String Periods in the Order-Preserving Model

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 $O(n)$, $O(n\log \log n)$, $O(n{\log }^2\log n\mathrm{/}\log \log \log n)$, $O(n\log n)$ depending on the type of periodicity. In the most general variant the number of different periods can be as big as $\mathrm{\Omega }(n^2)$, and a compact representation is needed. Our algorithms require novel combinatorial insight into the properties of such periods.