On the Worst-case Behavior of String-searching Algorithms

Abstract

Any algorithm for finding a pattern of length k in a string of length n must examine at least n-k+1 of the characters of the string in the worst case. By considering the pattern 00…0, we prove that this is the best possible result. Therefore there do not exist pattern matching algorithms whose worst-case behavior is "sublinear" in n (that is, linear with constant less than one), in contrast with the situation for average behavior (the Boyer-Moore algorithm is known to be sublinear on the average).