A new efficient algorithm for the gene-team problem on general sequences

Identifying conserved gene clusters is an important step toward understanding the evolution of genomes and predicting the functions of genes. A famous model to capture the essential biological features of a conserved gene cluster is called the gene-team model. The problem of finding the gene teams of two general sequences is the focus of this paper. For this problem, He and Goldwasser had an efficient algorithm that requires O(mn) time using O(m + n) working space, where m and n are, respectively, the numbers of genes in the two given sequences. In this paper, a new efficient algorithm is presented. Assume m ≤ n. Let C = Σ(α)(∈)(Σ) o(1)(α)o(2)(α), where Σ is the set of distinct genes, and o(1)(α) and o(2)(α) are, respectively, the numbers of copies of α in the two given sequences. Our new algorithm requires O(min{C lg n, mn}) time using O(m + n) working space. As compared with He and Goldwasser's algorithm, our new algorithm is more practical, as C is likely to be much smaller than mn in practice. In addition, our new algorithm is output sensitive. Its running time is O(lg n) times the size of the output. Moreover, our new algorithm can be efficiently extended to find the gene teams of k general sequences in O(k C lg (n(1)n(2). . .n(k)) time, where n(i) is the number of genes in the ith input sequence.