lemon-main: comparison lemon/planarity.h

equal deleted inserted replaced

-:dc25a8fbeaef
+:29265c806571
 /// \ingroup planar
 ///
 /// \brief Planarity checking of an undirected simple graph
 ///
 /// This function implements the Boyer-Myrvold algorithm for
-/// planarity checking of an undirected graph. It is a simplified
+/// planarity checking of an undirected simple graph. It is a simplified
 /// version of the PlanarEmbedding algorithm class because neither
-/// the embedding nor the kuratowski subdivisons are not computed.
+/// the embedding nor the Kuratowski subdivisons are computed.
 template <typename GR>
 bool checkPlanarity(const GR& graph) {
 _planarity_bits::PlanarityChecking<GR> pc(graph);
 return pc.run();
 }
 /// \ingroup planar
 ///
 /// \brief Planar embedding of an undirected simple graph
 ///
 /// This class implements the Boyer-Myrvold algorithm for planar
-/// embedding of an undirected graph. The planar embedding is an
+/// embedding of an undirected simple graph. The planar embedding is an
 /// ordering of the outgoing edges of the nodes, which is a possible
 /// configuration to draw the graph in the plane. If there is not
-/// such ordering then the graph contains a \f$ K_5 \f$ (full graph
+/// such ordering then the graph contains a K<sub>5</sub> (full graph
-/// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
+/// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on
-/// 3 ANode and 3 BNode) subdivision.
+/// 3 Red and 3 Blue nodes) subdivision.
 ///
 /// The current implementation calculates either an embedding or a
-/// Kuratowski subdivision. The running time of the algorithm is
+/// Kuratowski subdivision. The running time of the algorithm is O(n).
-/// \f$ O(n) \f$.
+///
+/// \see PlanarDrawing, checkPlanarity()
 template <typename Graph>
 class PlanarEmbedding {
 private:
 TEMPLATE_GRAPH_TYPEDEFS(Graph);
 INTERNAL = 12
 };
 public:
-/// \brief The map for store of embedding
+/// \brief The map type for storing the embedding
+///
+/// The map type for storing the embedding.
+/// \see embeddingMap()
 typedef typename Graph::template ArcMap<Arc> EmbeddingMap;
 /// \brief Constructor
 ///
-/// \note The graph should be simple, i.e. parallel and loop arc
+/// Constructor.
-/// free.
+/// \pre The graph must be simple, i.e. it should not
+/// contain parallel or loop arcs.
 PlanarEmbedding(const Graph& graph)
 : _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
-/// \brief Runs the algorithm.
+/// \brief Run the algorithm.
 ///
-/// Runs the algorithm.
+/// This function runs the algorithm.
-/// \param kuratowski If the parameter is false, then the
+/// \param kuratowski If this parameter is set to \c false, then the
 /// algorithm does not compute a Kuratowski subdivision.
-///\return %True when the graph is planar.
+/// \return \c true if the graph is planar.
 bool run(bool kuratowski = true) {
 typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
 PredMap pred_map(_graph, INVALID);
 TreeMap tree_map(_graph, false);
 }
 return true;
 }
-/// \brief Gives back the successor of an arc
+/// \brief Give back the successor of an arc
 ///
-/// Gives back the successor of an arc. This function makes
+/// This function gives back the successor of an arc. It makes
 /// possible to query the cyclic order of the outgoing arcs from
 /// a node.
 Arc next(const Arc& arc) const {
 return _embedding[arc];
 }
-/// \brief Gives back the calculated embedding map
+/// \brief Give back the calculated embedding map
 ///
-/// The returned map contains the successor of each arc in the
+/// This function gives back the calculated embedding map, which
-/// graph.
+/// contains the successor of each arc in the cyclic order of the
+/// outgoing arcs of its source node.
 const EmbeddingMap& embeddingMap() const {
 return _embedding;
 }
-/// \brief Gives back true if the undirected arc is in the
+/// \brief Give back \c true if the given edge is in the Kuratowski
-/// kuratowski subdivision
+/// subdivision
 ///
-/// Gives back true if the undirected arc is in the kuratowski
+/// This function gives back \c true if the given edge is in the found
-/// subdivision
+/// Kuratowski subdivision.
-/// \note The \c run() had to be called with true value.
+/// \pre The \c run() function must be called with \c true parameter
-bool kuratowski(const Edge& edge) {
+/// before using this function.
+bool kuratowski(const Edge& edge) const {
 return _kuratowski[edge];
 }
 private:
 /// \ingroup planar
 ///
 /// \brief Schnyder's planar drawing algorithm
 ///
 /// The planar drawing algorithm calculates positions for the nodes
-/// in the plane which coordinates satisfy that if the arcs are
+/// in the plane. These coordinates satisfy that if the edges are
-/// represented with straight lines then they will not intersect
+/// represented with straight lines, then they will not intersect
 /// each other.
 ///
-/// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid,
+/// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid,
-/// i.e. each node will be located in the \c [0,n-2]x[0,n-2] square.
+/// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square.
 /// The time complexity of the algorithm is O(n).
+///
+/// \see PlanarEmbedding
 template <typename Graph>
 class PlanarDrawing {
 public:
 TEMPLATE_GRAPH_TYPEDEFS(Graph);
-/// \brief The point type for store coordinates
+/// \brief The point type for storing coordinates
 typedef dim2::Point<int> Point;
-/// \brief The map type for store coordinates
+/// \brief The map type for storing the coordinates of the nodes
 typedef typename Graph::template NodeMap<Point> PointMap;
 /// \brief Constructor
 ///
 /// Constructor
-/// \pre The graph should be simple, i.e. loop and parallel arc free.
+/// \pre The graph must be simple, i.e. it should not
+/// contain parallel or loop arcs.
 PlanarDrawing(const Graph& graph)
 : _graph(graph), _point_map(graph) {}
 private:
 }
 public:
-/// \brief Calculates the node positions
+/// \brief Calculate the node positions
 ///
-/// This function calculates the node positions.
+/// This function calculates the node positions on the plane.
-/// \return %True if the graph is planar.
+/// \return \c true if the graph is planar.
 bool run() {
 PlanarEmbedding<Graph> pe(_graph);
 if (!pe.run()) return false;
 run(pe);
 return true;
 }
-/// \brief Calculates the node positions according to a
+/// \brief Calculate the node positions according to a
 /// combinatorical embedding
 ///
-/// This function calculates the node locations. The \c embedding
+/// This function calculates the node positions on the plane.
-/// parameter should contain a valid combinatorical embedding, i.e.
+/// The given \c embedding map should contain a valid combinatorical
-/// a valid cyclic order of the arcs.
+/// embedding, i.e. a valid cyclic order of the arcs.
+/// It can be computed using PlanarEmbedding.
 template <typename EmbeddingMap>
 void run(const EmbeddingMap& embedding) {
 typedef SmartEdgeSet<Graph> AuxGraph;
 if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
 drawing(aux_graph, aux_embedding, _point_map);
 }
 /// \brief The coordinate of the given node
 ///
-/// The coordinate of the given node.
+/// This function returns the coordinate of the given node.
 Point operator[](const Node& node) const {
 return _point_map[node];
 }
-/// \brief Returns the grid embedding in a \e NodeMap.
+/// \brief Return the grid embedding in a node map
 ///
-/// Returns the grid embedding in a \e NodeMap of \c dim2::Point<int> .
+/// This function returns the grid embedding in a node map of
+/// \c dim2::Point<int> coordinates.
 const PointMap& coords() const {
 return _point_map;
 }
 private:
 /// \ingroup planar
 ///
 /// \brief Coloring planar graphs
 ///
 /// The graph coloring problem is the coloring of the graph nodes
-/// that there are not adjacent nodes with the same color. The
+/// so that there are no adjacent nodes with the same color. The
-/// planar graphs can be always colored with four colors, it is
+/// planar graphs can always be colored with four colors, which is
-/// proved by Appel and Haken and their proofs provide a quadratic
+/// proved by Appel and Haken. Their proofs provide a quadratic
 /// time algorithm for four coloring, but it could not be used to
-/// implement efficient algorithm. The five and six coloring can be
+/// implement an efficient algorithm. The five and six coloring can be
-/// made in linear time, but in this class the five coloring has
+/// made in linear time, but in this class, the five coloring has
 /// quadratic worst case time complexity. The two coloring (if
 /// possible) is solvable with a graph search algorithm and it is
 /// implemented in \ref bipartitePartitions() function in LEMON. To
-/// decide whether the planar graph is three colorable is
+/// decide whether a planar graph is three colorable is NP-complete.
-/// NP-complete.
 ///
 /// This class contains member functions for calculate colorings
 /// with five and six colors. The six coloring algorithm is a simple
 /// greedy coloring on the backward minimum outgoing order of nodes.
-/// This order can be computed as in each phase the node with least
+/// This order can be computed by selecting the node with least
-/// outgoing arcs to unprocessed nodes is chosen. This order
+/// outgoing arcs to unprocessed nodes in each phase. This order
 /// guarantees that when a node is chosen for coloring it has at
 /// most five already colored adjacents. The five coloring algorithm
 /// use the same method, but if the greedy approach fails to color
 /// with five colors, i.e. the node has five already different
 /// colored neighbours, it swaps the colors in one of the connected
 class PlanarColoring {
 public:
 TEMPLATE_GRAPH_TYPEDEFS(Graph);
-/// \brief The map type for store color indexes
+/// \brief The map type for storing color indices
 typedef typename Graph::template NodeMap<int> IndexMap;
-/// \brief The map type for store colors
+/// \brief The map type for storing colors
+///
+/// The map type for storing colors.
+/// \see Palette, Color
 typedef ComposeMap<Palette, IndexMap> ColorMap;
 /// \brief Constructor
 ///
-/// Constructor
+/// Constructor.
-/// \pre The graph should be simple, i.e. loop and parallel arc free.
+/// \pre The graph must be simple, i.e. it should not
+/// contain parallel or loop arcs.
 PlanarColoring(const Graph& graph)
 : _graph(graph), _color_map(graph), _palette(0) {
 _palette.add(Color(1,0,0));
 _palette.add(Color(0,1,0));
 _palette.add(Color(0,0,1));
 _palette.add(Color(1,1,0));
 _palette.add(Color(1,0,1));
 _palette.add(Color(0,1,1));
 }
-/// \brief Returns the \e NodeMap of color indexes
+/// \brief Return the node map of color indices
 ///
-/// Returns the \e NodeMap of color indexes. The values are in the
+/// This function returns the node map of color indices. The values are
-/// range \c [0..4] or \c [0..5] according to the coloring method.
+/// in the range \c [0..4] or \c [0..5] according to the coloring method.
 IndexMap colorIndexMap() const {
 return _color_map;
 }
-/// \brief Returns the \e NodeMap of colors
+/// \brief Return the node map of colors
 ///
-/// Returns the \e NodeMap of colors. The values are five or six
+/// This function returns the node map of colors. The values are among
-/// distinct \ref lemon::Color "colors".
+/// five or six distinct \ref lemon::Color "colors".
 ColorMap colorMap() const {
 return composeMap(_palette, _color_map);
 }
-/// \brief Returns the color index of the node
+/// \brief Return the color index of the node
 ///
-/// Returns the color index of the node. The values are in the
+/// This function returns the color index of the given node. The value is
-/// range \c [0..4] or \c [0..5] according to the coloring method.
+/// in the range \c [0..4] or \c [0..5] according to the coloring method.
 int colorIndex(const Node& node) const {
 return _color_map[node];
 }
-/// \brief Returns the color of the node
+/// \brief Return the color of the node
 ///
-/// Returns the color of the node. The values are five or six
+/// This function returns the color of the given node. The value is among
-/// distinct \ref lemon::Color "colors".
+/// five or six distinct \ref lemon::Color "colors".
 Color color(const Node& node) const {
 return _palette[_color_map[node]];
 }
-/// \brief Calculates a coloring with at most six colors
+/// \brief Calculate a coloring with at most six colors
 ///
 /// This function calculates a coloring with at most six colors. The time
 /// complexity of this variant is linear in the size of the graph.
-/// \return %True when the algorithm could color the graph with six color.
+/// \return \c true if the algorithm could color the graph with six colors.
-/// If the algorithm fails, then the graph could not be planar.
+/// If the algorithm fails, then the graph is not planar.
-/// \note This function can return true if the graph is not
+/// \note This function can return \c true if the graph is not
-/// planar but it can be colored with 6 colors.
+/// planar, but it can be colored with at most six colors.
 bool runSixColoring() {
 typename Graph::template NodeMap<int> heap_index(_graph, -1);
 BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
 }
 }
 public:
-/// \brief Calculates a coloring with at most five colors
+/// \brief Calculate a coloring with at most five colors
 ///
 /// This function calculates a coloring with at most five
 /// colors. The worst case time complexity of this variant is
 /// quadratic in the size of the graph.
+/// \param embedding This map should contain a valid combinatorical
+/// embedding, i.e. a valid cyclic order of the arcs.
+/// It can be computed using PlanarEmbedding.
 template <typename EmbeddingMap>
 void runFiveColoring(const EmbeddingMap& embedding) {
 typename Graph::template NodeMap<int> heap_index(_graph, -1);
 BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
 kempeRecoloring(order[i], embedding);
 }
 }
 }
-/// \brief Calculates a coloring with at most five colors
+/// \brief Calculate a coloring with at most five colors
 ///
 /// This function calculates a coloring with at most five
 /// colors. The worst case time complexity of this variant is
 /// quadratic in the size of the graph.
-/// \return %True when the graph is planar.
+/// \return \c true if the graph is planar.
 bool runFiveColoring() {
 PlanarEmbedding<Graph> pe(_graph);
 if (!pe.run()) return false;
 runFiveColoring(pe.embeddingMap());

changeset 835	b9b2e8abe70b
parent 798	58c330ad0b5c
child 877	141f9c0db4a3