Finding all approximate gapped palindromes

Abstract

We study the problem of finding all maximal approximate gapped palindromes in a string. More specifically, given a string S of length n, a parameter q≥0 and a threshold k>0, the problem is to identify all substrings in S of the form uvw such that (1) the Levenshtein distance between u and w r is at most k, where w r is the reverse of w and (2) v is a string of length q. The best previous work requires O(k 2 n) time. In this paper, we propose an O(kn)-time algorithm for this problem by utilizing an incremental string comparison technique. It turns out that the core technique actually solves a more general incremental string comparison problem that allows the insertion, deletion, and substitution of multiple symbols. © 2009 Springer-Verlag Berlin Heidelberg.