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Consensus Halving for Sets of Items

Author

Listed:
  • Paul W. Goldberg

    (Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom)

  • Alexandros Hollender

    (Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom)

  • Ayumi Igarashi

    (Principles of Informatics Research Division, National Institute of Informatics, Tokyo 101-8430, Japan)

  • Pasin Manurangsi

    (Google Research, Mountain View, California 94043)

  • Warut Suksompong

    (School of Computing, National University of Singapore, Singapore 117417, Singapore)

Abstract

Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work shows that, when the resource is represented by an interval, a consensus halving with at most n cuts always exists but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting in which the resource consists of a set of items without a linear ordering. For agents with linear and additively separable utilities, we present a polynomial-time algorithm that computes a consensus halving with at most n cuts and show that n cuts are almost surely necessary when the agents’ utilities are randomly generated. On the other hand, we show that, for a simple class of monotonic utilities, the problem already becomes polynomial parity argument, directed version–hard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus k -splitting, with which we wish to divide the resource into k parts in possibly unequal ratios and provide some consequences of our results on the problem of computing small agreeable sets.

Suggested Citation

  • Paul W. Goldberg & Alexandros Hollender & Ayumi Igarashi & Pasin Manurangsi & Warut Suksompong, 2022. "Consensus Halving for Sets of Items," Mathematics of Operations Research, INFORMS, vol. 47(4), pages 3357-3379, November.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:4:p:3357-3379
    DOI: 10.1287/moor.2021.1249
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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