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Drawing Binary Tanglegrams: An Experimental Evaluation
, 2009
"... A tanglegram is a pair of trees whose leaf sets are in onetoone correspondence; matching leaves are connected by intertree edges. In applications such as phylogenetics or hierarchical clustering, it is required that the individual trees are drawn crossingfree. A natural optimization problem, deno ..."
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A tanglegram is a pair of trees whose leaf sets are in onetoone correspondence; matching leaves are connected by intertree edges. In applications such as phylogenetics or hierarchical clustering, it is required that the individual trees are drawn crossingfree. A natural optimization problem, denoted tanglegram layout problem, is thus to minimize the number of crossings between intertree edges. The tanglegram layout problem is NPhard even for complete binary trees, for general binary trees the problem is hard to approximate if the Unique Games Conjecture holds. In this paper we present an extensive experimental comparison of a new and several known heuristics for the general binary case. We measure the performance of the heuristics with a simple integer linear program and a new exact branchandbound algorithm. The new heuristic returns the first solution that the branchandbound algorithm computes (in quadratic time). Surprisingly, in most cases this simple heuristic is at least as good as the best of the other heuristics.
Untangling Tanglegrams: Comparing Trees by their Drawings ∗
, 2009
"... 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 optimi ..."
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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 optimizations 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, Kauffman and Poths (FSTTCS 2005). A similar reduction to a graph crossing problem also helps to solve an open problem they posed, showing a fixedparameter tractable algorithm for minimizing the number of crossings over all dary 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 (Austral. Symp. on Info. Vis. 2004) to minimize crossings. 1
Generalized binary tanglegrams: Algorithms and applications
 In Proc. of BICOP 2009, volume 5462 of LNCS
, 2009
"... Abstract. Several applications require the joint display of two phylogenetic trees whose leaves are matched by intertree edges. This issue arises, for example, when comparing gene trees and species trees or when studying the cospeciation of hosts and parasites. The tanglegram layout problem seeks ..."
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Abstract. Several applications require the joint display of two phylogenetic trees whose leaves are matched by intertree edges. This issue arises, for example, when comparing gene trees and species trees or when studying the cospeciation 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 intertree edges. This problem is wellstudied for the case when the mappings between the leaves of the two trees is onetoone. However, in typical biological applications, this mapping is seldom onetoone. 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. 1
Coevolution in Manufacturing Systems
, 2011
"... This online database contains the fulltext of PhD dissertations and Masters ’ theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license— ..."
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This online database contains the fulltext of PhD dissertations and Masters ’ theses of University of Windsor students from 1954 forward. These documents are made available for personal study and research purposes only, in accordance with the Canadian Copyright Act and the Creative Commons license—CC BYNCND (Attribution, NonCommercial, No Derivative Works). Under this license, works must always be attributed to the copyright holder (original author), cannot be used for any commercial purposes, and may not be altered. Any other use would require the permission of the copyright holder. Students may inquire about withdrawing their dissertation and/or thesis from this database. For additional inquiries, please contact the repository administrator via email (scholarship@uwindsor.ca) or by telephone at 5192533000ext. 3208.
Edinburgh
"... The visualisation of taxonomic hierarchies has evolved from indented lists of names to techniques that can display thousands of nodes and onto hundreds of thousands of nodes over multiple taxonomies. However, challenges remain within multiple hierarchy visualisation, and for taxonomic hierarchy visu ..."
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The visualisation of taxonomic hierarchies has evolved from indented lists of names to techniques that can display thousands of nodes and onto hundreds of thousands of nodes over multiple taxonomies. However, challenges remain within multiple hierarchy visualisation, and for taxonomic hierarchy visualisation in particular. Firstly, at present, there is no support for handling specific taxonomic information such as synonymy, with current visualisations matching solely on names. Synonymy is extremely important as it reflects expert opinion on the compatibility of data held in separate taxonomies, and is needed to produce an accurate picture of taxonomic overlap. Also, current techniques for exploring large hierarchies find it difficult to convey internal reorganisations between hierarchies, with most systems showing only addition, removal or wideranging fragmentation of information between taxonomies. Finding the source of changes that have occurred within an existing structure is currently only achievable through exhaustive drilldown exploration. This paper describes work that tackles these problems, incorporating synonymy information into a model for multiple hierarchy visualisation of large taxonomies, and also detailing techniques that aid navigation for discovering structural reorganisations between hierarchies and for revealing information about nodes that lie below the effective display resolution of the hierarchy layout. Two examples on real taxonomic data sets are annotated to show the effectiveness of these techniques in operation.
TANGLEGRAMS: A REDUCTION TOOL FOR MATHEMATICAL PHYLOGENETICS
"... Abstract. Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaflabeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of study in coevolutionary analysis. Although there has b ..."
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Abstract. Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairs of leaflabeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of study in coevolutionary analysis. Although there has been considerable work on planar drawings of tanglegrams, they have not been fully explored as combinatorial objects until recently. In this paper, we describe how many discrete mathematical questions on trees “factor ” through a problem on tanglegrams, and how understanding that factoring can simplify analysis. Depending on the problem, it may be useful to consider a unordered version of tanglegrams, and/or their unrooted counterparts. For all of these definitions, we show how the isomorphism types of tanglegrams can be understood in terms of double cosets of the symmetric group, and we investigate their automorphisms. Understanding tanglegrams better will isolate the distinct problems on leaflabeled pairs of trees and reveal natural symmetries of spaces associated with such problems. 1.
THE SHAPE OF RANDOM TANGLEGRAMS
"... Abstract. A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random plane binary trees. This fact is used to derive a ..."
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Abstract. A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random plane binary trees. This fact is used to derive a number of results on the shape of random tanglegrams, including theorems on the number of cherries and generally occurrences of subtrees, the root branches, the number of automorphisms, and the height. For each of these, we obtain limiting probabilities or distributions. Finally, we investigate the number of matched cherries, for which the limiting distribution is identified as well. 1.
ON THE ENUMERATION OF TANGLEGRAMS AND TANGLED CHAINS
"... Abstract. Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula to count the number of distinct binary rooted tangl ..."
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Abstract. Tanglegrams are a special class of graphs appearing in applications concerning cospeciation and coevolution in biology and computer science. They are formed by identifying the leaves of two rooted binary trees. We give an explicit formula to count the number of distinct binary rooted tanglegrams with n matched vertices, along with a simple asymptotic formula and an algorithm for choosing a tanglegram uniformly at random. The enumeration formula is then extended to count the number of tangled chains of binary trees of any length. This includes a new formula for the number of binary trees with n leaves. We also give a conjecture for the expected number of cherries in a large randomly chosen binary tree and an extension of this conjecture to other types of trees. 1.
Schematization in Cartography, Visualization, and Computational Geometry
"... The Dagstuhl Seminar 10461 “Schematization in Cartography, Visualization, and Computational Geometry ” was held November ..."
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The Dagstuhl Seminar 10461 “Schematization in Cartography, Visualization, and Computational Geometry ” was held November