139 research outputs found
Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots
Although taxonomy is often used informally to evaluate the results of
phylogenetic inference and find the root of phylogenetic trees, algorithmic
methods to do so are lacking. In this paper we formalize these procedures and
develop algorithms to solve the relevant problems. In particular, we introduce
a new algorithm that solves a "subcoloring" problem for expressing the
difference between the taxonomy and phylogeny at a given rank. This algorithm
improves upon the current best algorithm in terms of asymptotic complexity for
the parameter regime of interest; we also describe a branch-and-bound algorithm
that saves orders of magnitude in computation on real data sets. We also
develop a formalism and an algorithm for rooting phylogenetic trees according
to a taxonomy. All of these algorithms are implemented in freely-available
software.Comment: Version submitted to Algorithms for Molecular Biology. A number of
fixes from previous versio
On word-representability of polyomino triangulations
A graph is word-representable if there exists a word over the
alphabet such that letters and alternate in if and only if
is an edge in . Some graphs are word-representable, others are not.
It is known that a graph is word-representable if and only if it accepts a
so-called semi-transitive orientation.
The main result of this paper is showing that a triangulation of any convex
polyomino is word-representable if and only if it is 3-colorable. We
demonstrate that this statement is not true for an arbitrary polyomino. We also
show that the graph obtained by replacing each -cycle in a polyomino by the
complete graph is word-representable. We employ semi-transitive
orientations to obtain our results
Proper coloring of geometric hypergraphs
We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then m = 3 is sufficient. We prove that when F is the family of all homothetic copies of a given convex polygon, then such an m exists. We also study the problem in higher dimensions. © Balázs Keszegh and Dömötör Pálvölgyi
Proper Coloring of Geometric Hypergraphs
We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored so that anymember ofF that contains at leastm points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then such an m exists. We prove this in the special case when F is the family of all homothetic copies of a given convex polygon. We also study the problem in higher dimensions
Proper Coloring of Geometric Hypergraphs
We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then m=3 is sufficient. We prove that when F is the family of all homothetic copies of a given convex polygon, then such an m exists. We also study the problem in higher dimensions
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