Simple Optimal String Matching Algorithm

Abstract

We present a new string matching algorithm optimal on average (with equiprobability and independence of letters, in O(m+nlog|Σ|m/m), where n is the size of the text and m the size of the searched word, both taken on an alphabet Σ) and linear in the worst case (in O(m+n)). Of all the algorithms that verify these two complexities, ours is the simplest since it uses only a single structure, a suffix automaton. Moreover, its preprocessing phase is linearly dynamical; i.e., it is possible to search the words p1, then p1p2, p1p2p3,…,p−1p−2p−3···pi with O(∑|pi|) total preprocessing time. Among the algorithms that verify this property (for instance, the Knuth–Morris–Pratt algorithm) our algorithm is the only one to be optimal on average.