Constraint Graphical Models Foundations of Constraint Processing CSCE

Constraint Graphical Models Foundations of Constraint Processing CSCE 421/821, Spring 2018 www. cse. unl. edu/~choueiry/S 18 -421 -821/ Berthe Y. Choueiry (Shu-we-ri) Avery Hall, Room 360 Tel: +1(402)472 -5444 Foundations of Constraint Processing Odds & Ends 1

Outline • Graphical Representations • Graphical Models Foundations of Constraint Processing Odds & Ends 2

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 Foundations of Constraint Processing Odds & Ends 3

Binary CSPs Macrostructure G(P)=(V, E) • V= • E= V 1 a, b V 2 Micro-structure (P)=(V, E) • V= • E= a, c (V 1, a ) (V 2, c) Co-microstructure co- (P)=(V, E) • V= • E= (V 2, a ) b, c (V 1, b) (V 3, b ) (V 1, a ) (V 1, b) (V 2, c) (V 3, b ) V 3 Supports (V 3, c) No goods (V 3, c) Foundations of Constraint Processing Odds & Ends 4

Non-binary CSPs: Hypergraph • Hypergraph (non-binary CSP) – V= – E= B R 3 R 1 C R 6 R 4 A R 6 B E R 2 D R 5 R 1 R 3 F E R 2 C F A R 4 R 5 D Foundations of Constraint Processing Odds & Ends 5

Non-binary CSPs: Primal Graph • Primal graph B A R 4 – V= – E= E R 6 B R 1 R 3 E R 2 B A R 4 C F D A E B D A E R 5 D C F D Foundations of Constraint Processing Odds & Ends 6

Dual Graph • V= • G= R 6 B R 1 R 3 E R 2 A R 4 C F R 5 R 3 D AD BCD C A AD B BD R 5 AB R 6 D Hypergraph AB ABDE E R 4 R 1 CF F EF R 2 Dual graph Foundations of Constraint Processing Odds & Ends 7

Incidence Graph • V= • G= R 6 B R 1 R 3 E R 2 R 5 A R 4 C F R 3 R 4 R 5 R 2 D R 1 Hypergraph A B C D E F Incidence graph Foundations of Constraint Processing Odds & Ends 8