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

Travis Gagie, Sana Kashgouli, Gonzalo Navarro

Abstract: 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.