Approximation ratio

The approximation ratio is a measure used in optimization problems to evaluate how close a solution is to the best possible solution. It compares the value of an approximate solution to the value of the optimal solution. For example, if you are trying to find the shortest route and your solution is 10 miles while the best route is 8 miles, the approximation ratio is 10/8, or 1.25. A ratio of 1 means you found the best solution, while higher ratios indicate less optimal solutions. This helps understand the efficiency of various algorithms in practical applications.