1. Dynamic Symmetry breaking with AI and Algebra

2. Iain McDonald iain@dcs.st-and.ac.uk Dynamic Symmetry breaking with AI and Algebra

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

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

5. 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)

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

7. Using algebraic methods A symmetry is represented by a group element This permutation is: (1 4 16 13)(2 8 15 9)(3 12 14 5)(6 7 11 10)

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

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

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

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

12. Thank you…