A Fast Heuristic for Exact String Matching

Abstract

Given a pattern string P of length n consisting of δ distinct characters and a query string T of length m, where the characters of P and T are drawn from an alphabet Σ of size ∆, the exact string matching problem consists of finding all occurrences of P in T . For this problem, we present a randomized heuristic that in O(nδ) time preprocesses P to identify sparse(P ), a rarely occurring substring of P , and then use it to find all occurrences of P in T efficiently. This heuristic has an expected search time of O( m min(|sparse(P )|,∆) ), where |sparse(P )| is at least δ. We also show that for a pattern string P whose characters are chosen uniformly at random from an alphabet of size ∆, E[|sparse(P )|] is Ω(∆log( 2∆ 2∆−δ )).