The cooling box

We propose a data structure called the “cooling box” which can be used to efficiently process the energetic reasoning [1], [4] for the parallel machine scheduling problem and the Cumulative Scheduling Problem (CuSP) [2]. In this context, each task to schedule can be represented by an object whose resource demands vary according to the time. To efficiently process some adjustments of the release dates of the tasks, it is useful to identify the highest-priority task, i.e. the one using the highest resource quantity at a given time. The aim of the proposed data structure is to obtain a time complexity of O(n² ln C) [3] for these adjustments instead of O(n²C) [1], where C is the capacity of the cumulative resource and n is the number of tasks.