# Approximate string matching and local similarity

## Abstract

The best known rigorous method for biological sequence comparison has been the algorithm of Smith and Waterman. It computes in quadratic time the highest scoring local alignment of two sequences given a (nonmetric) similarity measure and gap penalty. In this paper, we describe how the distance-based sublinear expected time algorithm of Chang and Lawler can be extended to solve efficiently the local similarity problem. We present both a new theoretical result, *polynomialspace, constant-fraction-error matching* that is provably optimal, and a practical adaptation of it that produces nearly identical results as Smith-Waterman, at speedups of 2X (PAM 120, roughly corresponding to 33% identity) to 10X (PAM 90, 50% identity) or better. Further improvements are anticipated. What makes this possible is the addition of a new constraint on *unit score* (average score per residue), which filters out both very short alignments and very long alignments with unacceptably low average. This program is part of a package called *Genome Analyst* that is being developed at CSHL.

## Keywords

Dynamic Programming Relative Entropy Dynamic Programming Algorithm Edit Distance Suffix Tree## Preview

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