A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Introduction to Algorithms
Arc Consistency for Global Cardinality Constraints with Costs
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Modelling and Solving Employee Timetabling Problems
Annals of Mathematics and Artificial Intelligence
Constraint Processing
Propagating logical combinations of constraints
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
The range and roots constraints: specifying counting and occurrence problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Combination of among and cardinality constraints
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
An efficient generic network flow constraint
Proceedings of the 2011 ACM Symposium on Applied Computing
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Global constraints are used in constraint programming to help users specify patterns that occur frequently in the real world. In addition, global constraints facilitate the use of efficient constraint propagation algorithms for problem solving. Many of the most common global constraints used in constraint programming use filtering algorithms based on network flow theory. We show how we can formulate global constraints such as GCC, Among, and their combinations, in terms of a tractable set-intersection problem called Two Families Of Sets (TFOS). We demonstrate that the TFOS problem allows us to represent tasks that are often difficult to model in terms of a classical constraint satisfaction paradigm. In the final part of the paper we specify some tractable and intractable extensions of the TFOS problem. The contribution of this paper is the characterisation of a general framework that helps us to study the tractability of global constraints that rely on filtering algorithms based on network flow theory.