Nested Precedence Networks with Alternatives: Recognition, Tractability, and Models

Integrated modeling of temporal and logical constraints is important for solving real-life planning and scheduling problems. Logical constrains extend the temporal formalism by reasoning about alternative activities in plans/schedules. Temporal Networks with Alternatives (TNA) were proposed to model alternative and parallel processes, however the problem of deciding which activities can be consistently included in such networks is NP-complete. Therefore a tractable subclass of Temporal Networks with Alternatives was proposed. This paper shows formal properties of these networks where precedence constraints are assumed. Namely, an algorithm that effectively recognizes whether a given network belongs to the proposed sub-class is studied and the proof of tractability is given by proposing a constraint model where global consistency is achieved via arc consistency.