Question

If the solution obtained by an approximation algorithm is 10 and the optimal solution is 5, what will be the value of the approximation ratio?

1) 1
2) 5
3) 2
4) 0.5

Answer 1

The value of the approximation ratio when an approximation algorithm yields a solution of 10 and the optimal solution is 5 is 2.

Step-by-step explanation:

If an approximation algorithm yields a solution of 10 when the optimal solution is 5, the approximation ratio is computed as the algorithm's solution divided by the optimal solution. The formula for the approximation ratio can be written as:

• Approximation Ratio = Solution by Approximation Algorithm / Optimal Solution
  

In this case, the calculation would be:

• Approximation Ratio = 10 / 5 = 2

Therefore, the value of the approximation ratio is 2, which corresponds to option 3 in the given choices.