The indexing for one-dimensional proportionally-scaled strings

Related problems of scaled matching and indexing, which aim to determine all positions in a text T that a pattern P   occurs in its scaled form, are considered important because of their applications to computer vision. However, previous results only focus on enlarged patterns, and do not allow shrunk patterns since they may disappear. In this paper, we give the definition and an efficient indexing algorithm for proportionally-scaled patterns that can be visually enlarged or shrunk. The proposed indexing algorithm takes O(|T|)O(|T|) time in its preprocessing phase, and achieves O(|P|+Up+logm) time in its answering phase, where |T||T|, |P||P|, UpUp, and m denote the length of T, the length of P, the number of reported positions, and the length of T under run-length representation, respectively.

Research highlights
► We give the first algorithm for indexing strings that can be enlarged or shrunk.
► The proposed algorithm is nearly optimal.
► Our definition for scaled strings considers the visual effect to human eyes.