A simple grammar-based index for finding approximately longest common substrings.

Abstract

We show how, given positive constants $ϵ$ and $\delta$ , and an $\alpha$ -balanced straight-line program with $g$ rules for a text $T[1..n]$ , we can build an $O\left(g\right)$ -space index that, given a pattern $P[1..m]$ , in $O\left(m{\text{log}}^{\delta }g\right)$ time finds w.h.p. a substring of $P$ that occurs in $T$ and whose length is at least a ( $1-ϵ$ ) fraction of the longest common substring of $P$ and $T$ . The correctness can be ensured within the same expected query time.