An efficient algorithm for the All Pairs Suffix-Prefix Problem

For a pair of strings ( S 1, S 2), define the suffix-prefix match of ( S 1, S 2) to be the longest suffix of string S 1 that matches a prefix of string S 2. The following problem is considered in this paper. Given a collection of strings S 1, S 2,..., S k of total length m, find the suffix-prefix match for each of the k( k − 1) ordered pairs of strings. We present an algorithm that solves the problem in O( m + k 2) time, for any fixed alphabet. Since the size of the input is Ω(m) and the size of the output is Ω(k 2) this solution is optimal.