Design 2-approximation for metric TSP via MST doubling
Analyze the design 2-approximation for metric tsp via mst doubling.
Examples
Input: "test_input_1"
Output: "output_1"
Input: "test_input_2"
Output: "output_2"
Hints
Start by recalling the relationship between Minimum Spanning Trees (MST) and the Traveling Salesman Problem (TSP), particularly how an MST can be used to construct a tour that approximates the optimal TSP solution.
Consider how the doubling of edges in the MST (to form an Eulerian graph) relates to the triangle inequality in metric TSP, and why this step ensures the approximation ratio of 2.
Analyze the worst-case scenario where the MST-based tour deviates from the optimal TSP tour, and prove why the approximation ratio cannot exceed 2 in metric spaces.
Design 2-approximation for metric TSP via MST doubling
Analyze the design 2-approximation for metric tsp via mst doubling.