The goal of motif discovery algorithms is to efficiently find unknown recurring patterns in time series. Most available algorithms cannot utilize domain knowledge in any way which results in quadratic or at least sub-quadratic time and space complexity. For large time series datasets for which domain knowledge can be available this is a severe limitation. In this paper we define the Constrained Motif Discovery problem which enables utilization of domain knowledge into the motif discovery process. We also show that most unconstrained motif discovery problems be converted into constrained motif discovery problem using a change point detection algorithm.We provide two algorithms for solving this problem and compare their performance to state-of-the-art motif discovery algorithms on a large set of synthetic time series. The proposed algorithms can provide linear time and constant space complexity. The proposed algorithms provided four to ten folds increase in speed compared to two state of the art motif discovery algorithms without loss of accuracy and provided better noise robustness in high noise levels.