Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
On distances between phylogenetic trees
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings
Discrete & Computational Geometry
Optimal leaf ordering for two and a half dimensional phylogenetic tree visualisation
APVis '04 Proceedings of the 2004 Australasian symposium on Information Visualisation - Volume 35
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Comparing trees via crossing minimization
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Seeded tree alignment and planar tanglegram layout
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
Visual comparison of hierarchically organized data
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Untangling Tanglegrams: Comparing Trees by Their Drawings
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
A survey of multiple tree visualisation
Information Visualization
A satisfiability-based approach for embedding generalized tanglegrams on level graphs
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
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A binary tanglegram is a pair 〈S,T〉 of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a drawing with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number. We prove that under the Unique Games Conjecture there is no constant-factor approximation for general binary trees. We show that the problem is hard even if both trees are complete binary trees. For this case we give an O(n 3)-time 2-approximation and a new and simple fixed-parameter algorithm. We show that the maximization version of the dual problem for general binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.