L. Bordeaux, G. Katsirelos, N. Narodytska and M. Y. Vardi (2011) "The Complexity of Integer Bound Propagation", Volume 40, pages 657-676

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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.

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