AC3 Algorithm and Constraint Satisfaction

The video tutorial explains the AC3 algorithm, which simplifies constraint satisfaction problems by using constraints to prune values from variable domains. It describes how binary constraints are converted into arcs, which are then added to an agenda for processing. The algorithm checks each arc, ensuring values satisfy constraints, and prunes inconsistent values. An example problem with variables and constraints is solved step-by-step, demonstrating the algorithm's application and resulting in an arc-consistent problem that is easier to solve using standard methods like backtracking.

What is the primary goal of the AC3 algorithm?

• To add more variables to the problem

• To simplify constraint satisfaction problems

• To increase the number of constraints

• To make the problem more complex

How does the AC3 algorithm treat binary constraints?

• As a single arc

• As two separate arcs

• As a single constraint

• As a single node

In the AC3 algorithm, what happens if a value of Xi is not consistent with the constraint?

• It is duplicated

• It is ignored

• It is removed from the domain of Xi

• It is added to the domain of Xi

What are the initial domains for variables A, B, and C in the example?

• 1, 2 for A; 1, 2, 3 for B; 1, 2 for C

• 1, 2, 3 for A; 1, 2, 3 for B; 1, 2, 3 for C

• 1, 2 for A; 1, 2 for B; 1, 2 for C

• 1, 2, 3 for A; 1, 2 for B; 1, 2, 3 for C

What constraint is applied between variables A and B in the example?

• A must not be equal to B

• A must be equal to B

• A must be greater than B

• A must be less than B

What happens when the domain of a variable changes in the AC3 algorithm?

• The variable is removed

• The agenda is cleared

• The algorithm stops

• Arcs with the variable on the right-hand side are rechecked

In the example, what value is removed from B's domain after checking the constraint B < A?

• 1

• 2

• 3

• 4

Why is it necessary to check constraints in both directions in the AC3 algorithm?

• To maintain consistency in both directions

• To simplify the algorithm

• To increase the number of constraints

• To ensure all values are pruned

What is the final outcome of the AC3 algorithm once the agenda is empty?

• The problem has more variables

• The problem becomes more complex

• The problem is unsolvable

• The problem is arc consistent

Which method is suggested for solving the problem after achieving arc consistency?

• Local search

• Constraint propagation

• Forward checking

• Backtracking