Time-Dependent Simple Temporal Networks: Properties and Algorithms

Simple Temporal Networks (STN) allow conjunctions of minimum and maximum distance constraints between pairs of temporal positions to be represented. This paper introduces an extension of STN called Time–dependent STN (TSTN), which covers temporal constraints for which the minimum and maximum distances required between two temporal positions x and y are not necessarily constant but may depend on the assignments of x and y. Such constraints are useful to model problems in which the duration of an activity may depend on its starting time, or problems in which the transition time required between two activities may depend on the time at which the transition is triggered. Properties of the new framework are analyzed, and standard STN solving techniques are extended to TSTN. The contributions are applied to the management of temporal constraints for so-called agile Earth observation satellites.