Local Sequence Alignment Against a Database Problem

Local Sequence Algignment. The local sequence alignment problem is defined as follows: Given two strings S = s 1. .. s n and T = t 1. .. t m , a substitution matrix Score and an insertion/deletion penalty δ, find a pair of substrings s i. .. s i+k of S and t j. .. t j+l of T that have the best overall alignment score, and return the best alignment for them. Local Sequence Algignment against a database. The local sequence alignment against a database problem extends the local sequence alignment problem by introducing multiple strings against which a single query string is a aligned: Given a query string S = s 1. .. s n , and a collection of strings D = {D 1 ,. .. D M } (usually referred to as a sequence database), a substitution matrix Score and an insertion/deletion penalty δ, find the best local alignments of S with any/all strings from D. Note. Smith-Waterman algorithm for local sequence alignment has runtime complexity O(nm). When extended to a database D of M strings of average length m, the runtime complexity of applying Smith-Waterman to each pair of strings S, D j becomes O(nmM). This is unacceptable for practical applications. Idea. Smith-Waterman algorithm guarantees the correct solution-i.e., always finds the best local alignment between a pair of strings. We can sacrifice the accuracy in lieu of efficiency by requiring our algorithm to find pretty good local alignments against a database fast. Approximation algorithms. We consider two approximation algorithms: FASTA and BLAST. Both algorithms are faster than Smith-Waterman. Both do not guarantee that they return the best possible alignments. However, for both 1