Dynamic Symmetry breaking with AI and Algebra

Iain McDonald Dynamic Symmetry breaking with AI and Algebra

Symmetry Breaking Cut branches of the search tree SBDS Partial assignments are symmetrically equivalent

Symmetry Example This assignment results in failure From this we can infer that X is also no good

SBDS using AI State of partial assignment, A Next assignment of a value to a variable, var = val Symmetric equivalent of A is g(A) We can now say:  A and (var  val) and g(A)  g(var  val)

Problems with this method Overhead increases with the number of symmetries At the root of the search tree all symmetries are equivalent

Using algebraic methods A symmetry is represented by a group element This permutation is: ( )( )( )( )

Orbit finding Algorithm Finds all the places that a partial assignment can go to Orbit

Advantages of Algebra Does not have overhead Store only the generators Find unique symmetries at each node

Problems with Algebra Re-generating symmetries at each node Symmetries may be invalid

Ideas for the future Current progress Greater integration of the two techniques

Thank you…