Christofides' algorithm

Christofides' algorithm is a method for finding a near-optimal route that visits each city once and returns to the start, known as the Traveling Salesman Problem. It combines three steps: first, creating a minimum spanning tree connecting all cities with the shortest possible total length; second, identifying and pairing up odd-degree cities in this tree to ensure a balanced structure; third, finding a shortest path that covers these pairs and combining everything into a closed tour. The algorithm guarantees the route will be no longer than 1.5 times the shortest possible one, providing an efficient approximation for complex routing problems.