Computational Complexity
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COMPUTER SCIENCE
Computational Complexity
Travelling Salesman Problem
The quest for the shortest route reveals the limits of computational power
6 days ago
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Why is the Travelling Salesman Problem considered NP-hard and what does this imply for solving large instances?
Because it involves many cities, it can be solved quickly using brute force for any size problem.
Because it only requires visiting cities once, it is easy to find the shortest route using simple heuristics.
Because the number of possible routes grows factorially with cities, no known efficient algorithm can solve all instances quickly, implying exact solutions are impractical for large problems.
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COMPUTER SCIENCE
Computational Complexity
Travelling Salesman Problem
The Travelling Salesman Problem challenges finding the shortest route visiting all cities once
25 Jan 2026
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Why is the Travelling Salesman Problem classified as NP-hard in computational complexity theory?
Because no known algorithm can solve all instances of the problem efficiently in polynomial time
Because it can be solved quickly using simple greedy algorithms
Because it only applies to a small number of cities and is trivial for larger sets
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COMPUTER SCIENCE
Computational Complexity
Travelling Salesman Problem
The Travelling Salesman Problem challenges finding the shortest route visiting all cities once and returning home
20 Jan 2026
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Why is the Travelling Salesman Problem classified as NP-hard in computational complexity theory?
Because no known algorithm can solve all instances of the problem efficiently in polynomial time
Because it can be solved quickly using simple greedy algorithms
Because the problem only applies to a small number of cities and is trivial to solve
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