doc/groups.dox
changeset 1110 c0c2f5c87aa6
parent 1003 16f55008c863
parent 1036 dff32ce3db71
child 1049 7bf489cf624e
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50:417ab2c5a98f 54:cde5d133fe5d
   556 embedding and drawing.
   556 embedding and drawing.
   557 
   557 
   558 \image html planar.png
   558 \image html planar.png
   559 \image latex planar.eps "Plane graph" width=\textwidth
   559 \image latex planar.eps "Plane graph" width=\textwidth
   560 */
   560 */
       
   561  
       
   562 /**
       
   563 @defgroup tsp Traveling Salesman Problem
       
   564 @ingroup algs
       
   565 \brief Algorithms for the symmetric traveling salesman problem
       
   566 
       
   567 This group contains basic heuristic algorithms for the the symmetric
       
   568 \e traveling \e salesman \e problem (TSP).
       
   569 Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
       
   570 the problem is to find a shortest possible tour that visits each node exactly
       
   571 once (i.e. the minimum cost Hamiltonian cycle).
       
   572 
       
   573 These TSP algorithms are intended to be used with a \e metric \e cost
       
   574 \e function, i.e. the edge costs should satisfy the triangle inequality.
       
   575 Otherwise the algorithms could yield worse results.
       
   576 
       
   577 LEMON provides five well-known heuristics for solving symmetric TSP:
       
   578  - \ref NearestNeighborTsp Neareast neighbor algorithm
       
   579  - \ref GreedyTsp Greedy algorithm
       
   580  - \ref InsertionTsp Insertion heuristic (with four selection methods)
       
   581  - \ref ChristofidesTsp Christofides algorithm
       
   582  - \ref Opt2Tsp 2-opt algorithm
       
   583 
       
   584 \ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
       
   585 solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
       
   586 
       
   587 \ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
       
   588 approximation factor: 3/2.
       
   589 
       
   590 \ref Opt2Tsp usually provides the best results in practice, but
       
   591 it is the slowest method. It can also be used to improve given tours,
       
   592 for example, the results of other algorithms.
       
   593 
       
   594 \image html tsp.png
       
   595 \image latex tsp.eps "Traveling salesman problem" width=\textwidth
       
   596 */
   561 
   597 
   562 /**
   598 /**
   563 @defgroup approx_algs Approximation Algorithms
   599 @defgroup approx_algs Approximation Algorithms
   564 @ingroup algs
   600 @ingroup algs
   565 \brief Approximation algorithms.
   601 \brief Approximation algorithms.