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373 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a |
373 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a |
374 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum |
374 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum |
375 cut is the \f$X\f$ solution of the next optimization problem: |
375 cut is the \f$X\f$ solution of the next optimization problem: |
376 |
376 |
377 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} |
377 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} |
378 \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f] |
378 \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f] |
379 |
379 |
380 LEMON contains several algorithms related to minimum cut problems: |
380 LEMON contains several algorithms related to minimum cut problems: |
381 |
381 |
382 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut |
382 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut |
383 in directed graphs. |
383 in directed graphs. |
396 \brief Algorithms for discovering the graph properties |
396 \brief Algorithms for discovering the graph properties |
397 |
397 |
398 This group contains the algorithms for discovering the graph properties |
398 This group contains the algorithms for discovering the graph properties |
399 like connectivity, bipartiteness, euler property, simplicity etc. |
399 like connectivity, bipartiteness, euler property, simplicity etc. |
400 |
400 |
401 \image html edge_biconnected_components.png |
401 \image html connected_components.png |
402 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth |
402 \image latex connected_components.eps "Connected components" width=\textwidth |
403 */ |
403 */ |
404 |
404 |
405 /** |
405 /** |
406 @defgroup planar Planarity Embedding and Drawing |
406 @defgroup planar Planarity Embedding and Drawing |
407 @ingroup algs |
407 @ingroup algs |