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Les matroïdes et leur implication dans l'allocation de ressources indivisibles : algorithmes d'approximation avec garantie de performance

Editor

Listed:
  • Monnot, Jérôme

Author

Listed:
  • Tlilane, Lydia

Abstract

In this thesis, we are interested in collective decision-making. The objective is to find a tradeoff solution for problems that are evaluated by multiple points of view. We consider problems having a matroid structure. Matroid theory is significant in combinatorial optimization, it helped to unify apparently separated structures like forests and matchings in graphs and it includes efficient algorithms for solving non-trivial optimization problems in polynomial time. We are interested to provide polynomial time centralized and decentralized approximation algorithms for finding a tradeoff solution which is a base of the matroid. The tradeoff solution must also be fair for all the members of the community. We are particularly interested in the issue of the fair division of indivisible goods which is central in computational social choice and that can be modeled by matroids.

Suggested Citation

  • Tlilane, Lydia, 2014. "Les matroïdes et leur implication dans l'allocation de ressources indivisibles : algorithmes d'approximation avec garantie de performance," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14807 edited by Monnot, Jérôme.
    • Handle: RePEc:dau:thesis:123456789/14807
    Note: dissertation
    as

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    File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/14807/2/2014PA090068.pdf
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    References listed on IDEAS

    as
    1. Peng Zhang & Jin-Yi Cai & Lin-Qing Tang & Wen-Bo Zhao, 2011. "Approximation and hardness results for label cut and related problems," Journal of Combinatorial Optimization, Springer, vol. 21(2), pages 192-208, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Optimisation combinatoire; Approximation polynomiale à garantie de performance; Matroïdes; Allocation de biens indivisibles; Notions d’équité; Combinatorial optimization; Polynomial time approximation with guaranteed performance; Matroids; Allocation of indivisible goods; Fairness notions;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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