A very fast substring search algorithm
Communications of the ACM
A new approach to text searching
Communications of the ACM
Fast text searching: allowing errors
Communications of the ACM
Software—Practice & Experience
A fast string searching algorithm
Communications of the ACM
Efficient string matching: an aid to bibliographic search
Communications of the ACM
Communications of the ACM
Approximate string matching with gaps
Nordic Journal of Computing
Identifying Periodic Occurrences of a Template with Applications to Protein Structures
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
A Very Fast String Matching Algorithm for Small Alphabeths and Long Patterns (Extended Abstract)
CPM '98 Proceedings of the 9th Annual Symposium on Combinatorial Pattern Matching
δ γ --- Parameterized Matching
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
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We consider a version of pattern matching useful in processing large musical data: δ-matching, which consists in finding matches which are δ-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 a, b is measured as |a - b|. We also consider (δ, γ)-matching, where γ 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 δ-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 δ- BM1, δ-BM2 and δ-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 δ-versions of suffix tries and subword graphs. Surprisingly, in the context of δ-matching subword graphs appear to be superior compared with compact suffix trees.