The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Constraint propagation with interval labels
Artificial Intelligence
Simple local search problems that are hard to solve
SIAM Journal on Computing
Constraint reasoning based on interval arithmetic: the tolerance propagation approach
Artificial Intelligence - Special volume on constraint-based reasoning
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Tractable constraints on ordered domains
Artificial Intelligence
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
The essence of constraint propagation
Theoretical Computer Science
Accelerating filtering techniques for numeric CSPs
Artificial Intelligence
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Arc Consistency on n-ary Monotonic and Linear Constraints
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Heterogeneous Constraint Solving
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
When do bounds and domain propagation lead to the same search space?
ACM Transactions on Programming Languages and Systems (TOPLAS)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
The Max-Atom Problem and Its Relevance
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Propagating knapsack constraints in sublinear time
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
An analysis of slow convergence in interval propagation
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Feasibility-based bounds tightening via fixed points
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Finite domain bounds consistency revisited
AI'06 Proceedings of the 19th Australian joint conference on Artificial Intelligence: advances in Artificial Intelligence
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Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure ("branch and prune") and used at every node of the search tree to narrow down the search space, so it is critical that it be fast. The procedure invokes constraint propagators until a common fixpoint is reached, but the known algorithms for this have a pseudo-polynomial worst-case time complexity: they are fast indeed when the variables have a small numerical range, but they have the well-known problem of being prohibitively slow when these ranges are large. An important question is therefore whether strongly-polynomial algorithms exist that compute the common bound consistent fixpoint of a set of constraints. This paper answers this question. In particular we show that this fixpoint computation is in fact NP-complete, even when restricted to binary linear constraints.