Advanced Constraint Processing CSCE 990 02, Fall 2009

1. On the Relationship Between Partial Interchangeability and Subproblem InterchangeabilityShant Karakashian & Christopher Reeson Advanced Constraint Processing CSCE 990 02, Fall 2009

2. Outline • Definitions • Partial interchangeability (PI) • Subproblem interchangeability (SubPI) • Relationship between PI & SubPI • Theorem 5 of [Freuder, AAAI91] • Examples

3. Definitions Two values are partially interchangeable with respect to a subset S of variables iff any solution involving one implies a solution involving the other with possibly different values for S. Two values are subproblem interchangeable with respect to a subset of variables S iff they are fully interchangeable with respect to the solutions of the subproblem of the CSP induced by S. Topic

4. Theorem 5 of [Freuder AAAI91] Subproblem interchangeability wrt S implies partial interchangeability wrt S’=V\S SI PI Partial interchangeability wrt S’ does not imply subproblem interchangeability wrt S. PI(not) SI Examples: one for PI  SI; one for PI  SI Topic

5. Example: PI  SI CSP Values 0,1 for A are not SI in {A,B} Values 0,1 for A are PI wrt {C} B A C B C B 0 1 2 0 1 2 A 0 1 2 A 0 1 0 1 0 1 0 1 0 1 Topic

6. Example: PI  SI CSP Values 0,1 for A are SI in {A,B} Values 0,1 for A are not PI wrt {C} C B 0 1 A B 0 1 0 A 0 1 B 0 1 A 0 1 0 1 0 Topic