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Abstract:
We show an algorithm for bound consistency of {\em global cardinality
constraints}, which runs in time $O(n+n')$ plus the time required to sort
the
assignment variables by range endpoints, where $n$ is the number of
assignment
variables and $n'$ is the number of values in the union of their ranges.
We
thus offer a fast alternative to R\'egin's
arc consistency algorithm~\cite{Regin} which runs
in time $O(n^{3/2}n')$ and space $O(n\cdot n')$. Our algorithm
also achieves bound consistency for the number of occurrences
of each value, which has not been done before.
