Occurrence and Substring Heuristics for i-Matching

We consider a version of pattern matching useful in processing large musical data: matching, which consists in finding matches which are -approximate in the sense of the distance measured as maximum difference between symbols. The alphabet is an interval of integers, and the distance between two symbols , is measured as . We also consider -matching, where is a bound on the total sum of the differences. We first consider “occurrence heuristics” by adapting exact string matching algorithms to the two notions of approximate string matching. The resulting algorithms are efficient in practice. Then we consider “substring heuristics”. We present -matching algorithms fast on the average providing that the pattern is “non-flat” and the alphabet interval is large. The pattern is “flat” if its structure does not vary substantially. The algorithms, named BM1, -BM2 and -BM3 can be thought as members of the generalized Boyer-Moore family of algorithms. The algorithms are fast on average. This is the first paper on the subject, previously only “occurrence heuristics” have been considered. Our substring heuristics are much stronger and refer to larger parts of texts (not only to single positions). We use -versions of suffix tries and subword The work of these authors was partially supported by NATO grant PST.CLG.977017. The work of this author was partially supported by Welcome foundation, Royal Society and EPSRC grants. 2 Crochemore, Iliopoulos, Lecroq, Pinzon, Plandowski and Rytter / Occurrence and Substring Heuristics for -Matching graphs. Surprisingly, in the context of -matching subword graphs appear to be superior compared with compact suffix trees.