| 1 | /* -*- C++ -*- |
| 2 | * |
| 3 | * This file is a part of LEMON, a generic C++ optimization library |
| 4 | * |
| 5 | * Copyright (C) 2003-2008 |
| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
| 8 | * |
| 9 | * Permission to use, modify and distribute this software is granted |
| 10 | * provided that this copyright notice appears in all copies. For |
| 11 | * precise terms see the accompanying LICENSE file. |
| 12 | * |
| 13 | * This software is provided "AS IS" with no warranty of any kind, |
| 14 | * express or implied, and with no claim as to its suitability for any |
| 15 | * purpose. |
| 16 | * |
| 17 | */ |
| 18 | |
| 19 | #ifndef LEMON_GOMORY_HU_TREE_H |
| 20 | #define LEMON_GOMORY_HU_TREE_H |
| 21 | |
| 22 | #include <lemon/preflow.h> |
| 23 | #include <lemon/concept_check.h> |
| 24 | #include <lemon/concepts/maps.h> |
| 25 | |
| 26 | /// \ingroup min_cut |
| 27 | /// \file |
| 28 | /// \brief Gomory-Hu cut tree in graphs. |
| 29 | |
| 30 | namespace lemon { |
| 31 | |
| 32 | /// \ingroup min_cut |
| 33 | /// |
| 34 | /// \brief Gomory-Hu cut tree algorithm |
| 35 | /// |
| 36 | /// The Gomory-Hu tree is a tree on the nodeset of the digraph, but it |
| 37 | /// may contain arcs which are not in the original digraph. It helps |
| 38 | /// to calculate the minimum cut between all pairs of nodes, because |
| 39 | /// the minimum capacity arc on the tree path between two nodes has |
| 40 | /// the same weight as the minimum cut in the digraph between these |
| 41 | /// nodes. Moreover this arc separates the nodes to two parts which |
| 42 | /// determine this minimum cut. |
| 43 | /// |
| 44 | /// The algorithm calculates \e n-1 distinict minimum cuts with |
| 45 | /// preflow algorithm, therefore the algorithm has |
| 46 | /// \f$(O(n^3\sqrt{e})\f$ overall time complexity. It calculates a |
| 47 | /// rooted Gomory-Hu tree, the structure of the tree and the weights |
| 48 | /// can be obtained with \c predNode() and \c predValue() |
| 49 | /// functions. The \c minCutValue() and \c minCutMap() calculates |
| 50 | /// the minimum cut and the minimum cut value between any two node |
| 51 | /// in the digraph. |
| 52 | template <typename _Graph, |
| 53 | typename _Capacity = typename _Graph::template EdgeMap<int> > |
| 54 | class GomoryHuTree { |
| 55 | public: |
| 56 | |
| 57 | /// The graph type |
| 58 | typedef _Graph Graph; |
| 59 | /// The capacity on edges |
| 60 | typedef _Capacity Capacity; |
| 61 | /// The value type of capacities |
| 62 | typedef typename Capacity::Value Value; |
| 63 | |
| 64 | private: |
| 65 | |
| 66 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 67 | |
| 68 | const Graph& _graph; |
| 69 | const Capacity& _capacity; |
| 70 | |
| 71 | Node _root; |
| 72 | typename Graph::template NodeMap<Node>* _pred; |
| 73 | typename Graph::template NodeMap<Value>* _weight; |
| 74 | typename Graph::template NodeMap<int>* _order; |
| 75 | |
| 76 | void createStructures() { |
| 77 | if (!_pred) { |
| 78 | _pred = new typename Graph::template NodeMap<Node>(_graph); |
| 79 | } |
| 80 | if (!_weight) { |
| 81 | _weight = new typename Graph::template NodeMap<Value>(_graph); |
| 82 | } |
| 83 | if (!_order) { |
| 84 | _order = new typename Graph::template NodeMap<int>(_graph); |
| 85 | } |
| 86 | } |
| 87 | |
| 88 | void destroyStructures() { |
| 89 | if (_pred) { |
| 90 | delete _pred; |
| 91 | } |
| 92 | if (_weight) { |
| 93 | delete _weight; |
| 94 | } |
| 95 | if (_order) { |
| 96 | delete _order; |
| 97 | } |
| 98 | } |
| 99 | |
| 100 | public: |
| 101 | |
| 102 | /// \brief Constructor |
| 103 | /// |
| 104 | /// Constructor |
| 105 | /// \param graph The graph type. |
| 106 | /// \param capacity The capacity map. |
| 107 | GomoryHuTree(const Graph& graph, const Capacity& capacity) |
| 108 | : _graph(graph), _capacity(capacity), |
| 109 | _pred(0), _weight(0), _order(0) |
| 110 | { |
| 111 | checkConcept<concepts::ReadMap<Edge, Value>, Capacity>(); |
| 112 | } |
| 113 | |
| 114 | |
| 115 | /// \brief Destructor |
| 116 | /// |
| 117 | /// Destructor |
| 118 | ~GomoryHuTree() { |
| 119 | destroyStructures(); |
| 120 | } |
| 121 | |
| 122 | /// \brief Initializes the internal data structures. |
| 123 | /// |
| 124 | /// Initializes the internal data structures. |
| 125 | /// |
| 126 | void init() { |
| 127 | createStructures(); |
| 128 | |
| 129 | _root = NodeIt(_graph); |
| 130 | for (NodeIt n(_graph); n != INVALID; ++n) { |
| 131 | _pred->set(n, _root); |
| 132 | _order->set(n, -1); |
| 133 | } |
| 134 | _pred->set(_root, INVALID); |
| 135 | _weight->set(_root, std::numeric_limits<Value>::max()); |
| 136 | } |
| 137 | |
| 138 | |
| 139 | /// \brief Starts the algorithm |
| 140 | /// |
| 141 | /// Starts the algorithm. |
| 142 | void start() { |
| 143 | Preflow<Graph, Capacity> fa(_graph, _capacity, _root, INVALID); |
| 144 | |
| 145 | for (NodeIt n(_graph); n != INVALID; ++n) { |
| 146 | if (n == _root) continue; |
| 147 | |
| 148 | Node pn = (*_pred)[n]; |
| 149 | fa.source(n); |
| 150 | fa.target(pn); |
| 151 | |
| 152 | fa.runMinCut(); |
| 153 | |
| 154 | _weight->set(n, fa.flowValue()); |
| 155 | |
| 156 | for (NodeIt nn(_graph); nn != INVALID; ++nn) { |
| 157 | if (nn != n && fa.minCut(nn) && (*_pred)[nn] == pn) { |
| 158 | _pred->set(nn, n); |
| 159 | } |
| 160 | } |
| 161 | if ((*_pred)[pn] != INVALID && fa.minCut((*_pred)[pn])) { |
| 162 | _pred->set(n, (*_pred)[pn]); |
| 163 | _pred->set(pn, n); |
| 164 | _weight->set(n, (*_weight)[pn]); |
| 165 | _weight->set(pn, fa.flowValue()); |
| 166 | } |
| 167 | } |
| 168 | |
| 169 | _order->set(_root, 0); |
| 170 | int index = 1; |
| 171 | |
| 172 | for (NodeIt n(_graph); n != INVALID; ++n) { |
| 173 | std::vector<Node> st; |
| 174 | Node nn = n; |
| 175 | while ((*_order)[nn] == -1) { |
| 176 | st.push_back(nn); |
| 177 | nn = (*_pred)[nn]; |
| 178 | } |
| 179 | while (!st.empty()) { |
| 180 | _order->set(st.back(), index++); |
| 181 | st.pop_back(); |
| 182 | } |
| 183 | } |
| 184 | } |
| 185 | |
| 186 | /// \brief Runs the Gomory-Hu algorithm. |
| 187 | /// |
| 188 | /// Runs the Gomory-Hu algorithm. |
| 189 | /// \note gh.run() is just a shortcut of the following code. |
| 190 | /// \code |
| 191 | /// ght.init(); |
| 192 | /// ght.start(); |
| 193 | /// \endcode |
| 194 | void run() { |
| 195 | init(); |
| 196 | start(); |
| 197 | } |
| 198 | |
| 199 | /// \brief Returns the predecessor node in the Gomory-Hu tree. |
| 200 | /// |
| 201 | /// Returns the predecessor node in the Gomory-Hu tree. If the node is |
| 202 | /// the root of the Gomory-Hu tree, then it returns \c INVALID. |
| 203 | Node predNode(const Node& node) { |
| 204 | return (*_pred)[node]; |
| 205 | } |
| 206 | |
| 207 | /// \brief Returns the weight of the predecessor arc in the |
| 208 | /// Gomory-Hu tree. |
| 209 | /// |
| 210 | /// Returns the weight of the predecessor arc in the Gomory-Hu |
| 211 | /// tree. If the node is the root of the Gomory-Hu tree, the |
| 212 | /// result is undefined. |
| 213 | Value predValue(const Node& node) { |
| 214 | return (*_weight)[node]; |
| 215 | } |
| 216 | |
| 217 | /// \brief Returns the minimum cut value between two nodes |
| 218 | /// |
| 219 | /// Returns the minimum cut value between two nodes. The |
| 220 | /// algorithm finds the nearest common ancestor in the Gomory-Hu |
| 221 | /// tree and calculates the minimum weight arc on the paths to |
| 222 | /// the ancestor. |
| 223 | Value minCutValue(const Node& s, const Node& t) const { |
| 224 | Node sn = s, tn = t; |
| 225 | Value value = std::numeric_limits<Value>::max(); |
| 226 | |
| 227 | while (sn != tn) { |
| 228 | if ((*_order)[sn] < (*_order)[tn]) { |
| 229 | if ((*_weight)[tn] < value) value = (*_weight)[tn]; |
| 230 | tn = (*_pred)[tn]; |
| 231 | } else { |
| 232 | if ((*_weight)[sn] < value) value = (*_weight)[sn]; |
| 233 | sn = (*_pred)[sn]; |
| 234 | } |
| 235 | } |
| 236 | return value; |
| 237 | } |
| 238 | |
| 239 | /// \brief Returns the minimum cut between two nodes |
| 240 | /// |
| 241 | /// Returns the minimum cut value between two nodes. The |
| 242 | /// algorithm finds the nearest common ancestor in the Gomory-Hu |
| 243 | /// tree and calculates the minimum weight arc on the paths to |
| 244 | /// the ancestor. Then it sets all nodes to the cut determined by |
| 245 | /// this arc. The \c cutMap should be \ref concepts::ReadWriteMap |
| 246 | /// "ReadWriteMap". |
| 247 | template <typename CutMap> |
| 248 | Value minCutMap(const Node& s, const Node& t, CutMap& cutMap) const { |
| 249 | Node sn = s, tn = t; |
| 250 | |
| 251 | Node rn = INVALID; |
| 252 | Value value = std::numeric_limits<Value>::max(); |
| 253 | |
| 254 | while (sn != tn) { |
| 255 | if ((*_order)[sn] < (*_order)[tn]) { |
| 256 | if ((*_weight)[tn] < value) { |
| 257 | rn = tn; |
| 258 | value = (*_weight)[tn]; |
| 259 | } |
| 260 | tn = (*_pred)[tn]; |
| 261 | } else { |
| 262 | if ((*_weight)[sn] < value) { |
| 263 | rn = sn; |
| 264 | value = (*_weight)[sn]; |
| 265 | } |
| 266 | sn = (*_pred)[sn]; |
| 267 | } |
| 268 | } |
| 269 | |
| 270 | typename Graph::template NodeMap<bool> reached(_graph, false); |
| 271 | reached.set(_root, true); |
| 272 | cutMap.set(_root, false); |
| 273 | reached.set(rn, true); |
| 274 | cutMap.set(rn, true); |
| 275 | |
| 276 | for (NodeIt n(_graph); n != INVALID; ++n) { |
| 277 | std::vector<Node> st; |
| 278 | Node nn = n; |
| 279 | while (!reached[nn]) { |
| 280 | st.push_back(nn); |
| 281 | nn = (*_pred)[nn]; |
| 282 | } |
| 283 | while (!st.empty()) { |
| 284 | cutMap.set(st.back(), cutMap[nn]); |
| 285 | st.pop_back(); |
| 286 | } |
| 287 | } |
| 288 | |
| 289 | return value; |
| 290 | } |
| 291 | |
| 292 | }; |
| 293 | |
| 294 | } |
| 295 | |
| 296 | #endif |