String Periods in the Order-Preserving Model

01/04/2018

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by   Garance Gourdel, et al.

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The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis. We introduce several types of periods in this setting (op-periods). Then we give algorithms to compute these periods in time O(n), O(n n), O(n ^2 n/ n), O(n n) depending on the type of periodicity. In the most general variant the number of different periods can be as big as Ω(n^2), and a compact representation is needed. Our algorithms require novel combinatorial insight into the properties of such periods.