Compositional Derivation of Symmetries for Constraint Satisfaction

This paper reconsiders the problems of discovering symmetries in constraint satisfaction problems (CSPs). It proposes a compositional approach which derives symmetries of the applications from primitive constraints. The key insight is the recognition of the special role of global constraints in symmetry detection. Once the symmetries of global constraints are available, it often becomes much easier to derive symmetries compositionally and efficiently. The paper demonstrates the potential of this approach by studying several classes of value and variable symmetries and applying the resulting techniques to two non-trivial applications. The paper also discusses the potential of reformulations and high-level modeling abstractions to strengthen symmetry discovery.

[1]  Martin W. P. Savelsbergh,et al.  Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition , 2000, INFORMS J. Comput..

[2]  François Pachet,et al.  Using Symmetry of Global Constraints to Speed up the Resolution of Constraint Satisfaction Problems , 2002 .

[3]  Ian P. Gent,et al.  Symmetry Breaking in Constraint Programming , 2000, ECAI.

[4]  Berthe Y. Choueiry,et al.  Dynamic Bundling: Less Effort for More Solutions , 2002, SARA.

[5]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[6]  Jean-François Puget.  Symmetry Breaking Using Stabilizers , 2003, CP.

[7]  Pierre Flener,et al.  Detecting Symmetries in Relational Models of CSPs , 2005 .

[8]  Pascal Van Hentenryck.  Constraint and Integer Programming in OPL , 2002, INFORMS J. Comput..

[9]  Francesca Rossi,et al.  Principles and Practice of Constraint Programming – CP 2003 , 2003, Lecture Notes in Computer Science.

[10]  Toby Walsh,et al.  CGRASS: A System for Transforming Constraint Satisfaction Problems , 2002, International Workshop on Constraint Solving and Constraint Logic Programming.

[11]  Andrea Lodi,et al.  Optimization-Oriented Global Constraints , 2004, Constraints.

[12]  Jean-Charles Régin,et al.  Arc Consistency for Global Cardinality Constraints with Costs , 1999, CP.

[13]  Nicolas Beldiceanu,et al.  Introducing global constraints in CHIP , 1994 .

[14]  Zbigniew W. Ras,et al.  Methodologies for Intelligent Systems , 1991, Lecture Notes in Computer Science.

[15]  Rolf Backofen,et al.  Excluding Symmetries in Constraint-Based Search , 1999, CP.

[16]  Guevara Noubir,et al.  On the Computation of Local Interchangeability in Discrete Constraint Satisfaction Problems , 1998, AAAI/IAAI.

[17]  Jean-Daniel Zucker,et al.  Abstraction, Reformulation and Approximation, 6th International Symposium, SARA 2005, Airth Castle, Scotland, UK, July 26-29, 2005, Proceedings , 2005, SARA.

[18]  Ian P. Gent,et al.  Approaches to Conditional Symmetry Breaking ∗ , 2005 .

[19]  B. Choueiry.  Dynamic Detection and Exploitation of Value Symmetries for Non-Binary Finite CSPs , 2003 .

[20]  Joxan Jaffar,et al.  Principles and Practice of Constraint Programming – CP’99 , 1999, Lecture Notes in Computer Science.

[21]  Toby Walsh,et al.  Principles and Practice of Constraint Programming — CP 2001: 7th International Conference, CP 2001 Paphos, Cyprus, November 26 – December 1, 2001 Proceedings , 2001, Lecture Notes in Computer Science.

[22]  Ian P. Gent,et al.  Symmetry breaking during search in constraint programming , 1999 .

[23]  Jean-François Puget.  Symmetry Breaking Revisited , 2002, CP.

[24]  Jean-François Puget,et al.  On the Satisfiability of Symmetrical Constrained Satisfaction Problems , 1993, ISMIS.

[25]  Pascal Brisset,et al.  Solving the Kirkman's Schoolgirl Problem in a Few Seconds , 2002, CP.

[26]  Toby Walsh,et al.  Breaking Row and Column Symmetries in Matrix Models , 2002, CP.

[27]  Pascal Van Hentenryck,et al.  Tractable Symmetry Breaking for CSPs with Interchangeable Values , 2003, IJCAI.

[28]  Eugene C. Freuder.  Eliminating Interchangeable Values in Constraint Satisfaction Problems , 1991, AAAI.

[29]  Michela Milano,et al.  Global Cut Framework for Removing Symmetries , 2001, CP.

[30]  Meinolf Sellmann,et al.  Symmetry Breaking , 2001, CP.

[31]  Maria Fox,et al.  Extending the Exploitation of Symmetries in Planning , 2002, AIPS.

[32]  Pascal Van Hentenryck,et al.  A constraint-based architecture for local search , 2002, OOPSLA '02.