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Almost Envy-Free Allocations with Connected Bundles

Author

Listed:
  • Vittorio Bilò

    (Università del Salento = University of Salento [Lecce])

  • Ioannis Caragiannis

    (CTI - Computer Technology Institute - Computer Technology Institute)

  • Michele Flammini

    (GSSI - Gran Sasso Science Institute)

  • Ayumi Igarashi

    (NII - National Institute of Informatics)

  • Gianpiero Monaco

    (DI - Dipartimento di Informatica [Italy] - UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila)

  • Dominik Peters

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Cosimo Vinci

    (UNISA - Università degli Studi di Salerno = University of Salerno)

  • William Zwicker

    (Union College)

Abstract

We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph. If the graph is a path and the utility functions are monotonic over bundles, we show the existence of EF1 allocations for at most four agents, and the existence of EF2 allocations for any number of agents; our proofs involve discrete analogues of the Stromquist's moving-knife protocol and the Su-Simmons argument based on Sperner's lemma. For identical utilities, we provide a polynomial-time algorithm that computes an EF1 allocation for any number of agents. For the case of two agents, we characterize the class of graphs that guarantee the existence of EF1 allocations as those whose biconnected components are arranged in a path; this property can be checked in linear time.

Suggested Citation

  • Vittorio Bilò & Ioannis Caragiannis & Michele Flammini & Ayumi Igarashi & Gianpiero Monaco & Dominik Peters & Cosimo Vinci & William Zwicker, 2021. "Almost Envy-Free Allocations with Connected Bundles," Post-Print hal-03834506, HAL.
    • Handle: RePEc:hal:journl:hal-03834506
    DOI: 10.1016/j.geb.2021.11.006
    Note: View the original document on HAL open archive server: https://hal.science/hal-03834506
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    References listed on IDEAS

    as
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    Keywords

    Envy-free Division; Cake-cutting; Resource Allocation;
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