Quadratic Time Algorithms for Finding Common Intervals in Two and More Sequences

A popular approach in comparative genomics is to locate groups or clusters of orthologous genes in multiple genomes and to postulate functional association between the genes contained in such clusters. To this end, genomes are often represented as permutations of their genes, and common intervals, i.e. intervals containing the same set of genes, are interpreted as gene clusters. A disadvantage of modelling genomes as permutations is that paralogous copies of the same gene inside one genome can not be modelled. In this paper we consider a slightly modified model that allows paralogs, simply by representing genomes as sequences rather than permutations of genes. We define common intervals based on this model, and we present a simple algorithm that finds all common intervals of two sequences in Θ(n) time using Θ(n) space. Another, more complicated algorithm runs in O(n) time and uses only linear space. We also show how to extend the simple algorithm to more than two genomes, and we present results from the application of our algorithms to real data.