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@@ -36,10 +36,10 @@ |
| 36 | 36 |
/// |
| 37 | 37 |
/// \brief Gomory-Hu cut tree algorithm |
| 38 | 38 |
/// |
| 39 |
/// The Gomory-Hu tree is a tree on the node set of the graph, but it |
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/// may contain edges which are not in the original digraph. It has the |
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/// The Gomory-Hu tree is a tree on the node set of a given graph, but it |
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/// may contain edges which are not in the original graph. It has the |
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| 41 | 41 |
/// property that the minimum capacity edge of the path between two nodes |
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/// in this tree has the same weight as the minimum cut in the |
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/// in this tree has the same weight as the minimum cut in the graph |
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| 43 | 43 |
/// between these nodes. Moreover the components obtained by removing |
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/// this edge from the tree determine the corresponding minimum cut. |
| 45 | 45 |
/// |
| ... | ... |
@@ -53,22 +53,26 @@ |
| 53 | 53 |
/// by \c predNode(), \c predValue() and \c rootDist(). |
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/// |
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/// The members \c minCutMap() and \c minCutValue() calculate |
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/// the minimum cut and the minimum cut value between any two node |
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/// in the digraph. You can also list (iterate on) the nodes and the |
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/// |
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/// the minimum cut and the minimum cut value between any two nodes |
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/// in the graph. You can also list (iterate on) the nodes and the |
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/// edges of the cuts using \c MinCutNodeIt and \c MinCutEdgeIt. |
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| 59 | 59 |
/// |
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/// \tparam GR The undirected graph data structure the algorithm will run on |
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/// \tparam CAP type of the EdgeMap describing the Edge capacities. |
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/// |
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/// \tparam GR The type of the undirected graph the algorithm runs on. |
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/// \tparam CAP The type of the edge map describing the edge capacities. |
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/// It is \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>" by default. |
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#ifdef DOXYGEN |
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template <typename GR, |
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typename CAP = typename GR::template EdgeMap<int> |
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> |
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typename CAP> |
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#else |
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template <typename GR, |
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typename CAP = typename GR::template EdgeMap<int> > |
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#endif |
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class GomoryHu {
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public: |
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|
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/// The graph type |
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typedef GR Graph; |
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/// The type |
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/// The type of the edge capacity map |
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typedef CAP Capacity; |
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/// The value type of capacities |
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typedef typename Capacity::Value Value; |
| ... | ... |
@@ -114,8 +118,8 @@ |
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/// \brief Constructor |
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/// |
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/// Constructor |
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/// \param graph The graph the algorithm will run on. |
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/// \param capacity The capacity map. |
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/// \param graph The undirected graph the algorithm runs on. |
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/// \param capacity The edge capacity map. |
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| 119 | 123 |
GomoryHu(const Graph& graph, const Capacity& capacity) |
| 120 | 124 |
: _graph(graph), _capacity(capacity), |
| 121 | 125 |
_pred(0), _weight(0), _order(0) |
| ... | ... |
@@ -131,10 +135,9 @@ |
| 131 | 135 |
destroyStructures(); |
| 132 | 136 |
} |
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// \brief Initialize the internal data structures. |
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// |
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// This function initializes the internal data structures. |
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// |
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private: |
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|
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// Initialize the internal data structures |
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void init() {
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createStructures(); |
| 140 | 143 |
|
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@@ -148,12 +151,7 @@ |
| 148 | 151 |
} |
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// \brief Start the algorithm |
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// |
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// This function starts the algorithm. |
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// |
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// \pre \ref init() must be called before using this function. |
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// |
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// Start the algorithm |
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void start() {
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Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID); |
| 159 | 157 |
|
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@@ -198,6 +196,8 @@ |
| 198 | 196 |
} |
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} |
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public: |
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|
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///\name Execution Control |
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///@{
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@@ -215,8 +215,8 @@ |
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///\name Query Functions |
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///The results of the algorithm can be obtained using these |
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///functions.\n |
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///The \ref run() "run()" should be called before using them.\n |
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///See also MinCutNodeIt and MinCutEdgeIt |
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///\ref run() "run()" should be called before using them.\n |
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///See also \ref MinCutNodeIt and \ref MinCutEdgeIt. |
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///@{
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|
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@@ -250,7 +250,7 @@ |
| 250 | 250 |
/// |
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/// This function returns the minimum cut value between two nodes. The |
| 252 | 252 |
/// algorithm finds the nearest common ancestor in the Gomory-Hu |
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/// tree and calculates the minimum weight |
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/// tree and calculates the minimum weight edge on the paths to |
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| 254 | 254 |
/// the ancestor. |
| 255 | 255 |
Value minCutValue(const Node& s, const Node& t) const {
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| 256 | 256 |
Node sn = s, tn = t; |
| ... | ... |
@@ -271,21 +271,19 @@ |
| 271 | 271 |
/// \brief Return the minimum cut between two nodes |
| 272 | 272 |
/// |
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/// This function returns the minimum cut between the nodes \c s and \c t |
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/// the \r cutMap parameter by setting the nodes in the component of |
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/// \c \s to true and the other nodes to false. |
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/// in the \c cutMap parameter by setting the nodes in the component of |
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/// \c s to \c true and the other nodes to \c false. |
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/// |
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/// The \c cutMap should be \ref concepts::ReadWriteMap |
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/// "ReadWriteMap". |
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/// |
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/// For higher level interfaces, see MinCutNodeIt and MinCutEdgeIt |
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/// For higher level interfaces, see MinCutNodeIt and MinCutEdgeIt. |
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template <typename CutMap> |
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Value minCutMap(const Node& s, ///< |
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Value minCutMap(const Node& s, ///< The base node. |
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const Node& t, |
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///< The node you want to separate from |
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///< The node you want to separate from node \c s. |
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| 285 | 282 |
CutMap& cutMap |
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///< The cut will be return in this map. |
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/// It must be a \c bool \ref concepts::ReadWriteMap |
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/// |
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///< The cut will be returned in this map. |
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/// It must be a \c bool (or convertible) |
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/// \ref concepts::ReadWriteMap "ReadWriteMap" |
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/// on the graph nodes. |
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| 289 | 287 |
) const {
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| 290 | 288 |
Node sn = s, tn = t; |
| 291 | 289 |
bool s_root=false; |
| ... | ... |
@@ -348,8 +346,8 @@ |
| 348 | 346 |
/// \code |
| 349 | 347 |
/// GomoruHu<Graph> gom(g, capacities); |
| 350 | 348 |
/// gom.run(); |
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/// int sum=0; |
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/// for(GomoruHu<Graph>::MinCutNodeIt n(gom,s,t);n!=INVALID;++n) ++sum; |
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/// int cnt=0; |
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/// for(GomoruHu<Graph>::MinCutNodeIt n(gom,s,t); n!=INVALID; ++n) ++cnt; |
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/// \endcode |
| 354 | 352 |
class MinCutNodeIt |
| 355 | 353 |
{
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@@ -359,15 +357,15 @@ |
| 359 | 357 |
public: |
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/// Constructor |
| 361 | 359 |
|
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/// Constructor |
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/// Constructor. |
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| 363 | 361 |
/// |
| 364 | 362 |
MinCutNodeIt(GomoryHu const &gomory, |
| 365 | 363 |
///< The GomoryHu class. You must call its |
| 366 | 364 |
/// run() method |
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/// before initializing this iterator |
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const Node& s, ///< Base node |
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/// before initializing this iterator. |
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const Node& s, ///< The base node. |
|
| 369 | 367 |
const Node& t, |
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///< The node you want to separate from |
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///< The node you want to separate from node \c s. |
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| 371 | 369 |
bool side=true |
| 372 | 370 |
///< If it is \c true (default) then the iterator lists |
| 373 | 371 |
/// the nodes of the component containing \c s, |
| ... | ... |
@@ -398,9 +396,9 @@ |
| 398 | 396 |
_node_it!=INVALID && _cut[_node_it]!=_side; |
| 399 | 397 |
++_node_it) {}
|
| 400 | 398 |
} |
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/// Conversion to Node |
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/// Conversion to \c Node |
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| 402 | 400 |
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/// Conversion to Node |
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/// Conversion to \c Node. |
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| 404 | 402 |
/// |
| 405 | 403 |
operator typename Graph::Node() const |
| 406 | 404 |
{
|
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@@ -410,7 +408,7 @@ |
| 410 | 408 |
bool operator!=(Invalid) { return _node_it!=INVALID; }
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| 411 | 409 |
/// Next node |
| 412 | 410 |
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/// Next node |
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/// Next node. |
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/// |
| 415 | 413 |
MinCutNodeIt &operator++() |
| 416 | 414 |
{
|
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@@ -419,10 +417,10 @@ |
| 419 | 417 |
} |
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/// Postfix incrementation |
| 421 | 419 |
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/// Postfix incrementation |
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/// Postfix incrementation. |
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/// |
| 424 | 422 |
/// \warning This incrementation |
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/// returns a \c Node, not a \ |
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/// returns a \c Node, not a \c MinCutNodeIt, as one may |
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/// expect. |
| 427 | 425 |
typename Graph::Node operator++(int) |
| 428 | 426 |
{
|
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@@ -446,11 +444,11 @@ |
| 446 | 444 |
/// GomoruHu<Graph> gom(g, capacities); |
| 447 | 445 |
/// gom.run(); |
| 448 | 446 |
/// int value=0; |
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/// for(GomoruHu<Graph>::MinCutEdgeIt e(gom,s,t);e!=INVALID;++e) |
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/// for(GomoruHu<Graph>::MinCutEdgeIt e(gom,s,t); e!=INVALID; ++e) |
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| 450 | 448 |
/// value+=capacities[e]; |
| 451 | 449 |
/// \endcode |
| 452 | 450 |
/// the result will be the same as it is returned by |
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/// \ref GomoryHu:: |
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/// \ref GomoryHu::minCutValue() "gom.minCutValue(s,t)" |
|
| 454 | 452 |
class MinCutEdgeIt |
| 455 | 453 |
{
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| 456 | 454 |
bool _side; |
| ... | ... |
@@ -473,10 +471,10 @@ |
| 473 | 471 |
MinCutEdgeIt(GomoryHu const &gomory, |
| 474 | 472 |
///< The GomoryHu class. You must call its |
| 475 | 473 |
/// run() method |
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/// before initializing this iterator |
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const Node& s, ///< Base node |
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/// before initializing this iterator. |
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const Node& s, ///< The base node. |
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const Node& t, |
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///< The node you want to separate from |
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///< The node you want to separate from node \c s. |
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| 480 | 478 |
bool side=true |
| 481 | 479 |
///< If it is \c true (default) then the listed arcs |
| 482 | 480 |
/// will be oriented from the |
| ... | ... |
@@ -504,17 +502,17 @@ |
| 504 | 502 |
} |
| 505 | 503 |
while(_arc_it!=INVALID && _cut[_graph.target(_arc_it)]) step(); |
| 506 | 504 |
} |
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/// Conversion to Arc |
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/// Conversion to \c Arc |
|
| 508 | 506 |
|
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/// Conversion to Arc |
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/// Conversion to \c Arc. |
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/// |
| 511 | 509 |
operator typename Graph::Arc() const |
| 512 | 510 |
{
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| 513 | 511 |
return _arc_it; |
| 514 | 512 |
} |
| 515 |
/// Conversion to Edge |
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/// Conversion to \c Edge |
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| 516 | 514 |
|
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/// Conversion to Edge |
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/// Conversion to \c Edge. |
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/// |
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operator typename Graph::Edge() const |
| 520 | 518 |
{
|
| ... | ... |
@@ -524,7 +522,7 @@ |
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bool operator!=(Invalid) { return _node_it!=INVALID; }
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/// Next edge |
| 526 | 524 |
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/// Next edge |
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/// Next edge. |
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/// |
| 529 | 527 |
MinCutEdgeIt &operator++() |
| 530 | 528 |
{
|
| ... | ... |
@@ -534,11 +532,10 @@ |
| 534 | 532 |
} |
| 535 | 533 |
/// Postfix incrementation |
| 536 | 534 |
|
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/// Postfix incrementation |
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/// Postfix incrementation. |
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| 538 | 536 |
/// |
| 539 | 537 |
/// \warning This incrementation |
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/// returns a \c Arc, not a \ref MinCutEdgeIt, as one may |
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/// expect. |
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/// returns an \c Arc, not a \c MinCutEdgeIt, as one may expect. |
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typename Graph::Arc operator++(int) |
| 543 | 540 |
{
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| 544 | 541 |
typename Graph::Arc e=*this; |
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