Fast Algorithms for Exact String Matching

Given a pattern string P of length n and a query string T of length m, where the characters of P and T are drawn from an alphabet of size ∆, the exact string matching problem consists of finding all occurrences of P in T . For this problem, we present algorithms that in O(n∆) time preprocess P to essentially identify sparse(P ), a rarely occurring substring of P , and then use it to find occurrences of P in T efficiently. Our algorithms require a worst case search time of O(m), and expected search time of O(m/min(|sparse(P )|,∆)), where |sparse(P )| is atleast δ (i.e. the number of distinct characters in P ), and for most pattern strings it is observed to be Ω(n).