Optimal Algorithms for List Indexing and Subset Rank
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
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
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
Untangling Tanglegrams: Comparing Trees by Their Drawings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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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Several applications require the joint display of two phylogenetic trees whose leaves are matched by inter-tree edges. This issue arises, for example, when comparing gene trees and species trees or when studying the co-speciation of hosts and parasites. The tanglegram layout problem seeks to produce a layout of the two trees that minimizes the number of crossings between the inter-tree edges. This problem is well-studied for the case when the mappings between the leaves of the two trees is one-to-one. However, in typical biological applications, this mapping is seldom one-to-one. In this work we (i) define a generalization of the tanglegram layout problem, called the Generalized Tanglegram Layout (GTL) problem, which allows for arbitrary interconnections between the leaves of the two trees, (ii) provide efficient algorithms for the case when the layout of one tree is fixed, (iii) discuss the fixed parameter tractability and approximability of the GTL problem, (iv) formulate heuristic solutions for the GTL problem, and (v) evaluate our algorithms experimentally.