For all 8192 combinations of Allen's 13 relations between one task with origin oi and fixed length li and another task with origin oj and fixed length lj, we give a formula F(min(oj), max(oj), li, lj), where min(oj) and max(oj) respectively denote the earliest and the latest origin of task j, evaluating to a set of integers which are infeasible for oi for the given combination. Such forbidden regions are useful e.g. in a range-consistency maintaining propagator for an Allen constraint in finite domain constraint programming.
['Nicolas Beldiceanu', 'Mats Carlsson', 'A. Derrien', 'A. Schutt', 'P. Stuckey']
Range-consistent forbidden regions of Allen's relations