1. Foundations of Constraint Processing Constraint Graphical Models 1Odds & Ends Foundations of Constraint Processing CSCE421/821, Fall 2015 www.cse.unl.edu/~choueiry/F15-421-821/ Berthe Y. Choueiry (Shu-we-ri) Avery Hall, Room 360 Tel: +1(402)472-5444

2. Foundations of Constraint Processing Outline Graphical Representations Graphical Models Odds & Ends2

3. Foundations of Constraint Processing Graphical Representations Always specify V, E for a graph as G =( V, E ) Main representations – Binary CSPs Graph (for binary CSPs) Microstructure (supports) Co-microstructure (conflicts) – Non-binary CSPs Hypergraph Primal graph – Dual graph – Incidence graph Odds & Ends3

4. Foundations of Constraint Processing (V 3, b ) ( V 3,c) (V 2, a ) (V 2, c) (V 1, a ) (V 1, b) Macrostructure G(P)=( V, E ) V = E = Micro-structure  (P)=( V, E ) V = E = Co-microstructure co-  (P) =( V, E ) V = E = Binary CSPs Odds & Ends4 a, b a, c b, c    V1V1 V2V2 V3V3 (V 1, a ) (V 1, b) (V 2, a ) (V 2, c) (V 3, b ) ( V 3,c) No goods Supports

5. Foundations of Constraint Processing Non-binary CSPs: Hypergraph Hypergraph (non-binary CSP) – V = – E = Odds & Ends5 R3R3 A B C D E F R1R1 R4R4 R2R2 R5R5 R6R6 R3R3 A B C D E F R1R1 R4R4 R2R2 R5R5 R6R6

6. Foundations of Constraint Processing Primal graph – V= – E= Non-binary CSPs: Primal Graph Odds & Ends6 A B D E R4R4 A B C D E F R3R3 A B C D E F R1R1 R4R4 R2R2 R5R5 R6R6 A B D E

7. Foundations of Constraint Processing Dual Graph V= G= Odds & Ends7 R4R4 BCD ABDE CF EF AB R3R3 R1R1 R2R2 C F E BD AB D AD A B R5R5 R6R6 R3R3 A B C D E F R1R1 R4R4 R2R2 R5R5 R6R6 HypergraphDual graph

8. Foundations of Constraint Processing V= G= Incidence Graph Odds & Ends8 R3R3 A B C D E F R1R1 R4R4 R2R2 R5R5 R6R6 HypergraphIncidence graph A B C D E F R1R1 R2R2 R3R3 R4R4 R5R5 R6R6