The order-preserving pattern matching problem in practice

Given a pattern x of length m and a text y of length n, both over a totally ordered alphabet, the order-preserving pattern matching (OPPM) problem consists in finding all substrings of the text with the same relative order as the pattern. The OPPM problem, which might be viewed as an approximate variant of the well-known exact pattern matching problem, has gained attention in recent years. This interesting problem finds applications in such diverse fields as time series analysis (as share prices on stock markets or weather data analysis) and musical melody matching, just to mention a few. In this paper we present two new filtering approaches which turn out to be much more effective in practice than the previously presented methods, reducing the number of false positives up to 99%. We also present a new efficient approach inspired by the well-known Skip Search algorithm for the exact string matching problem. It makes use of efficient SIMD SSE instructions for speeding up the searching phase. Experimental results show that our proposed algorithms are up to twice faster than previous solutions.