Purely functional representations of catenable sorted lists
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
Theoretical Computer Science
Journal of the ACM (JACM)
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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
A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Finger trees: a simple general-purpose data structure
Journal of Functional Programming
Visualising phylogenetic trees
AUIC '06 Proceedings of the 7th Australasian User interface conference - Volume 50
Computing crossing number in linear time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Generalized Binary Tanglegrams: Algorithms and Applications
BICoB '09 Proceedings of the 1st International Conference on Bioinformatics and Computational Biology
Untangling Tanglegrams: Comparing Trees by Their Drawings
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
A Faster Fixed-Parameter Approach to Drawing Binary Tanglegrams
Parameterized and Exact Computation
GD'05 Proceedings of the 13th international conference on Graph Drawing
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
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
Generalized k-ary tanglegrams on level graphs: A satisfiability-based approach and its evaluation
Discrete Applied Mathematics
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A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in biology—to compare evolutionary histories of host and parasite species and to analyze genes of species in the same geographical area. We consider optimization problems in tanglegram drawings. We show a linear time algorithm to decide if a tanglegram admits a planar embedding by a reduction to the planar graph drawing problem. This problem was also studied by Fernau et al. [15]. A similar reduction to a graph crossing problem also helps to solve an open problem they posed, showing a fixed-parameter tractable algorithm for minimizing the number of crossings over all d-ary trees. For the case where one tree is fixed, we show an O(n{\log} n) algorithm to determine the drawing of the second tree that minimizes the number of crossings. This improves the bound from earlier methods. We introduce a new optimization criterion using Spearman's footrule distance and give an O(n^2) algorithm. We also show integer programming formulations to quickly obtain tanglegram drawings that minimize the two optimization measures discussed. We prove lower bounds on the maximum gap between the optimal solution and the heuristic of Dwyer and Schreiber [13] to minimize crossings.