# HG changeset patch
# User Balazs Dezso <deba@inf.elte.hu>
# Date 1267694222 3600
# Node ID 86613aa28a0ce5afcae34ad41acd910079f97394
# Parent 61120524af27864803c669d537d0b9f2484abeb6
Fix documentation issues (#314)
diff r 61120524af27 r 86613aa28a0c lemon/fractional_matching.h
a

b


111  111  /// solution) can be obtained using the query functions. 
112  112  /// 
113  113  /// The primal solution is multiplied by 
114   /// \ref MaxWeightedMatching::primalScale "2". 
 114  /// \ref MaxFractionalMatching::primalScale "2". 
115  115  /// 
116  116  /// \tparam GR The undirected graph type the algorithm runs on. 
117  117  #ifdef DOXYGEN 
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632  632  /// \brief Weighted fractional matching in general graphs 
633  633  /// 
634  634  /// This class provides an efficient implementation of fractional 
635   /// matching algorithm. The implementation is based on extensive use 
636   /// of priority queues and provides \f$O(nm\log n)\f$ time 
637   /// complexity. 
 635  /// matching algorithm. The implementation uses priority queues and 
 636  /// provides \f$O(nm\log n)\f$ time complexity. 
638  637  /// 
639  638  /// The maximum weighted fractional matching is a relaxation of the 
640  639  /// maximum weighted matching problem where the odd set constraints 
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653  652  /// problem is the following. 
654  653  /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f] 
655  654  /// \f[y_u \ge 0 \quad \forall u \in V\f] 
656   /// \f[\min \sum_{u \in V}y_u \f] /// 
 655  /// \f[\min \sum_{u \in V}y_u \f] 
657  656  /// 
658  657  /// The algorithm can be executed with the run() function. 
659  658  /// After it the matching (the primal solution) and the dual solution 
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661  660  /// 
662  661  /// If the value type is integer, then the primal and the dual 
663  662  /// solutions are multiplied by 
664   /// \ref MaxWeightedMatching::primalScale "2" and 
665   /// \ref MaxWeightedMatching::dualScale "4" respectively. 
 663  /// \ref MaxWeightedFractionalMatching::primalScale "2" and 
 664  /// \ref MaxWeightedFractionalMatching::dualScale "4" respectively. 
666  665  /// 
667  666  /// \tparam GR The undirected graph type the algorithm runs on. 
668  667  /// \tparam WM The type edge weight map. The default type is 
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1270  1269  
1271  1270  /// \brief Run the algorithm. 
1272  1271  /// 
1273   /// This method runs the \c %MaxWeightedMatching algorithm. 
 1272  /// This method runs the \c %MaxWeightedFractionalMatching algorithm. 
1274  1273  /// 
1275  1274  /// \note mwfm.run() is just a shortcut of the following code. 
1276  1275  /// \code 
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1400  1399  /// \brief Weighted fractional perfect matching in general graphs 
1401  1400  /// 
1402  1401  /// This class provides an efficient implementation of fractional 
1403   /// matching algorithm. The implementation is based on extensive use 
1404   /// of priority queues and provides \f$O(nm\log n)\f$ time 
1405   /// complexity. 
 1402  /// matching algorithm. The implementation uses priority queues and 
 1403  /// provides \f$O(nm\log n)\f$ time complexity. 
1406  1404  /// 
1407  1405  /// The maximum weighted fractional perfect matching is a relaxation 
1408  1406  /// of the maximum weighted perfect matching problem where the odd 
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1420  1418  /// used to check the result of the algorithm. The dual linear 
1421  1419  /// problem is the following. 
1422  1420  /// \f[ y_u + y_v \ge w_{uv} \quad \forall uv\in E\f] 
1423   /// \f[\min \sum_{u \in V}y_u \f] /// 
 1421  /// \f[\min \sum_{u \in V}y_u \f] 
1424  1422  /// 
1425  1423  /// The algorithm can be executed with the run() function. 
1426  1424  /// After it the matching (the primal solution) and the dual solution 
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1428  1426  
1429  1427  /// If the value type is integer, then the primal and the dual 
1430  1428  /// solutions are multiplied by 
1431   /// \ref MaxWeightedMatching::primalScale "2" and 
1432   /// \ref MaxWeightedMatching::dualScale "4" respectively. 
 1429  /// \ref MaxWeightedPerfectFractionalMatching::primalScale "2" and 
 1430  /// \ref MaxWeightedPerfectFractionalMatching::dualScale "4" respectively. 
1433  1431  /// 
1434  1432  /// \tparam GR The undirected graph type the algorithm runs on. 
1435  1433  /// \tparam WM The type edge weight map. The default type is 
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2005  2003  
2006  2004  /// \brief Run the algorithm. 
2007  2005  /// 
2008   /// This method runs the \c %MaxWeightedMatching algorithm. 
 2006  /// This method runs the \c %MaxWeightedPerfectFractionalMatching 
 2007  /// algorithm. 
2009  2008  /// 
2010  2009  /// \note mwfm.run() is just a shortcut of the following code. 
2011  2010  /// \code 