Tournament games and positive tournaments
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SIAM Journal on Discrete Mathematics
Computational properties of argument systems satisfying graph-theoretic constraints
Artificial Intelligence
Computing slater rankings using similarities among candidates
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Linear-time modular decomposition of directed graphs
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Cloning in elections: finding the possible winners
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Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Kemeny elections with bounded single-peaked or single-crossing width
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
On the computation of fully proportional representation
Journal of Artificial Intelligence Research
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Tournament solutions, i.e., functions that associate with each complete and asymmetric relation on a set of alternatives a non-empty subset of the alternatives, play an important role within social choice theory and the mathematical social sciences at large. Laffond et al. have shown that various tournament solutions satisfy composition-consistency, a structural invariance property based on the similarity of alternatives. We define the decomposition degree of a tournament as a parameter that reflects its decomposability and show that computing any composition-consistent tournament solution is fixed-parameter tractable with respect to the decomposition degree. Furthermore, we experimentally investigate the decomposition degree of two natural distributions of tournaments and its impact on the running time of computing the tournament equilibrium set.