Approximate String Matching

Years and Authors of Summarized Original Work

1980; Sellers

1989; Landau, Vishkin

1999; Myers

2003; Crochemore, Landau, Ziv-Ukelson

2004; Fredriksson, Navarro

Problem Definition

Given a text string $T = t_{1}t_{2}\ldots t_{n}$ and a pattern string $P = p_{1}p_{2}\ldots p_{m}$, both being sequences over an alphabet $\Sigma$ of size σ, and given a distance function among strings d and a thresholdk, the approximate string matching (ASM) problem is to find all the text positions that finish the so-called approximate occurrence of P in T, that is, compute the set $\{j,\exists i,1 \leq i \leq j,d(P,t_{i}\ldots t_{j}) \leq k\}$. In the sequential version of the problem, T, P, and k are given together, whereas the algorithm can be tailored for a specific d.

The solutions to the problem vary widely depending on the distance d used. This entry focuses on a very popular one, called Levenshtein distance or edit distance, defined as the minimum number of character insertions, deletions,...