## Traveling Salesman Problem

The *Traveling Salesman Problem* (TSP) consists in finding a Hamilton Circuit on a weighted graph with the least total weight. The problem is usually posted on nearly complete graphs.

The applet below lets you practice with three algorithms used for solving the TSP: the Brute-Force, Nearest-Neighbor and the Cheapest-Link algorithms. The instructions for using the applet are available on a separate page and can also be read under the first tab directly in the applet.

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(This applet was created to accompany *Excursions in Modern Mathematics*, Seventh Edition, by Peter Tannenbaum © Pearson Education. Reproduced with permission.)

The *Brute-Force* algorithm consists in simply listing all Hamiltonean circuits (if there are any) and choosing one (perhaps of many) with the least total weight. The *Nearest-Neighbor* algorithm forms a path, one vertex at a time, choosing a node joined to the previous one with an edge of the least possible weight. The *Cheapest-Link* algorithm picks edges almost randomly among those of the least weight, subject to two natural restrictions: there should not be three selected edges incident to the same node and no circuits should be formed until the very last step.

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