2,767 research outputs found
Strongly Monotone Drawings of Planar Graphs
A straight-line drawing of a graph is a monotone drawing if for each pair of
vertices there is a path which is monotonically increasing in some direction,
and it is called a strongly monotone drawing if the direction of monotonicity
is given by the direction of the line segment connecting the two vertices.
We present algorithms to compute crossing-free strongly monotone drawings for
some classes of planar graphs; namely, 3-connected planar graphs, outerplanar
graphs, and 2-trees. The drawings of 3-connected planar graphs are based on
primal-dual circle packings. Our drawings of outerplanar graphs are based on a
new algorithm that constructs strongly monotone drawings of trees which are
also convex. For irreducible trees, these drawings are strictly convex
Inferring ancestral sequences in taxon-rich phylogenies
Statistical consistency in phylogenetics has traditionally referred to the
accuracy of estimating phylogenetic parameters for a fixed number of species as
we increase the number of characters. However, as sequences are often of fixed
length (e.g. for a gene) although we are often able to sample more taxa, it is
useful to consider a dual type of statistical consistency where we increase the
number of species, rather than characters. This raises some basic questions:
what can we learn about the evolutionary process as we increase the number of
species? In particular, does having more species allow us to infer the
ancestral state of characters accurately? This question is particularly
relevant when sequence site evolution varies in a complex way from character to
character, as well as for reconstructing ancestral sequences. In this paper, we
assemble a collection of results to analyse various approaches for inferring
ancestral information with increasing accuracy as the number of taxa increases.Comment: 32 pages, 5 figures, 1 table
Monotone Drawings of -Inner Planar Graphs
A -inner planar graph is a planar graph that has a plane drawing with at
most {internal vertices}, i.e., vertices that do not lie on the boundary of
the outer face of its drawing. An outerplanar graph is a -inner planar
graph. In this paper, we show how to construct a monotone drawing of a
-inner planar graph on a grid. In the special case
of an outerplanar graph, we can produce a planar monotone drawing on a grid, improving previously known results.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018). Revised introductio
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