Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Comparing trailing and copying for constraint programming
Proceedings of the 1999 international conference on Logic programming
Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
A New Multi-resource cumulatives Constraint with Negative Heights
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Entropy: a consolidation manager for clusters
Proceedings of the 2009 ACM SIGPLAN/SIGOPS international conference on Virtual execution environments
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
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
Timetable edge finding filtering algorithm for discrete cumulative resources
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Bin repacking scheduling in virtualized datacenters
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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
Extending chip in order to solve complex scheduling and placement problems
Mathematical and Computer Modelling: An International Journal
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This paper presents a sweep based algorithm for the cumulative constraint, which can operate in filtering mode as well as in greedy assignment mode. Given n tasks, this algorithm has a worst-case time complexity of O(n2). In practice, we use a variant with better average-case complexity but worst-case complexity of O(n2 logn), which goes down to O(n logn) when all tasks have unit duration, i.e. in the bin-packing case. Despite its worst-case time complexity, this algorithm scales well in practice, even when a significant number of tasks can be scheduled in parallel. It handles up to 1 million tasks in one single cumulative constraint in both Choco and SICStus.