SIAM Journal on Computing
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Proceedings of the 24th annual international ACM SIGIR conference on Research and development in information retrieval
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Cranking: Combining Rankings Using Conditional Probability Models on Permutations
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Web metasearch: rank vs. score based rank aggregation methods
Proceedings of the 2003 ACM symposium on Applied computing
The complexity of Kemeny elections
Theoretical Computer Science
SIAM Journal on Discrete Mathematics
Deterministic Pivoting Algorithms for Constrained Ranking and Clustering Problems
Mathematics of Operations Research
Determining possible and necessary winners under common voting rules given partial orders
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
Fixed-parameter algorithms for Kemeny rankings
Theoretical Computer Science
Fixed-parameter tractability results for feedback set problems in tournaments
Journal of Discrete Algorithms
Towards a dichotomy for the Possible Winner problem in elections based on scoring rules
Journal of Computer and System Sciences
The nearest neighbor spearman footrule distance for bucket, interval, and partial orders
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Kernels for feedback arc set in tournaments
Journal of Computer and System Sciences
Parameterized Complexity
The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders
Journal of Combinatorial Optimization
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Comparing and ranking information is an important topic in social and information sciences, and in particular on the web. Its objective is to measure the difference of the preferences of voters on a set of candidates and to compute a consensus ranking. Commonly, each voter provides a total order or a bucket order of all candidates, where bucket orders allow ties. In this work we consider the generalization of total and bucket orders to partial orders and compare them by the nearest neighbor and the Hausdorff Kendall tau distances. For total and bucket orders these distances can be computed in $\mathcal{O}(n \log n)$ time. We show that the computation of the nearest neighbor Kendall tau distance is NP-hard, 2-approximable and fixed-parameter tractable for a total and a partial order. The computation of the Hausdorff Kendall tau distance for a total and a partial order is shown to be coNP-hard. The rank aggregation problem is known to be NP-complete for total and bucket orders, even for four voters and solvable in $\mathcal{O}(n\log n)$ for two voters. It is NP-complete for two partial orders and the nearest neighbor Kendall tau distance. For the Hausdorff Kendall tau distance it is in $\mathbf{\Sigma_2^p}$, but not in NP or coNP unless $\ensuremath{\mathbf{NP}} = \ensuremath{\mathbf{coNP}} $, even for four voters.