Edge-Finding Constraint Propagation Algorithms for Disjunctive and Cumulative Scheduling

Edge-finding bounding techniques are particular constraint propagation techniques which reason about the order in which several activities can execute on a given resource. The aim of the following paper is to provide a rather comprehensive (although necessarily incomplete) review of existing edge-finding algorithms. The simplest case of non-preemptive disjunctive scheduling is reviewed first, followed by generalizations to preemptive disjunctive and non-preemptive cumulative scheduling. A new quadratic algorithm for non-preemptive disjunctive scheduling is also introduced. This algorithm can be used in association with a traditional edge-finding algorithm, in order to update the earliest start time (or the latest end time) of an activity A, when it is shown that A cannot precede (respectively, cannot follow) all the activities in a set Ω. To our knowledge, this is the first reported algorithm to perform all the corresponding deductions in O(n) where n denotes the number of activities that require the resource under consideration.