String Periods in the Order-Preserving Model

TL;DR

This paper explores various types of periods in the order-preserving model, providing efficient algorithms for their computation and addressing the complexity of representing numerous periods.

Contribution

It introduces multiple types of op-periods and develops algorithms with optimal time complexities for their detection in the order-preserving model.

Findings

Algorithms for op-periods run in linear or near-linear time.

The number of op-periods can be quadratic, requiring compact representations.

Novel combinatorial insights underpin the algorithms.

Abstract

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