Seeded Tree Alignment and Planar Tanglegram Layout

Lozano, Antoni; Pinter, Ron Y.; Rokhlenko, Oleg; Valiente, Gabriel; Ziv-Ukelson, Michal

doi:10.1007/978-3-540-74126-8_10

Cited by 14 publications

(19 citation statements)

References 19 publications

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“…From the application point of view it makes sense to insist that (a) the trees under consideration are drawn plane, that is, without edge crossings, (b) each leaf of one tree is connected by an inter-tree edge to the corresponding leaf in the other tree, and (c) the number of crossings among the inter-tree edges is minimized. Following the bioinformatics literature (e.g., [11,10]), we call this the tanglegram layout problem; Fernau et al [5] refer to it as two-tree crossing minimization.…”

Section: Introductionmentioning

confidence: 99%

Drawing Binary Tanglegrams: An Experimental Evaluation

Nöllenburg¹,

Völker²,

Wolff³

et al. 2009

2009 Proceedings of the Eleventh Workshop on Algorithm Engineering and Experiments (ALENEX)

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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 or software engineering, it is required that the individual trees are drawn crossing-free. A natural optimization problem, denoted tanglegram layout problem, is thus to minimize the number of crossings between inter-tree edges. The tanglegram layout problem is NP-hard and is currently considered both in application domains and theory. In this paper we present an experimental comparison of a recursive algorithm of Buchin et al. [2], our variant of their algorithm, the algorithm hierarchy sort of Holten and van Wijk [8], and an integer quadratic program that yields optimal solutions.

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Section: Introductionmentioning

confidence: 99%

Drawing Binary Tanglegrams: An Experimental Evaluation

Nöllenburg¹,

Völker²,

Wolff³

et al. 2009

2009 Proceedings of the Eleventh Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…Specifically, they demonstrated that the optimal ordering of the children of any internal node can be found independently. For binary trees, a number of quadratic algorithms have been developed which make use of this independence property [13][14][15]. However, minimizing the number of crossings for a general k-ary node is equivalent to finding a solution to a common graph layout problem known as the one-sided crossing minimization (OSCM) problem.…”

Section: A Important Theoretical Resultsmentioning

confidence: 99%

Quantitative visualizations of hierarchically organized data in a geographic context

Parks

Beiko

2009

2009 17th International Conference on Geoinformatics

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Here we introduce a novel quantitative technique for visualizing hierarchically organized data in a geographic context. In contrast to existing techniques, our visualization emphasizes the hierarchical relationships in the data by depicting them in a standard tree format that takes advantage of many fundamental perceptual properties. Our technique allows users to define a geographic axis and visualize how well a tree correlates with the ordering of geographical locations along this axis. This is accomplished by finding the ordering of leaf nodes, subject to the constraints of the tree topology, which minimizes the number of crossings that occur between lines that connect leaf nodes to their associated geographic locations. In this optimal layout, any crossings that occur between these lines indicate discordance between the topology of the tree and the user defined geographic axis. We have developed a branch-and-bound algorithm that allows optimal leaf orderings to be determined quickly enough to support interactive exploration of different geographic axes even for large multifurcating hierarchies. The quantitative nature of our visualization has allowed us to specify a permutation test for determining if the relationship between a tree topology and a geographic axis is statistically significant. In this paper, the utility of our visualization is demonstrated on biological data sets, but our method is applicable to any hierarchical data where geographic structure may be of interest.

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“…2) while minimizing the tangled-ness of those trees. Most tree reconciliation techniques start with an already chosen pair of cladograms, then start the untangling process to produce planar graphs (Page 1998;Lozano et al 2007;Buchin et al 2009). It depends on the user's choice of the pair of cladograms that are felt to best represent alleged associations.…”

Section: The Comparative Study Of Evolution Courses Associationmentioning

confidence: 99%

Co-evolution of products and manufacturing capabilities and application in auto-parts assembly

ElMaraghy

AlGeddawy

2011

Flex Serv Manuf J

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Automotive engine accessories change frequently due to changes in design and market demands and their assembly lines also adapt to the new product requirements and new technologies. This paper presents novel co-evolution hypotheses and a model for products and their manufacturing capabilities, inspired by the biological co-evolution, which uses Cladistics analysis of the historical development data of both. The model embodies a three-fold approach; first it identifies evolution courses of products and manufacturing capabilities, then it searches for the best matching courses to ascertain manufacturing co-evolution, and finally informs future planning guided by the established co-evolution scheme. A case study of a class of automobile engine accessories and their corresponding assembly lines are modeled and used for illustration and validation. The results reveal the existence of strong symbiotic co-evolution relationships. The use of the proposed hypotheses and coevolution model increases the efficiency of synthesizing and co-developing those accessories and their assembly lines in the future by highlighting their most evolved features and revealing the need for modifying product features and/or fully exploring the available manufacturing capabilities before acquiring new ones. Nomenclature Taxa (taxon)A product variant or a manufacturing system capability n Number of taxa in one group (products or manufacturing capabilities) N Number of characters (features) of one group T P Cladogram (evolution hypothesis) of products T M Cladogram (evolution hypothesis) of manufacturing capabilities LðTÞLength of cladogram T (i.e. the number of emergent features of products or manufacturing capabilities through an evolution hypothesis) T P min Most parsimonious product cladogram (minimum length) T M min Most parsimonious manufacturing capabilities cladogram dðT P ; T M Þ Cladistic difference between two cladograms D t dðT P min ; T M min Þ Cladistic difference between products and manufacturing capabilities over two generations at t and t ? 1 dðT tþ1 ; T t Þ Cladistic difference between one side cladograms (products or manufacturing capabilities) over two generations at t and t ? 1 iIndex for x-axis location of a node in a cladogram topology jIndex for x-axis location of a node in a cladogram topology I A reference for a specific taxon J A reference for a specific terminal K A reference for a specific character (feature) b KIJ Cost of characters emergence through an evolution path (value 1 per occurrence) X ij Evolutionary branching events representation through nodes connectivity to a cladogram topology Y IJ A representation of taxa arrangement to cladogram topology terminals C KI Accounting for the existence of a specific character in a specific taxon a Kij Accounting for nodes that do not hold a specific character c J Cost of nonconforming cladogram topologies for a specific terminal w QJ Converting nodes connectivity to indices (upper matrix triangle) x QJ Converting nodes connectivity to indices (lower matrix triangle) k ...

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Seeded Tree Alignment and Planar Tanglegram Layout

Cited by 14 publications

References 19 publications

Drawing Binary Tanglegrams: An Experimental Evaluation

Drawing Binary Tanglegrams: An Experimental Evaluation

Quantitative visualizations of hierarchically organized data in a geographic context

Co-evolution of products and manufacturing capabilities and application in auto-parts assembly

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