Among the biological sequences, sequential pattern mining reveals implicit motifs/patterns, which are of functional significance and have specific structures. Small alphabets and long sequences, such as DNA and protein sequences, are difficult to handle by traditional sequential pattern mining algorithms. Furthermore, the intra- and inter-blocked gap constraints can deal with the substitutions, insertions, loops, and deletions in evolution process. Hence we propose an approach called Depth-first spelling algorithm for mining structural motifs with Intra- and inter-Block gap constraints in biological sequences (referred to as DIB). DIB has two execution steps. First, it constructs a three-dimensional table of sequences by scanning the given dataset once. Second, DIB-Exuberance generates intra- and inter-blocked gap sequential patterns. Candidate intra- and inter-blocked gap sequential pattern spelling and pattern verification are carried out by DIB-Exuberance in a depth-first manner. Intra and inter gap constraints are handled by the intra- and inter-block counting matrices. The block size matrix deals with intra- and inter-block size constraints. In biological sequences, DIB's runtime is much shorter than BASIC.
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