A local sequence alignment finds the highest-scoring pair of subsequences, allowing unmatched flanks.
The FASTA sequence search algorithm locates promising matching words and diagonals before refining a limited set of alignments. The FASTA format is a separate sequence-file convention.
BLAST, the Basic Local Alignment Search Tool, searches a sequence database for high-scoring local similarities. It uses promising short matches to guide extension rather than exhaustively evaluating every possible alignment. Reported scores and expected counts help evaluate matches under a background model; they do not directly establish common function. A short conserved domain can produce a strong local match even when the complete proteins have different overall architectures. [ref]
Basic local alignment search tool by Stephen F. Altschul and others. 1990, word hits, extension and local similarity search
The Smith-Waterman algorithm finds an optimal local sequence alignment for a specified additive scoring scheme. For a linear gap penalty , a dynamic programming score satisfiesZero permits an alignment to restart; tracing back from the largest entry to zero recovers a highest-scoring segment pair. Every optimal ending must have one of the listed final steps, which proves the recurrence by induction over the table. Optimality concerns this score, not guaranteed biological ancestry. [ref]
Identification of common molecular subsequences by Temple F. Smith and Michael S. Waterman. Smith and Waterman, 1981, Identification of common molecular subsequences
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