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Motivated by the problem in computational biology of reconstructing the series of chromosome inversions by which one organism evolved from another, we consider the problem of computing the shortest series of reversals that transform one permutation to another. The permutations describe the order of genes on corresponding chromosomes, and a reversal takes an(More)
The inference of genome rearrangement requires detailed gene maps of related species. For most multichromosomal species, however , knowledge of chromosomal assignment of genes outstrips mapping data. Comparison of these species is thus a question of comparing sets of syntenic genes, without any gene order or gene orientation information. Given synteny data(More)
Multiple alignment of macromolecular sequences generalizes from N = 2 to N > or = 3 the comparison of N sequences which have diverged through the local processes of insertion, deletion and substitution. Gene-order sequences diverge through non-local genome rearrangement processes such as inversion (or reversal) and transposition. In this paper we show which(More)
We study the problem of comparing two circular chromosomes that have evolved by chromosome inversion, assuming that the order of corresponding genes is known, as well as their orientation. Determining the minimum number of inversions is equivalent to finding the minimum of reversals to sort a signed circular permutation, where a reversal takes an arbitrary(More)
We present some experiences with the problem of multiple genome comparison , analogous to multiple sequence alignment in sequence comparison, under the inversion and transposition distance metrics, given a xed phylogeny. We rst describe a heuristic for the case in which phylogeny is a star on three vertices and then use this to approximate the multiple(More)
The number of chromosomal segments conserved during the evolution of two species can be used to measure their genomic distance. The number of conserved segments containing ho-mologous genes can be estimated by comparing synteny relations within and between the two genomes. There are three sources of underestimation, however. The first stems from conserved(More)
MOTIVATION The total order of the genes or markers on a chromosome inherent in its representation as a signed per-mutation must often be weakened to a partial order in the case of real data. This is due to lack of resolution (where several genes are mapped to the same chromosomal position) to missing data from some of the datasets used to compile a gene(More)