RhodeCode

  ///

  /// The algorithm can be executed with the run() function.  After it

  /// the matching (the primal solution) and the barrier (the dual

  /// solution) can be obtained using the query functions.

  ///

  /// The primal solution is multiplied by

  ///

  /// \tparam GR The undirected graph type the algorithm runs on.

#ifdef DOXYGEN

  template <typename GR, typename TR>

#else

  template <typename GR,

  /// \ingroup matching

  ///

  /// \brief Weighted fractional matching in general graphs

  ///

  /// This class provides an efficient implementation of fractional

  ///

  /// The maximum weighted fractional matching is a relaxation of the

  /// maximum weighted matching problem where the odd set constraints

  /// are omitted.

  /// It can be formulated with the following linear program.

  /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]

  /// The algorithm calculates an optimal fractional matching and a

  /// proof of the optimality. The solution of the dual problem can be

  /// used to check the result of the algorithm. The dual linear

  /// problem is the following.

  /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f]

  /// \f[y_u \ge 0 \quad \forall u \in V\f]

  ///

  /// The algorithm can be executed with the run() function.

  /// After it the matching (the primal solution) and the dual solution

  /// can be obtained using the query functions.

  ///

  /// If the value type is integer, then the primal and the dual

  /// solutions are multiplied by

  ///

  /// \tparam GR The undirected graph type the algorithm runs on.

  /// \tparam WM The type edge weight map. The default type is

  /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".

#ifdef DOXYGEN

  template <typename GR, typename WM>

        }

      }

    }

    /// \brief Run the algorithm.

    ///

    ///

    /// \note mwfm.run() is just a shortcut of the following code.

    /// \code

    ///   mwfm.init();

    ///   mwfm.start();

    /// \endcode

  /// \ingroup matching

  ///

  /// \brief Weighted fractional perfect matching in general graphs

  ///

  /// This class provides an efficient implementation of fractional

  ///

  /// The maximum weighted fractional perfect matching is a relaxation

  /// of the maximum weighted perfect matching problem where the odd

  /// set constraints are omitted.

  /// It can be formulated with the following linear program.

  /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]

  ///

  /// The algorithm calculates an optimal fractional matching and a

  /// proof of the optimality. The solution of the dual problem can be

  /// used to check the result of the algorithm. The dual linear

  /// problem is the following.

  /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f]

  ///

  /// The algorithm can be executed with the run() function.

  /// After it the matching (the primal solution) and the dual solution

  /// can be obtained using the query functions.

  /// If the value type is integer, then the primal and the dual

  /// solutions are multiplied by

  ///

  /// \tparam GR The undirected graph type the algorithm runs on.

  /// \tparam WM The type edge weight map. The default type is

  /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".

#ifdef DOXYGEN

  template <typename GR, typename WM>

      }

      return true;

    }

    /// \brief Run the algorithm.

    ///

    ///

    /// \note mwfm.run() is just a shortcut of the following code.

    /// \code

    ///   mwpfm.init();

    ///   mwpfm.start();

    /// \endcode