New results on the computation of median orders
Proceedings of an international symposium on Graphs and combinatorics
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Drawing graphs: methods and models
Drawing graphs: methods and models
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Breaking cycles for minimizing crossings
Journal of Experimental Algorithmics (JEA)
Approximate and dynamic rank aggregation
Theoretical Computer Science - Special papers from: COCOON 2003
An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings
Discrete & Computational Geometry
Aggregating inconsistent information: ranking and clustering
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Untangling Tanglegrams: Comparing Trees by Their Drawings
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
Crossing minimization in weighted bipartite graphs
Journal of Discrete Algorithms
Crossing minimization in weighted bipartite graphs
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
A new exact algorithm for the two-sided crossing minimization problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Bipartite graph representation of multiple decision table classifiers
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Untangling Tanglegrams: Comparing Trees by Their Drawings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Ranking and drawing in subexponential time
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
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We investigate crossing minimization problems for a set of permutations, where a crossing expresses a disarrangement between elements. The goal is a common permutation π* which minimizes the number of crossings. This is known as the Kemeny optimal aggregation problem minimizing the Kendall-τ distance. Recent interest into this problem comes from application to meta-search and spam reduction on the Web. This rank aggregation problem can be phrased as a one-sided two-layer crossing minimization problem for an edge coloured bipartite graph, where crossings are counted only for monochromatic edges. Here we introduce the max version of the crossing minimization problem, which attempts to minimize the discrimination against any permutation. We show the NP-hardness of the common and the max version for k ≥ 4 permutations (and k even), and establish a 2-2/k and a 2-approximation, respectively. For two permutations crossing minimization is solved by inspecting the drawings, whereas it remains open for three permutations.