[table][br][tr][br][td][b]Factual Questions:[/b][br]What is the Travelling Salesman Problem (TSP) and its objective in graph theory?[br][br]How does the nearest neighbor algorithm approach solving the TSP?[br][br]Describe the vertex deletion method for addressing the TSP.[br][/td][br][br][td][b]Conceptual Questions:[/b][br]Why is the TSP considered a significant challenge in the fields of optimization and computer science?[br][br]How do different algorithms for the TSP, like the nearest neighbor and vertex deletion, compare in terms of efficiency and accuracy?[br][br]In what ways do the constraints of the TSP (visiting each vertex once and returning to the origin) complicate finding a solution?[br][/td][br][br][td][b]Debatable Questions:[/b][br]Is the nearest neighbor algorithm or the vertex deletion method more effective for solving the TSP in most practical scenarios?[br][br]Given the NP-hard nature of the TSP, can we ever expect to find a universally optimal solution algorithm?[br][br]How do the limitations of current algorithms for solving the TSP impact their applicability to real-world routing and scheduling problems?[br][/td][br][/tr][br][/table][br]

Travelling Salesman Problem (TSP): This is a classic problem in optimization and computer science. The problem asks for the shortest possible route that visits each vertex once and returns to the origin vertex, creating a Hamiltonian cycle with the least total weight (if it's a weighted graph). [br][br]For example planning an intinerary for a European trip landing in London, travelling around and finally returning to London to fly home.