Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
IEEE Transactions on Computers
Maintaining Generalized Arc Consistency on Ad-hoc n-ary Boolean Constraints
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Programming constraint services: high-level programming of standard and new constraint services
Programming constraint services: high-level programming of standard and new constraint services
A hybrid BDD and SAT finite domain constraint solver
PADL'06 Proceedings of the 8th international conference on Practical Aspects of Declarative Languages
BDDs in a branch and cut framework
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Length-Lex Bounds Consistency for Knapsack Constraints
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Approximate Compilation of Constraints into Multivalued Decision Diagrams
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Propagating separable equalities in an MDD store
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A systematic approach to MDD-based constraint programming
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Manipulating MDD relaxations for combinatorial optimization
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
MDD propagators with explanation
Constraints
Variable ordering for the application of BDDs to the maximum independent set problem
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Representing CSPs with set-labeled diagrams: a compilation map
GKR'11 Proceedings of the Second international conference on Graph Structures for Knowledge Representation and Reasoning
Oblivious bounds on the probability of boolean functions
ACM Transactions on Database Systems (TODS)
BDD-based heuristics for binary optimization
Journal of Heuristics
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The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation algorithms can be developed to exploit the structure of particular constraints, much as is done for domain filtering algorithms. We propose specialized propagation algorithms for alldiff and inequality constraints. Preliminary experiments show that MDD propagation solves multiple alldiff problems an order of magnitude more rapidly than traditional domain propagation. It also significantly reduces the search tree for inequality problems, but additional research is needed to reduce the computation time.