Edge Finding for Cumulative Scheduling

Edge-finding algorithms for cumulative scheduling are at the core of commercial constraint-based schedulers. This paper shows that Nuijten’s edge finder for cumulative scheduling, and its derivatives, are incomplete and use an invalid dominance rule. The paper then presents a new edgefinding algorithm for cumulative resources which runs in time O(nk), where n is the number of tasks and k the number of different capacity requirements of the tasks. The new algorithm is organized in two phases and first uses dynamic programming to precompute the innermost maximization in the edge-finder specification. Finally, this paper also proposes the first extended edge-finding algorithm that runs in time O(nk), improving the running time of available algorithms.