Breaking Value Symmetry

Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. We can eliminate such value symmetry either statically by adding constraints to prune symmetric solutions or dynamically by modifying the search procedure to avoid symmetric branches. We show that either method has computational limitations. With static methods, pruning all symmetric values is NP-hard in general. With dynamic methods, we can take exponential time on problems which static methods solve without search. Finally, we consider a common type of value symmetry, that due to interchangeable values, where polynomial methods have been proposed to break symmetries. We show that despite these theoretical limitations, the methods proposed to break the symmetries introduced by interchangeable values are both effective in theory and in practice.

• Type: Conference
• Year: 2007
• Where: CP
• Authors: Toby Walsh
• Keywords: Common Type, CP 2007, Programming Languages, Symmetric Values, Value Symmetry