The document describes the Knuth-Morris-Pratt (KMP) string matching algorithm. It uses two pointers i and j to iterate through the original and input strings respectively. If the characters at i and j match, both pointers advance. If they do not match, j returns to an index stored in a preprocessing table. This allows j to skip already matched substrings, resulting in an overall O(n+m) runtime where n and m are the lengths of the original and input strings. The document provides an example run of the algorithm on two strings.