A Nearly Exact Propagation Algorithm for Energetic Reasoning in $$\mathcal O(n^2 \log n)$$

Abstract

In constraint programming, energetic reasoning constitutes a powerful start time propagation rule for cumulative scheduling problems (CuSP). This article first presents an improved time interval checking algorithm that is derived from a polyhedral model. In a second step, we extend this algorithm to an energetic reasoning propagation algorithm with time complexity \(\mathcal O(n^2 \log n)\) where n denotes the number of jobs. The idea is based on a new sweep line subroutine that efficiently evaluates energy overloads of each job on the relevant time intervals. In particular, our algorithm performs energetic reasoning propagations for every job. In addition, we show that on the vast number of relevant intervals our approach achieves the maximum possible propagations according to the energetic reasoning rule.