CGG90] L. Colussi, Z. Galil, R. Giancarlo. On the Exact Complexity of String Matching. Pro- ceedings of the Thirty First Annual IEEE Symposium on the Foundations of Computer Science, 1990, 135-143.

The problem of nding all occurrences of a pattern of length m in a text of length n is considered. It is shown that the Boyer-Moore string matching algorithm performs roughly 3n comparisons and that this bound is tight up to O(n=m); more precisely, an upper bound of 3n n m comparisons is shown, as is a lower bound of 3n(1 o(1)) comparisons, as n m !1 and m!1. While the upper bound is somewhat involved, its main elements provide a quite simple proof of a 4n upper bound for the same algorithm.