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Computing (FOLDOC) dictionary
travelling salesman problem
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algorithm, complexity (TSP or "shortest path", US:
"traveling") Given a set of towns and the distances between
them, determine the shortest path starting from a given town,
passing through all the other towns and returning to the first
This is a famous problem with a variety of solutions of
varying complexity and efficiency. The simplest solution (the
brute force approach) generates all possible routes and
takes the shortest. This becomes impractical as the number of
towns, N, increases since the number of possible routes is
!(N-1). A more intelligent algorithm (similar to iterativedeepening) considers the shortest path to each town which can
be reached in one hop, then two hops, and so on until all
towns have been visited. At each stage the algorithm
maintains a "frontier" of reachable towns along with the
shortest route to each. It then expands this frontier by one
hop each time.