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

Nicolas Beldiceanu, Mats Carlsson, Claude-Guy Quimper, Maria-Isabel Restrepo-Ruiz

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.