OPTIMAL EXTRACTION OF IRREDUNDANT MOTIF BASES

Abstract

The problem of extracting a basis of irredundant motifs from a sequence is considered. In previous work such bases were built incrementally for all suffixes of the input string s in O(n3), where n is the length of s. Faster, non-incremental algorithms have been based on the landmark approach to string searching due to Fischer and Paterson, and exhibit respective time bounds of O(n2log n log |Σ|) and O(|Σ|n2log2n log log n), with Σ denoting the alphabet. The algorithm by Fischer and Paterson makes crucial use of the FFT, which is impractical with long sequences.The present paper describes an off-line algorithm for binary strings that takes O(n2) time. The algorithm does not need to resort to the FFT and yet its performance is optimal for finite Σ.