The Nearest Neighbor Method is a heuristic algorithm used to find an approximate solution to the Traveling Salesperson Problem. It starts at a chosen vertex and repeatedly visits the nearest unvisited vertex until all vertices have been visited.
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It prioritizes choosing the shortest edge leading to an unvisited vertex at each step.
The method does not guarantee an optimal solution but often yields a good approximation quickly.
The initial starting vertex can affect the final path length.
It is easy to implement and computationally efficient for small graphs.
The method may result in suboptimal solutions with longer overall paths due to locally optimal choices.
Review Questions
How does the Nearest Neighbor Method determine which vertex to visit next?
Why might the Nearest Neighbor Method not always produce an optimal solution?
What impact does the choice of starting vertex have on the solution produced by the Nearest Neighbor Method?
Related terms
Traveling Salesperson Problem: A problem that seeks to find the shortest possible route visiting each city exactly once and returning to the origin city.
Heuristic Algorithm: An approach designed to solve problems faster than classical methods, typically providing good-enough solutions.
Hamiltonian Circuit: A circuit that visits every vertex of a graph exactly once and returns to the starting vertex.
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