Download presentation
Presentation is loading. Please wait.
Published byHenry Bruce Modified over 9 years ago
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…
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.