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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. Hudry, Olivier, 2009. "A survey on the complexity of tournament solutions," Mathematical Social Sciences, Elsevier, vol. 57(3), pages 292-303, May.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    2. Olivier Hudry, 2015. "Complexity results for extensions of median orders to different types of remoteness," Annals of Operations Research, Springer, vol. 225(1), pages 111-123, February.
    3. Juan Aparicio & Mercedes Landete & Juan F. Monge, 2020. "A linear ordering problem of sets," Annals of Operations Research, Springer, vol. 288(1), pages 45-64, May.
    4. Burak Can & Mohsen Pourpouneh & Ton Storcken, 2021. "An axiomatic characterization of the Slater rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 835-853, May.
    5. Olivier Hudry & Bernard Monjardet, 2010. "Consensus theories: an oriented survey," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00504974, HAL.
    6. 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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