NDLI: Untangling Tanglegrams: Comparing Trees by Their Drawings

Content Provider	ACM Digital Library
Author	Apple, Jim Gusfield, Daniel St. john, Katherine Venkatachalam, Balaji
Abstract	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.
Starting Page	588
Ending Page	597
Page Count	10
File Format	PDF
ISSN	15455963
DOI	10.1109/TCBB.2010.57
Volume Number	7
Issue Number	4
Journal	IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-10-01
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Optimization, combinatorial algorithms, graph algorithms, trees, analysis of algorithms, phylogeny, tree comparison, graph drawing, combinatorics.
Content Type	Text
Resource Type	Article
Subject	Genetics Biotechnology Applied Mathematics

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Untangling Tanglegrams: Comparing Trees by Their Drawings

Untangling tanglegrams: comparing trees by their drawings ∗ (2009).

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