travelling salesman problem

(algorithm, complexity)(TSP or "shortest path", US:"traveling") Given a set of towns and the distances betweenthem, determine the shortest path starting from a given town,passing through all the other towns and returning to the firsttown.

This is a famous problem with a variety of solutions ofvarying complexity and efficiency. The simplest solution (thebrute force approach) generates all possible routes andtakes the shortest. This becomes impractical as the number oftowns, N, increases since the number of possible routes is!(N-1). A more intelligent algorithm (similar to iterative deepening) considers the shortest path to each town which canbe reached in one hop, then two hops, and so on until alltowns have been visited. At each stage the algorithmmaintains a "frontier" of reachable towns along with theshortest route to each. It then expands this frontier by onehop each time.

Pablo Moscato's TSP bibliography.Fractals and the TSP.

单词	travelling salesman problem
释义	travelling salesman problem travelling salesman problem (algorithm, complexity)(TSP or "shortest path", US:"traveling") Given a set of towns and the distances betweenthem, determine the shortest path starting from a given town,passing through all the other towns and returning to the firsttown. This is a famous problem with a variety of solutions ofvarying complexity and efficiency. The simplest solution (thebrute force approach) generates all possible routes andtakes the shortest. This becomes impractical as the number oftowns, N, increases since the number of possible routes is!(N-1). A more intelligent algorithm (similar to iterative deepening) considers the shortest path to each town which canbe reached in one hop, then two hops, and so on until alltowns have been visited. At each stage the algorithmmaintains a "frontier" of reachable towns along with theshortest route to each. It then expands this frontier by onehop each time. Pablo Moscato's TSP bibliography.Fractals and the TSP.
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