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Computing the rotation distance between two binary trees with $n$ internal nodes efficiently (in $poly(n)$ time) is a long standing open question in the study of height balancing in tree data structures. In this paper, we initiate the study…
We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that…
It is known that the size of the largest common subtree (i.e., the maximum agreement subtree) of two independent random binary trees with $n$ given labeled leaves is of order between $n^{0.366}$ and $n^{1/2}$. We improve the lower bound to…
Throughout the last decade, we have seen much progress towards characterising and computing the minimum hybridisation number for a set P of rooted phylogenetic trees. Roughly speaking, this minimum quantifies the number of hybridisation…
In this paper it is considered rule reduct generation problem, based on Rough Set Theory. Rule Reduct Generation (RG) and Modified Rule Generation (MRG) algorithms are well-known. Alternative to these algorithms Pruning Algorithm of…
We consider the problem of estimating species trees from unrooted gene tree topologies in the presence of incomplete lineage sorting, a common phenomenon that creates gene tree heterogeneity in multilocus datasets. One popular class of…
Phylogenetic networks are notoriously difficult to reconstruct. Here we suggest that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits. This…
Within the field of phylogenetics there is great interest in distance measures to quantify the dissimilarity of two trees. Recently, a new distance measure has been proposed: the Maximum Parsimony (MP) distance. This is based on the…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…
Reconstructing the tree of life from molecular sequences is a fundamental problem in computational biology. Modern data sets often contain a large number of genes, which can complicate the reconstruction problem due to the fact that…
Motivation: Millions of genes in the modern species belong to only thousands of `gene families'. A gene family includes instances of the same gene in different species (orthologs) and duplicate genes in the same species (paralogs). Genes…
Thin spanning trees lie at the intersection of graph theory, approximation algorithms, and combinatorial optimization. They are central to the long-standing \emph{thin tree conjecture}, which asks whether every $k$-edge-connected graph…
There exist several methods dealing with the reconstruction of rooted phylogenetic networks explaining different evolutionary histories given by rooted binary phylogenetic trees. In practice, however, due to insufficient information of the…
Species tree reconstruction from genomic data is increasingly performed using methods that account for sources of gene tree discordance such as incomplete lineage sorting. One popular method for reconstructing species trees from unrooted…
Given an edge-weighted graph and a set of known seed vertices, a network scientist often desires to understand the graph relationships to explain connections between the seed vertices. When the seed set is 3 or larger Steiner minimal tree -…
We present a new method for inferring species trees from multi-copy gene trees. Our method is based on a generalization of the Robinson-Foulds (RF) distance to multi-labeled trees (mul-trees), i.e., gene trees in which multiple leaves can…
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…
We introduce our new binary tree code for neighbour search and gravitational force calculations in an N-particle system. The tree is built in a "top-down" fashion by "recursive coordinate bisection" where on each tree level we split the…
Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…
Phylogenomics, even more so than traditional phylogenetics, needs to represent the uncertainty in evolutionary trees due to systematic error. Here we illustrate the analysis of genome-scale alignments of yeast, using robust measures of the…