A Simple Grammar-Based Index for Finding Approximately Longest Common Substrings

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