Speeding Up Two String-Matching Algorithms

We show how to speed up two string-matching algorithms: the Boyer-Moore algorithm (BM algorithm), and its version called here the reverse factor algorithm (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. The BM algorithm goes as far as the scanned segment (factor) is a suffix of the pattern. The RF algorithm scans while the segment is a factor of the pattern. Both algorithms 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 (represented by two pointers to the text) to speed up the RF algorithm considerably (to make a linear number of inspections of text symbols, with small coefficient), and to speed up the BM algorithm (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 RF algorithm: the first one is based on combinatorial properties of primitive words, and the other two use the power of suffix trees extensively. The paper demonstrates the techniques to transform algorithms, and also shows interesting new applications of data structures representing all subwords of the pattern in compact form

Fast practical multi-pattern matching

The multi-pattern matching problem consists in finding all occurrences of the patterns from a finite set X in a given text T of length n. We present a new and simple algorithm combining the ideas of the Aho–Corasick algorithm and the directed acyclic word graphs. The algorithm has time complexity which is linear in the worst case (it makes at most 2n symbol comparisons) and has good average-case time complexity assuming the shortest pattern is sufficiently long. Denote the length of the shortest pattern by m, and the total length of all patterns by M. Assume that M is polynomial with respect to m, the alphabet contains at least 2 symbols and the text (in which the pattern is to be found) is random, for each position each letter occurs independently with the same probability. Then the average number of comparisons is O((n/m) · log m), which matches the lower bound of the problem. For sufficiently large values of m the algorithm has a good behavior in practice