Related papers: Computing nearest neighbour interchange distances …
Tree rearrangements such as Nearest Neighbor Interchange (NNI) and Subtree Prune and Regraft (SPR) are commonly used to explore phylogenetic treespace. Computing distances based on them, however, is often intractable, so the efficiently…
Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree…
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…
Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of…
Phylogenetic networks generalize phylogenetic trees by allowing reticulate evolutionary events such as horizontal gene transfer and hybridization. Among the many subclasses of phylogenetic networks, orchard networks have attracted…
In this paper, we lay the groundwork on the comparison of phylogenetic networks based on edge contractions and expansions as edit operations, as originally proposed by Robinson and Foulds to compare trees. We prove that these operations…
The number of the non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the nearest…
We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…
A rearrangement operation makes a small graph-theoretical change to a phylogenetic network to transform it into another one. For unrooted phylogenetic trees and networks, popular rearrangement operations are tree bisection and reconnection…
A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for reconstructing trees, it is crucial to understand the size and structure of the…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
One of the main challenges in Computational Biology is to find the evolutionary distance between two organisms. In the field of comparative genomics, one way to estimate such distance is to find a minimum cost sequence of rearrangements…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
The nni-distance is a well-known distance measure for phylogenetic trees. We construct an efficient parallel approximation algorithm for the nni-distance in the CRCW-PRAM model running in O(log n) time on O(n) processors. Given two…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean…
Genome rearrangements are events where large blocks of DNA exchange places during evolution. The analysis of these events is a promising tool for understanding evolutionary genomics, providing data for phylogenetic reconstruction based on…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
This paper introduces constNJ, the first algorithm for phylogenetic reconstruction of sets of trees with constrained pairwise rooted subtree-prune regraft (rSPR) distance. We are motivated by the problem of constructing sets of trees which…