Dynamic structural symmetry breaking for constraint satisfaction problems

In recent years, symmetry breaking for constraint satisfaction problems (CSPs) has attracted considerable attention. Various general schemes have been proposed to eliminate symmetries. In general, these schemes may take exponential space or time to eliminate all the symmetries. We identify several classes of CSPs that encompass many practical problems and for which symmetry breaking for various forms of value or variable interchangeability is tractable using dedicated search procedures. We also show the limits of efficient symmetry breaking for such dominance-detection schemes by proving intractability results for some classes of CSPs.

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

[2]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

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

[4]  Meinolf Sellmann,et al.  Dynamic Symmetry Breaking Restarted , 2006, CP.

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

[6]  Peter Jeavons,et al.  Symmetry Definitions for Constraint Satisfaction Problems , 2005, CP.

[7]  Ilya Shlyakhter Generating effective symmetry-breaking predicates for search problems , 2007, Discret. Appl. Math..

[8]  Sally C. Brailsford,et al.  The progressive party problem: Integer linear programming and constraint programming compared , 1995, Constraints.

[9]  Toby Walsh,et al.  Proceedings of AAAI-96 , 1996 .

[10]  Sally C. Brailsford,et al.  The Progressive Party Problem: Integer Linear Programming and Constraint Programming Compared , 1995, CP.

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

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

[13]  Carme Torras,et al.  Exploiting symmetries within constraint satisfaction search , 2001, Artif. Intell..

[14]  Toby Walsh,et al.  Breaking Symmetry of Interchangeable Variables and Values , 2007, CP.

[15]  Meinolf Sellmann,et al.  Cost-Based Filtering for Shorter Path Constraints , 2003, CP.

[16]  Barbara M. Smith,et al.  Reducing Symmetry in a Combinatorial Design Problem , 2001 .

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

[18]  Pascal Van Hentenryck,et al.  Structural symmetry breaking for constraint satisfaction problems , 2007 .

[19]  Meinolf Sellmann,et al.  Cost-based Filtering for Shorter Path Constraints , 2003, Constraints.

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

[21]  Pascal Van Hentenryck,et al.  Compositional Derivation of Symmetries for Constraint Satisfaction , 2005, SARA.

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

[23]  James M. Crawford,et al.  Symmetry-Breaking Predicates for Search Problems , 1996, KR.

[24]  Steve Linton,et al.  Tractable Symmetry Breaking Using Restricted Search Trees , 2004, ECAI.

[25]  Y. Law,et al.  Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction , 2006, Constraints.

[26]  P. Flener,et al.  Symmetry in matrix models , 2001 .

[27]  M. C. Er,et al.  A Fast Algorithm for Generating Set Partitions , 1988, Comput. J..

[28]  Pascal Van Hentenryck,et al.  Static and Dynamic Structural Symmetry Breaking , 2006, CP.

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

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

[31]  Jean-François Puget An Efficient Way of Breaking Value Symmetries , 2006, AAAI.

[32]  P. Cameron,et al.  PERMUTATION GROUPS , 2019, Group Theory for Physicists.

[33]  Pascal Van Hentenryck,et al.  Structural Symmetry Breaking , 2005, IJCAI.

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

[35]  Toby Walsh Breaking Value Symmetry , 2007, CP.

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

[37]  Marek Kubale,et al.  A generalized implicit enumeration algorithm for graph coloring , 1985, CACM.