Improving Tree Decomposition Methods With Function Filtering

Iterative MCTEf IMCTE φ(u, v) = M (v, u) the approximated MCTEf message of a previous execution (one with minor r) procedure IMCTEf(〈X,D,C, k〉, 〈〈V,E〉, χ, ψ〉) INPUT: P = 〈X,D,C, k〉 is a WCSP instance TD = 〈〈V,E〉, χ, ψ〉 is a tree decomposition. 1 for each (u, v) ∈ E do φ(u, v) := {∅}; 2 r := 1; 3 repeat 4 MCTEf(r); 5 for each (u, v) ∈ E do φ(u, v) :=M(u,v); 6 r := r + 1; 7 until exact solution or exhausted resources Experiments Experiments are focused in two aspects: 1. Showing that CTEf versus state of the art CTE uses less tuples to find the exact solution. 2. Inside an approximation schema we show that MCTEf(r), exhausts resources at a smaller r and finds worst LB than the iterative version IMCTEf where the previous messages of MCTEf(r) execution are used as filters.