Matched drawability of graph pairs and of graph triples

Grilli, Luca; Hong, Seok‐Hee; Liotta, Giuseppe; Meijer, Henk; Wismath, Stephen K.

doi:10.1016/j.comgeo.2010.03.005

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…Grilli et al [59] present further positive results on matched drawings. They show how to draw the pairs outerplane plus wheel, wheel plus wheel, outerplane plus maximal outerpillar (outerplane graph with triangulated inner faces and caterpillar as weak dual), and outerplane plus generalized outerpath (outerpath where some edges on the outer face may be replaced by some small subgraphs).…”

Section: Matched Drawingsmentioning

confidence: 87%

Simultaneous Embedding of Planar Graphs

Bläsius¹,

Kobourov²,

Rutter³

2012

Preprint

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Simultaneous embedding is concerned with simultaneously representing a series of graphs sharing some or all vertices. This forms the basis for the visualization of dynamic graphs and thus is an important field of research. Recently there has been a great deal of work investigating simultaneous embedding problems both from a theoretical and a practical point of view. We survey recent work on this topic.

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Section: Matched Drawingsmentioning

confidence: 87%

Simultaneous Embedding of Planar Graphs

Bläsius¹,

Kobourov²,

Rutter³

2012

Preprint

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“…For example, simultaneous geometric embedding of two or more planar graphs requires planar straight-line drawings of each of the graphs, such that common vertices have the same 2D coordinates in all drawings [7]. Matched drawings require straightline drawings of the two or more input graphs such that each common vertex has the same y-coordinate in all drawings [13].…”

Section: Previous Workmentioning

confidence: 99%

Embedding Neighborhoods Simultaneously t-SNE (ENS-t-SNE)

Huroyan¹,

Navarrete²,

Hossain³

et al. 2022

Preprint

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Fig. 1: The ENS-t-SNE embedding of a 400-point dataset with three perspectives: in each perspective there are two clusters. The dataset is created as follows: half of the points are randomly assigned to one group and the other half to the other group. The distance between points within the same group is 1 (plus small Gaussian noise) while the distance between points in different groups is 2 (plus small Gaussian noise). The left figure shows one view of the 3D ENS-t-SNE embedding; the next three figures show the corresponding three projections. The original clusters are shown in color (blue, orange), shape (square or circle) and texture (filled or not). The ENS-t-SNE algorithm recovers the clusters and creates an embedding which respects all 3 types of clusters simultaneously.

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“…Matched drawings require straight-line drawings of the two or more input graph such that each common vertex has the same y-coordinate in all drawings. Pairs of trees and triples of cycles always have a matched drawing [18]. In general, instances with no solution can be constructed from a pair of planar graphs, or even a (planar graph, tree) pair [12].…”

Section: Previous Workmentioning

confidence: 99%