Related papers: Genome Halving by Block Interchange
In this work, we consider a restricted case of the well studied Sorting by Block Interchanges problem. We put an upper bound k on the length of the blocks (substrings) to be interchanged at each step. We call the problem Sorting by k-Block…
The genome rearrangement problem computes the minimum number of operations that are required to sort all elements of a permutation. A block-interchange operation exchanges two blocks of a permutation which are not necessarily adjacent and…
We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…
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…
We use an interesting result of probabilistic flavor concerning the product of two permutations consisting of one cycle each to find an explicit formula for the average number of block interchanges needed to sort a permutation of length…
In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. These…
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…
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…
Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in…
Genome rearrangement distances are an established method in genome comparison. Works in this area may include various rearrangement operations representing large-scale mutations, gene orientation information, the number of nucleotides in…
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 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 can be modeled as $k$-breaks, which break a genome at k positions and glue the resulting fragments in a new order. In particular, reversals, translocations, fusions, and fissions are modeled as $2$-breaks, and…
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 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…
In the context of the genome rearrangement problem, we analyze two well known models, namely the block transposition and the prefix block transposition models, by exploiting the connection with the notion of permutation pattern. More…
In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is,…
The study of genetic map linearization leads to a combinatorial hard problem, called the {\em minimum breakpoint linearization} (MBL) problem. It is aimed at finding a linearization of a partial order which attains the minimum breakpoint…
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…
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…