Gapped Local Similarity Search with Provable Guarantees

1 Introduction Problem and Significance. A gapped local similarity between two sequencesis a pair of fixed length substrings, one from each sequence, that align with few mismatches and indels (insertions/deletions). We address the problem offinding all such similarities between two sequences. This is a core problem in bio-sequence similarity search, as it is a variant of the basic local alignmentproblem [29] with edit distance as the scoring function. Edit distance is simpler than a general scoring function as it treats mismatches and indels via unitcosts, nevertheless it is important and very relevant for comparing genomic DNA sequences as discussed next