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.

Abstract. Here we consider computational problems on ffi-approximate and(ffi; fl)-approximate string matching. These are two new notions of approximate matching that arise naturally in applications of computer assisted music analy-sis. We present fast, efficient and practical algorithms for these two notions of approximate string matching.

In this paper we consider several new versions of approximate string matching with gaps. The main characteristic of these new versions is the existence of gaps in the matching of a given pattern in a text. Algorithms are sketched for each version and their time and space complexity is stated. The specific versions of approximate string matching have various applications in computerized music analysis.

Normally compressed data needs to be decompressed before it is processed, but if the compression has been done in the fight way, it is often possible to search the data without having to decompress it, or at least only partially decompress it. The problem can be divided into lossless and lossy compression methods, and then in each of these cases the pattern matching can be either exact or inexact. Much work has been reported in the literature on techniques for all of these cases, including algorithms that are suitable for pattern matching for various compression methods, and compression methods designed specifically for pattern matching. This work is surveyed in this paper. The paper also exposes the important relationship between pattern matching and compression, and proposes some performance measures for compressed pattern matching algorithms. Ideas and directions for future work are also described.