Propagating Temporal Constraints for Scheduling

Jean-Francois Rit

We give in this article a general frame for propagating temporal constraints over events, these events being exclusively considered as sets of possible occurrences (SOPOs). These SOPOs are the numerical expression of an uncertainty about the exact occurrence of an event, while this exact occurrence is constrained by the possible occurrence of other events. This key-problem of scheduling is an instance of the consistent labeling problem and is known to be NP-complete. We introduce a graphical representation of SOPOs which is a useful tool to understand and help solving the problem. We give a constraint propagation algorithm which is a Waltz-type filtering algorithm. Theoretically, it does not discard all the inconsistent occurrences; however, under a number of relatively weak assumptions, the problem can be transformed into a solvable one.

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