Look Ahead: Forward checking checks only the constraints between the current variable and the future variables. So why not to perform full arc consistency that will further reduces the domains and removes possible conflicts? This approach is called (full) look ahead or maintaining arc consistency (MAC).

The advantage of look ahead is that it detects also the conflicts between future variables and therefore allows branches of the search tree that will lead to failure to be pruned earlier than with forward checking. Also as with forward checking, whenever a new variable is considered, all its remaining values are guaranteed to be consistent with the past variables, so the checking an assignment against the past assignments is no necessary.

Look ahead prunes the search tree further more than forward checking but, again, it should be noted that look ahead does even more work when each assignment is added to the current partial solution than forward checking.

 

Comparison of Propagation Techniques: The following figure shows which constraints are tested when the above described propagation techniques are applied.

 

 

More constraint propagation at each node will result in the search tree containing fewer nodes, but the overall cost may be higher, as the processing at each node will be more expensive. In one extreme, obtaining strong n-consistency for the original problem would completely eliminate the need for search, but as mentioned before, this is usually more expensive than simple backtracking. Actually, in some cases even the full look ahead may be more expensive than simple backtracking. That is the reason why forward checking and simple backtracking are still used in applications.