Tighter upper bounds on the exact complexity of string matching

This paper considers how many character comparisons are needed to find all occurrences of a pattern of length m in a text of length n. The main contribution is to show an upper bound of the form of n + O(n/m) character comparisons, following preprocessing. Specifically, we show an upper bound of n + 8/3(m+1)(n - m) character comparisons. This bound is achieved by an online algorithm which performs O(n) work in total and requires O(m) space and O(m²) time for preprocessing. The current best lower bound for online algorithms is n + 16/7m+27(n - m) character comparisons for m = 16k + 19, for any integer k ≥ 1, and for general algorithms is n + 2/m+3 (n - m) character comparisons, for m = 2k + 1, for any integer k ≥ 1.