Pruning while sweeping over task intervals

Overload checking, forbidden regions, edge finding, and not-first/not-last detection are well-known propagation rules to prune the start times of tasks which have to be processed without any interruption and overlapping on an exclusively available resource, i.e. machine. We show that these rules are correct and that "sweeping" over task intervals is an efficient and sufficient technique to achieve maximal pruning with respect to all these propagation rules. All the presented algorithms have quadratic time and linear space complexity with respect to the number of tasks. To our knowledge, this is the first presentation where the correctness of all these rules is proved and where it is shown and proved that the combination of these algorithms achieves the same pruning of the start times achieved by other algorithms with cubic time and quadratic space complexity