# 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
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| 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 |