Same-Relation Constraints

Christopher Jefferson, Serdar Kadioglu, Karen E. Petrie, Meinolf Sellmann, Stanislav Zivny

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)


The ALLDIFFERENT constraint was one of the first global constraints [17] and it enforces the conjunction of one binary constraint, the not-equal constraint, for every pair of variables. By looking at the set of all pairwise not-equal relations at the same time, AllDifferent offers greater filtering power. The natural question arises whether we can generally leverage the knowledge that sets of pairs of variables all share the same relation. This paper studies exactly this question. We study in particular special constraint graphs like cliques, complete bipartite graphs, and directed acyclic graphs, whereby we always assume that the same constraint is enforced on all edges in the graph. In particular, we study whether there exists a tractable GAC propagator for these global Same-Relation constraints and show that AllDifferent is a huge exception: most Same-Relation Constraints pose NP-hard filtering problems. We present algorithms, based on AC-4 and AC-6, for one family of Same-Relation Constraints, which do not achieve GAC propagation but outperform propagating each constraint individually in both theory and practice.

Original languageEnglish
Title of host publicationPrinciples and Practice of Constraint Programming - CP 2009: 15th International Conference, CP 2009 Lisbon, Portugal, September 20-24, 2009: Proceedings
EditorsI. P. Gent
Number of pages16
ISBN (Print)978-3-642-04243-0
Publication statusPublished - 2009

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


  • ARC


Dive into the research topics of 'Same-Relation Constraints'. Together they form a unique fingerprint.

Cite this