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On the complexity of Slater's problems

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  • Hudry, Olivier

Abstract

Given a tournament T, Slater's problem consists in determining a linear order (i.e. a complete directed graph without directed cycles) at minimum distance from T, the distance between T and a linear order O being the number of directed edges with different orientations in T and in O. This paper studies the complexity of this problem and of several variants of it: computing a Slater order, computing a Slater winner, checking that a given vertex is a Slater winner and so on.

Suggested Citation

  • Hudry, Olivier, 2010. "On the complexity of Slater's problems," European Journal of Operational Research, Elsevier, vol. 203(1), pages 216-221, May.
  • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:216-221
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    References listed on IDEAS

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    1. Gerhard J. Woeginger, 2003. "Banks winners in tournaments are difficult to recognize," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 523-528, June.
    2. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    3. Olivier Hudry, 2004. "A note on “Banks winners in tournaments are difficult to recognize” by G. J. Woeginger," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 113-114, August.
    4. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
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    Cited by:

    1. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories : An oriented survey," Documents de travail du Centre d'Economie de la Sorbonne 10057, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Hudry, Olivier, 2012. "On the computation of median linear orders, of median complete preorders and of median weak orders," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 2-10.

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