Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Ordering by weighted number of wins gives a good ranking for weighted tournaments
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of Kemeny elections
Theoretical Computer Science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Consensus Genetic Maps as Median Orders from Inconsistent Sources
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Aggregating inconsistent information: Ranking and clustering
Journal of the ACM (JACM)
Fixed-Parameter Algorithms for Kemeny Scores
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Improved bounds for computing Kemeny rankings
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Deterministic Pivoting Algorithms for Constrained Ranking and Clustering Problems
Mathematics of Operations Research
Fixed-parameter algorithms for Kemeny rankings
Theoretical Computer Science
Improved Parameterized Algorithms for the Kemeny Aggregation Problem
Parameterized and Exact Computation
The Clarke tax as a consensus mechanism among automated agents
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
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We present a parameterized enumeration algorithm for Kemeny Rank Aggregation, the problem of determining an optimal aggregation, a total order that is at minimum total τ-distance (kt) from the input multi-set of m total orders (votes) over a set of alternatives (candidates), where the τ-distance between two total orders is the number of pairs of candidates ordered differently. Our $O^*(4^{k_t\over m})$-time algorithm constitutes a significant improvement over the previous $O^*(36^{k_t\over m})$ upper bound. The analysis of our algorithm relies on the notion of locally-optimal aggregations, total orders whose total τ-distances from the votes do not decrease by any single swap of two candidates adjacent in the ordering. As a consequence of our approach, we provide not only an upper bound of $4^{k_t\over m}$ on the number of optimal aggregations, but also the first parameterized bound, $4^{k_t\over m}$, on the number of locally-optimal aggregations, and demonstrate that it is tight. Furthermore, since our results rely on a known relation to Weighted Directed Feedback Arc Set, we obtain new results for this problem along the way.