New Algorithms for Bidirectional Singleton Arc Consistency

Algorithm 1

BiSAC-1.

(1)  repeat

(2)    𝐶𝐻𝐴𝑁𝐺𝐸←  false;

(3)    foreach  (𝑋,𝑎)∈𝐷^𝑃  do

(4)     𝐷^𝑇←∅;

(5)     foreach  (𝑌,𝑏)∈𝐷^𝑃  do

(6)      if  (𝑋,𝑎)∈  AC(𝑃|_𝑌=𝑏) then  𝐷^𝑇←𝐷^𝑇∪{(𝑌,𝑏)};

(7)     if AC(𝑉, 𝐷^𝑇, 𝐶) = ⟂  then

(8)      D(X) ← D(X)⧵{𝑎};

(9)      if  D(X) = ∅  then return false;

(10)       CHANGE← true;

(11) until not  CHANGE;

(12) return true;