An O(n2) algorithm for time-bound adjustments for the cumulative scheduling problem

•Energetic Reasoning is one of the most powerful methods for efficient cumulative scheduling.•Energetic Reasoning computes destructive bounds and time-bound adjustments.•Energetic Reasoning is not commonly used in practice due to its time complexity.•We present a new algorithm for time-bound adjustments for the cumulative scheduling problem.•We reduce the complexity of time-bound adjustments from O(n2log n) to O(n2). Energetic Reasoning (ER) is one of the most powerful methods for efficient cumulative scheduling. It computes destructive bounds and adjustments of task time intervals. ER is not commonly used in practice due to its time complexity, and its efficiency is highly dependent on the tightness of the time intervals. Here, we present a new algorithm with a better complexity than previous algorithms for speeding up time bound adjustments. More precisely, we show how to reduce the complexity of heads and tails adjustments from O(n2log n) to O(n2), which is an important theoretical advance.