Speeding up two string-Matching algorithms

Abstract

We show how to speed up two string-matching algorithms: the Boyer-Moore algorithm (BM algorithm) and its version called here the reversed-factor algorithm (the RF algorithm). The RF algorithm is based on factor graphs for the reverse of the pattern. The main feature of both algorithms is that they scan the text right-to-left from the supposed right position of the pattern, BM algorithm goes as far as the scanned segment is a suffix of the pattern, while the RF algorithm is scanning while it is a factor of the pattern. Then they make a shift of the pattern, forget the history and start again. The RF algorithm usually makes bigger shifts than BM, but is quadratic in the worst case. We show that it is enough to remember the last matched segment to speed up considerably the RF algorithm (to make linear number of comparisons with small coefficient) and to speed up BM algorithm with match-shifts (to make at most 2.n comparisons). Only a constant additional memory is needed for the search phase. We give alternative versions of an accelerated algorithm RF: the first one is based on combinatorial properties of primitive words, and two others use extensively the power of suffix trees.