Gapped permutation pattern discovery for gene order comparisons.

The list of species whose complete DNA sequence have been read is growing steadily, and it is believed that comparative genomics is in its early days. Permutations patterns (groups of genes in some "close" proximity) on gene sequences of genomes across species is being studied under different models, to cope with this explosion of data. The challenge is to (intelligently and efficiently) analyze the genomes in the context of other genomes. In this paper, we present a generalized model that uses three notions, gapped permutation patterns (with gap g), genome clusters, via quorum, K>1, parameter, and, possible multiplicity in the patterns. The task is to automatically discover all permutation patterns (with possible multiplicity), that occur with gap g in at least K of the given m genomes. We present (log mN (I) + /Sigma/log/Sigma/N (O)) time algorithm where m is the number of sequences, each defined on Sigma, N (I) is the size of the input and N (O) is the size of the maximal gene clusters that appear in at least K of the m genomes.