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

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.

47 pages, 5 figures, 5 tables