A Left-to-Right Preprocessing Computation for the Boyer-Moore String Matching Algorithm

Abstract

The string matching algorithm is generally divided into two phases : the preprocessing phase to obtain the shift tables and the main matching process with the tables. In the off-line version, we computed the tables after the whole pattern has been input, while in the on-line version, we computed the tables as the new character of the pattern is input, that is, on the fly. The shift table for the Knuth-Morris-Pratt (KMP) is computed from left to right, and hence suitable for the on-line version. The d-table and Horspool table in the Boyer-Moore (BM) algorithm are also computed from left to right in linear time. We show in this paper that the dd-table for the BM algorithm can be computed in O(m log m) expected time from left to right for a random pattern, and hence can be incorporated into an on-line version.