Counting Sorting Scenarios and Intermediate Genomes for the Rank Distance.

An important problem in genome comparison is the genome sorting problem, that is, the problem of finding a sequence of basic operations that transforms one genome into another whose length (possibly weighted) equals the distance between them. These sequences are called optimal sorting scenarios. However, there is usually a large number of such scenarios, and a naïve algorithm is very likely to be biased towards a specific type of scenario, impairing its usefulness in real-world applications.

Generalizations of the genomic rank distance to indels.

Motivation: The rank distance model represents genome rearrangements in multi-chromosomal genomes as matrix operations, which allows the reconstruction of parsimonious histories of evolution by rearrangements. We seek to generalize this model by allowing for genomes with different gene content, to accommodate a broader range of biological contexts. We approach this generalization by using a matrix representation of genomes.

On the rank-distance median of 3 permutations.

Background: Recently, Pereira Zanetti, Biller and Meidanis have proposed a new definition of a rearrangement distance between genomes. In this formulation, each genome is represented as a matrix, and the distance d is the rank distance between these matrices. Although defined in terms of matrices, the rank distance is equal to the minimum total weight of a series of weighted operations that leads from one genome to the other, including inversions, translocations, transpositions, and others.

Median Approximations for Genomes Modeled as Matrices.

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 between it and the three input genomes. In this paper, we model genomes as matrices and study the matrix median problem using the rank distance.

Algorithms and Complexity Results for Genome Mapping Problems.

Genome mapping algorithms aim at computing an ordering of a set of genomic markers based on local ordering information such as adjacencies and intervals of markers. In most genome mapping models, markers are assumed to occur uniquely in the resulting map. We introduce algorithmic questions that consider repeats, i.