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Possible winner problems on partial tournaments: a parameterized study

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  • Yongjie Yang

    (Universität des Saarlandes)

  • Jiong Guo

    (Shandong University)

Abstract

We study possible winner problems related to the uncovered set and the Banks set on partial tournaments from the viewpoint of parameterized complexity. We first study a problem where given a partial tournament D and a subset X of vertices, we are asked to add some arcs to D such that all vertices in X are included in the uncovered set. We focus on two parameterizations: parameterized by |X| and parameterized by the number of arcs to be added. In addition, we study a parameterized variant of the problem which is to determine whether all vertices of X can be included in the uncovered set by reversing at most k arcs. Finally, we study some parameterizations of a possible winner problem on partial tournaments, where we are given a partial tournament D and a distinguished vertex p, and asked whether D has a maximal transitive subtournament with p being the 0-indegree vertex. These parameterized problems are related to the Banks set. We achieve $$\mathcal {XP}$$ XP results, $$\mathcal {W}$$ W -hardness results as well as $$\mathcal {FPT}$$ FPT results along with a kernelization lower bound for the problems studied in this paper.

Suggested Citation

  • Yongjie Yang & Jiong Guo, 2017. "Possible winner problems on partial tournaments: a parameterized study," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 882-896, April.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:3:d:10.1007_s10878-016-0012-1
    DOI: 10.1007/s10878-016-0012-1
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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.
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    Cited by:

    1. Yongjie Yang & Dinko Dimitrov, 2021. "Weak transitivity and agenda control for extended stepladder tournaments," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 27-37, April.

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