Graph Theory Questions Medium
The traveling salesman problem (TSP) is a well-known problem in graph theory that seeks to find the shortest possible route that a salesman can take to visit a set of cities and return to the starting city, while visiting each city exactly once. In other words, it is a problem of finding the optimal Hamiltonian cycle in a complete weighted graph.
The TSP is classified as an NP-hard problem, meaning that there is no known efficient algorithm to solve it for large instances. The difficulty arises from the exponential growth of possible solutions as the number of cities increases.
The TSP has numerous real-world applications, such as route optimization for delivery services, circuit board drilling, DNA sequencing, and even in computer chip manufacturing. Despite its computational complexity, various approximation algorithms and heuristics have been developed to find near-optimal solutions for practical purposes.