# Ticket #314: 86613aa28a0c.patch

File 86613aa28a0c.patch, 4.2 KB (added by Balazs Dezso, 10 years ago)

Fix doc issues

• ## lemon/fractional_matching.h

# HG changeset patch
# User Balazs Dezso <deba@inf.elte.hu>
# Date 1267694222 -3600
diff -r 61120524af27 -r 86613aa28a0c lemon/fractional_matching.h
 a /// solution) can be obtained using the query functions. /// /// The primal solution is multiplied by /// \ref MaxWeightedMatching::primalScale "2". /// \ref MaxFractionalMatching::primalScale "2". /// /// \tparam GR The undirected graph type the algorithm runs on. #ifdef DOXYGEN /// \brief Weighted fractional matching in general graphs /// /// This class provides an efficient implementation of fractional /// matching algorithm. The implementation is based on extensive use /// of priority queues and provides \f$O(nm\log n)\f$ time /// complexity. /// matching algorithm. The implementation uses priority queues and /// provides \f$O(nm\log n)\f$ time complexity. /// /// The maximum weighted fractional matching is a relaxation of the /// maximum weighted matching problem where the odd set constraints /// 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] /// \f[\min \sum_{u \in V}y_u \f] /// /// \f[\min \sum_{u \in V}y_u \f] /// /// The algorithm can be executed with the run() function. /// After it the matching (the primal solution) and the dual solution /// /// If the value type is integer, then the primal and the dual /// solutions are multiplied by /// \ref MaxWeightedMatching::primalScale "2" and /// \ref MaxWeightedMatching::dualScale "4" respectively. /// \ref MaxWeightedFractionalMatching::primalScale "2" and /// \ref MaxWeightedFractionalMatching::dualScale "4" respectively. /// /// \tparam GR The undirected graph type the algorithm runs on. /// \tparam WM The type edge weight map. The default type is /// \brief Run the algorithm. /// /// This method runs the \c %MaxWeightedMatching algorithm. /// This method runs the \c %MaxWeightedFractionalMatching algorithm. /// /// \note mwfm.run() is just a shortcut of the following code. /// \code /// \brief Weighted fractional perfect matching in general graphs /// /// This class provides an efficient implementation of fractional /// matching algorithm. The implementation is based on extensive use /// of priority queues and provides \f$O(nm\log n)\f$ time /// complexity. /// matching algorithm. The implementation uses priority queues and /// provides \f$O(nm\log n)\f$ time complexity. /// /// The maximum weighted fractional perfect matching is a relaxation /// of the maximum weighted perfect matching problem where the odd /// 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[\min \sum_{u \in V}y_u \f] /// /// \f[\min \sum_{u \in V}y_u \f] /// /// The algorithm can be executed with the run() function. /// After it the matching (the primal solution) and the dual solution /// If the value type is integer, then the primal and the dual /// solutions are multiplied by /// \ref MaxWeightedMatching::primalScale "2" and /// \ref MaxWeightedMatching::dualScale "4" respectively. /// \ref MaxWeightedPerfectFractionalMatching::primalScale "2" and /// \ref MaxWeightedPerfectFractionalMatching::dualScale "4" respectively. /// /// \tparam GR The undirected graph type the algorithm runs on. /// \tparam WM The type edge weight map. The default type is /// \brief Run the algorithm. /// /// This method runs the \c %MaxWeightedMatching algorithm. /// This method runs the \c %MaxWeightedPerfectFractionalMatching /// algorithm. /// /// \note mwfm.run() is just a shortcut of the following code. /// \code