# Item

ITEM ACTIONSEXPORT

Released

Report

#### Fast bound consistency for the global cardinality constraint

##### MPS-Authors

##### Locator

There are no locators available

##### Fulltext (public)

2003-1-013

(Any fulltext), 10KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Katriel, I., & Thiel, S.(2003). *Fast bound consistency
for the global cardinality constraint* (MPI-I-2003-1-013). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6B1F-D

##### 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.