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Complexity Of The Travelling Salesman Problem

Satisfactory Essays

Complexity and Tractability
Complexity refers to the time taken to solve the problem. Tractability refers to how difficult it is to solve, if it can’t be solved it is said to be intractable. An example of an intractable problem is the Travelling Salesman problem.
Key Problem
Finding optimal solutions to problems that would take a very long time to find, an example is the Travelling salesman problem, this is an algorithmic problem. It involves a salesman trying to find the shortest route between cities and places without going through the same place twice. It is considered intractable because it would take years to solve it. The number of possible routes can be defined as n! With n being the number of places to go to. If for example n were 10 there would be 36288000 possible routes to be measured, (10! Or 10x9x8x7x6x5x4x3x2x1) as the number of n goes up so does the number of possible routes. With so many ways to go, finding the most practical way would take ages. You would be finished before you find the answer. Making this problem intractable. This would be the optimal solution but another solution is the “greedy heuristic” solution. This involves finding the closest place from where you are and then next the closest place to where you are, and so on. It is an algorithm that takes “what looks like the best choice at each step.” [1] To repeatedly take the route to the next closest place. If the travelling salesman had a small amount of cities to go to, finding the optimal

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