Strong polynomiality of resource constraint propagation
نویسندگان
چکیده
Constraint-based schedulers have been widely successful to tackle complex, disjunctive and cumulative, scheduling applications by combining tree search and constraint propagation. The constraint-propagation step is a fixpoint algorithm that applies pruning operators to tighten the release and due dates of activities using precedence or resource constraints. A variety of pruning operators for resource constraints have been proposed: they are based on edge finding or energetic reasoning and handle a single resource. Complexity results in this area are only available for a single application of these pruning operators, which is problematic for at least two reasons. On the one hand, the operators are not idempotent so a single application is rarely sufficient. On the other hand, the operators are not used in isolation but interact with each other. Existing results thus provide a very partial picture of the complexity of propagating resource constraints in constraint-based scheduling. This paper aims at addressing these limitations. It studies, for the first time, the complexity of applying pruning operators for resource constraints to a fixpoint. In particular, it shows that (1) the fixpoint of the edge finder for both release and due dates can be reached in strongly polynomial time for disjunctive scheduling; (2) the fixpoint can be reached in strongly polynomial time for updating the release dates or the due dates but not both for the cumulative scheduling; (3) the fixpoint of “reasonable” energetic operators cannot be reached in strongly polynomial time, even for disjunctive scheduling and even when only the release dates or the due dates are considered.
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ورودعنوان ژورنال:
- Discrete Optimization
دوره 4 شماره
صفحات -
تاریخ انتشار 2007