf. Artificial Intelligence (AAAI Press, Palo Alto, CA), 4826–4833.Google Scholar
- (2016) Characterizing conflicts in fair division of indivisible goods using a scale of criteria. Autonomous Agents Multi Agent Systems 30(2):259–290.Crossref, Google Scholar
- (1996) Fair Division—From Cake-Cutting to Dispute Resolution (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- (2017) Maximin envy-free division of indivisible items. Group Decision Negotiation 26(1):115–131.Crossref, Google Scholar
- (2011) The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. J. Political Econom. 119(6):1061–1103.Crossref, Google Scholar
- (2010) The multi-unit assignment problem: Theory and evidence from course allocation at Harvard. Amer. Econom. Rev. 102(5):2237–2271.Crossref, Google Scholar
- (2019) Envy-freeness up to any item with high Nash welfare: The virtue of donating items. Proc. 20th ACM Conf. Econom. Comput. (ACM, New York), 527–545.Google Scholar
- (2016) The unreasonable fairness of maximum Nash welfare. Conitzer V, Bergemann D, Chen Y, eds. Proc. 2016 ACM Conf. Econom. Comput. EC ’16 (ACM, New York), 305–322.Google Scholar
- (2020) EFX exists for three agents. Biro P, Hartline JD, Ostrovsky M, Procaccia AD, eds. EC ’20: 21st ACM Conf. Econom. Comput. (ACM, New York), 1–19.Google Scholar
- (2021a) A little charity guarantees almost envy-freeness. SIAM J. Comput. 50(4):1336–1358.Crossref, Google Scholar
- (2021b) Improving EFX guarantees through rainbow cycle number. Bior P, Chawla S, Echenique F, eds. EC ’21: 22nd ACM Conf. Econom. Comput. (ACM, New York), 310–311.Google Scholar
- (2005) Spectrum sharing for unlicensed bands. First IEEE Internat. Sympos. New Frontiers Dynam. Spectrum Access Networks (IEEE, Piscataway, NJ), 251–258.Google Scholar
- (2021) An improved approximation algorithm for maximin shares. Artificial Intelligence 300:103547.Crossref, Google Scholar
- (2019) Approximating maximin share allocations. Fineman JT, Mitzenmacher M, eds. 2nd Sympos. Simplicity Algorithms, SOSA 2019, vol. 69 (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Wadern, Germany), 20:1–20:11.Google Scholar
- (2018) Fair allocation of indivisible goods: Improvements and generalizations. Tardos E, Elkind E, Vohra R, eds. Proc. 2018 ACM Conf. Econom. Comput. (ACM, New York), 539–556.Google Scholar
- (2020) Fair division with binary valuations: One rule to rule them all. Chen X, Gravin N, Hoefer M, Mehta R, eds. Web Internet Econom. 16th Internat. Conf. WINE 2020, vol. 12495 (Springer, New York), 370–383.Google Scholar
- (2023) Rainbow cycle number and EFX allocations: (Almost) closing the gap. Proc. Thirty-Second Internat. Joint Conf. Artificial Intelligence, IJCAI 2023 (ijcai.org), 2572–2580.Google Scholar
- (2018) Fair enough: Guaranteeing approximate maximin shares. J. ACM 65(2):1–27.Google Scholar
- (2004) On approximately fair allocations of indivisible goods. Breese JS, Feigenbaum J, Seltzer MI, eds. Proc. 5th ACM Conf. Electronic Commerce (EC-2004) (ACM, New York), 125–131.Google Scholar
- (2021) Extension of additive valuations to general valuations on the existence of EFX. Mutzel P, Pagh R, Herman G, eds. 29th Annu. Eur. Sympos. Algorithms, ESA 2021 (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Wadern, Germany), 66:1–66:15.Google Scholar
- (2021) Zero sum cycles in complete digraphs. Eur. J. Combin. 98:103399.Crossref, Google Scholar
- (2019) Fair division in the internet age. Annual Rev. Econom. 11(1):407–441.Crossref, Google Scholar
- (2021) On fair and efficient allocations of indivisible goods. Thirty-Fifth AAAI Conf. Artificial Intelligence, AAAI 2021 (AAAI Press, Palo Alto, CA), 5595–5602.Google Scholar
- (2020) Almost envy-freeness with general valuations. SIAM J. Discrete Math. 34(2):1039–1068.Crossref, Google Scholar
- (1990) The fair and efficient division of the Winsor family silver. Management Sci. 36(11):1293–1301.Link, Google Scholar
- (2020) Technical perspective: An answer to fair division’s most enigmatic question. Comm. ACM 63(4):118.Google Scholar
- (1948) The problem of fair division. Econometrica 16(1):101–104.Google Scholar
- (2002) Fair allocation concepts in air traffic management. Unpublished PhD thesis, University of Maryland, College Park.Google Scholar

