Possible winner problems on partial tournaments: a parameterized study

Yongjie Yang () and Jiong Guo ()
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Yongjie Yang: Universität des Saarlandes
Jiong Guo: Shandong University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 3, No 5, 882-896

Abstract: 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.

Keywords: Tournament solution; Banks set; Uncovered set; Parameterized complexity; Fixed-parameter tractable (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0012-1

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