MPI-INF/SWS Research Reports 1991-2021

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Fast bound consistency for the global cardinality constraint

Katriel, Irit and Thiel, Sven

September 2003, 30 pages.

Status: available - back from printing

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.

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  AUTHOR = {Katriel, Irit and Thiel, Sven},
  TITLE = {Fast bound consistency for the global cardinality constraint},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2003-1-013},
  MONTH = {September},
  YEAR = {2003},
  ISSN = {0946-011X},