diff -r 4936be66d2f5 -r a2d142bb5d3c doc/groups.dox --- a/doc/groups.dox Tue Feb 12 07:15:52 2013 +0100 +++ b/doc/groups.dox Fri Mar 01 17:59:08 2013 +0100 @@ -558,6 +558,42 @@ \image html planar.png \image latex planar.eps "Plane graph" width=\textwidth */ + +/** +@defgroup tsp Traveling Salesman Problem +@ingroup algs +\brief Algorithms for the symmetric traveling salesman problem + +This group contains basic heuristic algorithms for the the symmetric +\e traveling \e salesman \e problem (TSP). +Given an \ref FullGraph "undirected full graph" with a cost map on its edges, +the problem is to find a shortest possible tour that visits each node exactly +once (i.e. the minimum cost Hamiltonian cycle). + +These TSP algorithms are intended to be used with a \e metric \e cost +\e function, i.e. the edge costs should satisfy the triangle inequality. +Otherwise the algorithms could yield worse results. + +LEMON provides five well-known heuristics for solving symmetric TSP: + - \ref NearestNeighborTsp Neareast neighbor algorithm + - \ref GreedyTsp Greedy algorithm + - \ref InsertionTsp Insertion heuristic (with four selection methods) + - \ref ChristofidesTsp Christofides algorithm + - \ref Opt2Tsp 2-opt algorithm + +\ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest +solution methods. Furthermore, \ref InsertionTsp is usually quite effective. + +\ref ChristofidesTsp is somewhat slower, but it has the best guaranteed +approximation factor: 3/2. + +\ref Opt2Tsp usually provides the best results in practice, but +it is the slowest method. It can also be used to improve given tours, +for example, the results of other algorithms. + +\image html tsp.png +\image latex tsp.eps "Traveling salesman problem" width=\textwidth +*/ /** @defgroup approx_algs Approximation Algorithms