Optimal-Hash Exact String Matching Algorithms

String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal values $q$ such that each $q$-grams of the pattern has a unique hash value. The new algorithms are fastest than algorithm of the HASH family for short patterns on large size alphabets.