Improved CLP scheduling with task intervals
Proceedings of the eleventh international conference on Logic programming
Constraint-Based Scheduling
Sweep as a Generic Pruning Technique Applied to the Non-overlapping Rectangles Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Realising the alternative resources constraint
INAP'04/WLP'04 Proceedings of the 15th international conference on Applications of Declarative Programming and Knowledge Management, and 18th international conference on Workshop on Logic Programming
Max Energy Filtering Algorithm for Discrete Cumulative Resources
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A new o(n2log n) not-first/not-last pruning algorithm for cumulative resource constraints
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Explaining the cumulative propagator
Constraints
A quadratic edge-finding filtering algorithm for cumulative resource constraints
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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Overload checking is an important method for unary as well as for cumulative resource constraints in constraint-based scheduling, as it tests for a sufficient inconsistency property. While an algorithm with time complexity ${\cal O}(n \log n)$ exists that is known for unary resource constraints, to our knowledge no such algorithms have been established to date for overload checking in cumulative constraints on n tasks. In this paper, an ${\cal O}(n \log n)$ overload checking algorithm is presented as well as its application to a more specific problem domain: the non-overlapping placement of n rectangles in a two-dimensional area. There, the runtime complexity of overload checking is ${\cal O}(n^3 \log n)$.