The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) asks: given a list of cities and the distances between them, what is the shortest possible route that visits each city once and returns to the starting point? It’s a challenge because the number of possible routes grows rapidly as more cities are added, making it difficult to find the optimal solution quickly. TSP is important in logistics, planning, and optimization because it models real-world problems of efficient routing and resource management. Despite its simplicity in statement, solving the TSP efficiently remains a complex task in computer science and operations research.