Multiple String Matching

Years and Authors of Summarized Original Work

• 1975; Aho, Corasick

• 1979; Commentz-Walter

• 1999; Crochemore, Czumaj, Ga̧sieniec, Lecroq, Plandowski, Rytter

Problem Definition

Given a finite set of k pattern strings$\mathcal{P} =\{ P^{1},P^{2},\ldots ,P^{k}\}$ and a text string$T = t_{1}t_{2}\ldots t_{n}$, T and the Pⁱs being sequences over an alphabet Σ of size σ, the multiple string matching (MSM) problem is to find one or, more generally, all the text positions where a Pⁱ occurs in T. More precisely the problem is to compute the set $\{j\mid \exists i,P^{i} = t_{j}t_{j+1}\ldots t_{j+\vert P^{i}\vert -1}\}$, or equivalently the set $\{j\mid \exists i,P^{i} = t_{j-\vert P^{i}\vert +1}t_{j-\vert P^{i}\vert +2}\ldots t_{j}\}$. Note that reporting all the occurrences of the patterns may lead to a quadratic output (e.g., when Pⁱs and T are drawn from a one-letter alphabet). The length of the shortest pattern in $\mathcal{P}$ is denoted by $\ell\mathit{min}$. This problem is an...