COIN-OR::LEMON - Graph Library

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    r1038 r1003  
    559559\image latex planar.eps "Plane graph" width=\textwidth
    560560*/
    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 */
    597561
    598562/**
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