Hybrid CSP Solving

model K.R. Apt [CP99] for propagation (based on chaotic iterations) Reduction functions of functions Abstraction Constraint CSP Fixed point Partial Ordering Application Hybrid Constraint Solving – p. 55 A Generic Algorithm: propagation for constraint propagation: ordering on size of domains work on a CSP F = { set of propagation functions} X = initial CSP G = F While G 6= ∅ choose g ∈ G G = G− {g} G = G ∪ update(G, g,X) X = g(X) EndWhile Hybrid Constraint Solving – p. 56 Idea1: integrate split in GI avoid the CP framework algorithm split and reduction at the same level work on union of CSP Hybrid Constraint Solving – p. 57 Theoretical model for CSP solving (1) Partial ordering: 3 Ω4 Ω5 Terminates with a fixed point : set of solutions or inconsistent CSP Set of CSP Application of a reduction : domain reduction function or Ω splitting function 1 Ω2 Ω Hybrid Constraint Solving – p. 59 Theoretical model for CSP solving (2) Reduction: by constraint propagation: Ω’ CSP1 Constraint Propagation CSP3 Ω Ω CSP2’ CSP3 CSP1 Ω CSP2 Hybrid Constraint Solving – p. 60 Theoretical model for CSP solving (3) Reduction by domain splitting: Ω’ CSP1 CSP2’ CSP2’’’ CSP2’’ CSP3 Ω CSP1 CSP3 Ω Split Ω CSP2 Hybrid Constraint Solving – p. 61