New Algorithms for Bidirectional Singleton Arc Consistency

Algorithm 3

Judge-DF.

(1)  𝑜𝑐𝑐𝑢𝑟←∅;

(2)  𝐵𝑃←𝑃;

(3)  repeat

(4)   get (𝑋, 𝑎) from 𝑄𝑢𝑒𝑢𝑒 s.t. 𝑋∉ vars(𝑜𝑐𝑐𝑢𝑟) and (𝑋, 𝑎) ∈ 𝐵𝑃;

(5)   𝐵𝑃← AC(𝐵𝑃|_𝑋=𝑎);

(6)   if  BP = ⟂  then goto  𝐿;

(7)   flag ←false;

(8)   foreach (𝑌, 𝑏) ∈ 𝐵𝑃  do

(9)     if (𝑋, 𝑎) ∉  AC(𝑃|_𝑌=𝑏) then

(10)      𝐵𝑃←𝐵𝑃⧵{(𝑌,𝑏)}

(11)      flag ←true;

(12)   if flag = true then

(13)    𝐵𝑃← AC(𝐵𝑃|_𝑋=𝑎);

(14)    if  𝐵𝑃 = ⟂  then goto  𝐿;

(15)        else 𝑜𝑐𝑐𝑢𝑟←𝑜𝑐𝑐𝑢𝑟∪{(𝑋,𝑎)};

(16)   else 𝑜𝑐𝑐𝑢𝑟←𝑜𝑐𝑐𝑢𝑟∪{(𝑋,𝑎)};

(17)  until vars(𝑜𝑐𝑐𝑢𝑟) = vars(𝑃);

(18)  return Solution;

(19) L:

(20)  if 𝑜𝑐𝑐𝑢𝑟=∅  then

(21)  CHANGE ←true;

(22)  𝑃←𝑃⧵{(𝑋,𝑎)};

(23)  if  𝑃 = ⟂  then return  ⟂;

(24)  else

(25)  𝑄𝑢𝑒𝑢𝑒←𝑄𝑢𝑒𝑢𝑒⧵𝑜𝑐𝑐𝑢𝑟;

(26)  𝑄𝑢𝑒𝑢𝑒←𝑄𝑢𝑒𝑢𝑒∪{(𝑋,𝑎)};