The essence of constraint propagation
Theoretical Computer Science
Constraint-Based Scheduling
Edge Finding for Cumulative Scheduling
INFORMS Journal on Computing
Complete MCS-based search: application to resource constrained project scheduling
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Why cumulative decomposition is not as bad as it sounds
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Edge finding filtering algorithm for discrete cumulative resources in O(kn log n)
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Explaining the cumulative propagator
Constraints
Not-First and not-last detection for cumulative scheduling in O(n3 log n)
INAP'05 Proceedings of the 16th international conference on Applications of Declarative Programming and Knowledge Management
A scalable sweep algorithm for the cumulative constraint
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
On the complexity of global scheduling constraints under structural restrictions
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Edge Finding filtering algorithm is one of the reasons why Constraint Programming is a successful approach in the scheduling domain. However edge finding for cumulative resources was never as successful as edge finding for disjunctive resources. This paper presents a new variant of the edge finding algorithm which improves filtering by taking into account minimum capacity profile - a data structure known from timetabling algorithm. In comparison with standard and extended edge finding algorithms the new algorithm is stronger but it may need more iterations in order to reach the fixpoint. Time complexity of the algorithm is O(n2) where n is number of activities on the resource. We also propose further improvement of the filtering by incorporating some ideas from not-first/not-last and energetic reasoning algorithms. The filtering power of the algorithm is tested on computation of destructive lower bounds for 438 open RCPSP problems. For 169 of them we improve current best lower bound, in 9 cases backtrack free.