Towards a dichotomy for the Possible Winner problem in elections based on scoring rules
Journal of Computer and System Sciences
Average parameterization and partial kernelization for computing medians
Journal of Computer and System Sciences
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Average parameterization and partial kernelization for computing medians
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Parameterized enumeration of (locally-) optimal aggregations
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Kemeny elections with bounded single-peaked or single-crossing width
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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We give improvements over fixed parameter tractable (FPT) algorithms to solve the Kemeny aggregation problem, where the task is to summarize a multi-set of preference lists, called votes, over a set of alternatives, called candidates, into a single preference list that has the minimum total 驴-distance from the votes. The 驴-distance between two preference lists is the number of pairs of candidates that are ordered differently in the two lists. We study the problem for preference lists that are total orders. We develop algorithms of running times $O^*(1.403^{k_t})$, $O^*(5.823^{k_t/m})\leq O^*(5.823^{k_{avg}})$ and $O^*(4.829^{k_{max}})$ for the problem, ignoring the polynomial factors in the O * notation, where k t is the optimum total 驴-distance, m is the number of votes, and k avg (resp. k max ) is the average (resp. maximum) over pairwise 驴-distances of votes. Our algorithms improve the best previously known running times of $O^*(1.53^{k_t})$ and $O^*(16^{k_{avg}})\leq O^*(16^{k_{max}})$ [3,4], which also implies an $O^*(16^{2k_t/m})$ running time. We also show how to enumerate all optimal solutions in $O^*(36^{k_t/m}) \leq O^*(36^{k_{avg}})$ time.