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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…

Genome rearrangement has been an active area of research in computational comparative genomics for the last three decades. While initially mostly an interesting algorithmic endeavor, now the practical application by applying rearrangement…

Two genomes over the same set of gene families form a canonical pair when each of them has exactly one gene from each family. Different distances of canonical genomes can be derived from a structure called breakpoint graph, which represents…

During the course of evolution, an organism's genome can undergo changes that affect the large-scale structure of the genome. These changes include gene gain, loss, duplication, chromosome fusion, fission, and rearrangement. When gene gain…

The Genome Median Problem is an important problem in phylogenetic reconstruction under rearrangement models. It can be stated as follows: given three genomes, find a fourth that minimizes the sum of the pairwise rearrangement distances…

Early literature on genome rearrangement modelling views the problem of computing evolutionary distances as an inherently combinatorial one. In particular, attention was given to estimating distances using the minimum number of events…

The computation of genomic distances has been a very active field of computational comparative genomics over the last 25 years. Substantial results include the polynomial-time computability of the inversion distance by Hannenhalli and…

A classical problem in comparative genomics is to compute the rearrangement distance, that is the minimum number of large-scale rearrangements required to transform a given genome into another given genome. While the most traditional…

Genome rearrangements are events in which large blocks of DNA exchange pieces during evolution. The analysis of such events is a tool for understanding evolutionary genomics, based on finding the minimum number of rearrangements to…

Genomic distance between two genomes, i.e., the smallest number of genome rearrangements required to transform one genome into the other, is often used as a measure of evolutionary closeness of the genomes in comparative genomics studies.…

The circular median problem in the Double-Cut-and-Join (DCJ) distance asks to find, for three given genomes, a fourth circular genome that minimizes the sum of the mutual distances with the three other ones. This problem has been shown to…

Considering a pair of genomes, the goal of rearrangement distance problems is to estimate how distant these genomes are from each other based on genome rearrangements. Seminal works in genome rearrangements assumed that both genomes being…

The ability to estimate the evolutionary distance between extant genomes plays a crucial role in many phylogenomic studies. Often such estimation is based on the parsimony assumption, implying that the distance between two genomes can be…

The edit distance under the DCJ model can be computed in linear time for genomes with equal content or with Indels. But it becomes NP-Hard in the presence of duplications, a problem largely unsolved especially when Indels are considered. In…

In this paper, we study the problem of sorting unichromosomal linear genomes by prefix double-cut-and-joins (or DCJs) in both the signed and the unsigned settings. Prefix DCJs cut the leftmost segment of a genome and any other segment, and…

We study complexity of rearrangement problems in the generalized breakpoint model and settle several open questions. The model was introduced by Tannier et al. (2009) who showed that the median problem is solvable in polynomial time in the…

This paper introduces a new way to define a genome rearrangement distance, using the concept of mean first passage time from probability theory. Crucially, this distance estimate provides a genuine metric on genome space. We develop the…

Genome rearrangement is a common model for molecular evolution. In this paper, we consider the Pairwise Rearrangement problem, which takes as input two genomes and asks for the number of minimum-length sequences of permissible operations…

The study of genome rearrangement has many flavours, but they all are somehow tied to edit distances on variations of a multi-graph called the breakpoint graph. We study a weighted 2-break distance on Eulerian 2-edge-colored multi-graphs,…

A central problem in comparative genomics consists in computing a (dis-)similarity measure between two genomes, e.g. in order to construct a phylogeny. All the existing measures are defined on genomes without duplicates. However, we know…