travelling salesman problem

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travelling salesman problem - Free On-line Dictionary of Computing (26 May 2007) :

  travelling salesman problem
  TSP
  
     <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
     town.
  
     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 iterative deepening
     ) 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.
  
     Pablo Moscato's TSP bibliography (http://densis.fee.unicamp.br/~moscato/TSPBIB_home.html)
     .
     Fractals and the TSP (http://ing.unlp.edu.ar/cetad/mos/FRACTAL_TSP_home.html)
     .
  
     (1998-03-24)