Real scaled matching - Amir, Amihood; Butman, Ayelet; Lewenstein, Moshe (Information processing letters, 1999)
Scaled matching refers to the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary integral scale, appears. Scaled matching is an important problem that was originally inspired by problems in Vision. However, in real life, a more natural model of scaled matching is the real scaled matching model. Real scaled matching is an extended version of the scaled matching problem allowing arbitrary real-sized scales, approximated by some function, e.g., truncation. It has been shown that the scaled matching problem can be solved in linear time. However, even though there has been follow-up work on the problem, it remained an open question whether real scaled matching could be solved faster than the simple solution of O(nm) time, where n is the text size and m is the pattern size. Using a new approach we show how to solve the real scaled matching problem in linear time.