Incremental discovery of the irredundant motif bases for all suffixes of a string in O(n2logn) time

Compact bases formed by motifs called irredundant and capable of generating all other motifs in a sequence have been proposed in recent years and successfully tested in tasks of biosequence analysis and classi cation. Given a sequence s of n characters drawn from an alphabet Σ, the problem of extracting such a base from s had been previously solved in time O(n2 log n log |Σ|) and O(|Σ|n2 log n log log n), respectively, through resort to the FFT-based string searching by Fischer and Paterson. More recently, a solution taking time O(|Σ|n2) without resort to the FFT was also proposed. In the present paper, the problem is considered of extracting the bases of all su xes of a string incrementally. This problem was solved in previous work in time O(n3). A much faster incremental algorithm is described here, which takes time O(|Σ|n2 log n). Whereas also this algorithm does not make use of the FFT, its performance is comparable to the one exhibited by the previous FFTbased algorithms computing only one base. The implicit representation of a single base requires O(n) space, whence for nite alphabets the proposed solution is within a log n factor from optimality.