Short Communication: On Tuning the Boyer-Moore-Horspool String Searching Algorithm

In the string-searching problem we have a pattern pat, of length m, all occurrences of which are to be found in a text string text, of length n (usually n m). This problem has been studied extensively; see e.g. Reference 1. One of the fastest known algorithms is that of Boyer and Moore . 2 The theoretical time complexity (measured in the number of symbol comparisons) of the method is O ( n + rm ) in the worst case, where r is the total number of matches. The method is fast also in practice: experiments have shown that on the average the algorithm has a sublinear behaviour on the length of a typical text. The workspace needed is m + c + O (1), where c is the size of the alphabet over which text and pat are written. In the preprocessing phase of the Boyer–Moore algorithm, pat is scanned to form two tables which express how much the pattern is to be shifted forward in relation to the text when a match/mismatch is found. The first table defines a match heuristic and the second one an occurrence heuristic. The pattern is matched from right to left, i.e. starting from pat[m]. When a mismatch is found between pat[i] and the text symbol x, the match heuristic tells how much the pattern can be shifted in order to align the tested portion of the text with an identical portion in the pattern, i.e. it defines the rightmost repetition of pat[i + 1 ].. .pat[ml in pat. The occurrence heuristic expresses the rightmost occurrence of x in the pattern. The pattern is shifted according to the larger shift given by the two heuristics. The original algorithm has been analysed extensively, and several variants of it have been introduced. 3–9 The fastest variant has been shown 1 to be that of Horspool. 7 This method uses only the occurrence heuristic. Moreover, the text symbol that