Classifying Pattern and Feature Properties to Get a $\Theta(n)$ Checker and Reformulation for Sliding Time-Series Constraints

TL;DR

The paper introduces a linear-time checker and reformulation for sliding time-series constraints, enabling efficient validation of constraints on sequences.

Contribution

It presents a novel $ ext{O}(n)$ time and space complexity method for checking and reformulating sliding time-series constraints with sum aggregators.

Findings

Achieved $ ext{O}(n)$ complexity for constraint checking

Developed a reformulation for sliding constraints

Enhanced efficiency in time-series constraint validation

Abstract

Given, a sequence $\mathcal{X}$ of $n$ variables, a time-series constraint ctr using the Sum aggregator, and a sliding time-series constraint enforcing the constraint ctr on each sliding window of $\mathcal{X}$ of $m$ consecutive variables, we describe a $\Theta(n)$ time complexity checker, as well as a $\Theta(n)$ space complexity reformulation for such sliding constraint.