Question: Design and analyze an algorithm for the Traveling Salesman Problem (TSP) that finds the optimal tour in polynomial time. Explain the time and space complexity

Design and analyze an algorithm for the Traveling Salesman Problem (TSP) that finds the optimal tour in polynomial time. Explain the time and space complexity of your algorithm, and compare it with existing algorithms such as brute force, nearest neighbor, and Christofides algorithm. Also, discuss the limitations and challenges of implementing TSP algorithms for large-scale problems with millions of cities. Finally, suggest some possible solutions or improvements to overcome these challenges.

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