Given, a sequence 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 X of m consecutive variables, we describe a Θ(n) time complexity checker, as well as a Θ(n) space complexity reformulation for such sliding constraint.
@article{arxiv.1912.01532,
title = {Classifying Pattern and Feature Properties to Get a $\Theta(n)$ Checker and Reformulation for Sliding Time-Series Constraints},
author = {Nicolas Beldiceanu and Mats Carlsson and Claude-Guy Quimper and Maria-Isabel Restrepo-Ruiz},
journal= {arXiv preprint arXiv:1912.01532},
year = {2019}
}