1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/capacity_scaling.h Tue Dec 20 18:15:14 2011 +0100
1.3 @@ -0,0 +1,990 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2010
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_CAPACITY_SCALING_H
1.23 +#define LEMON_CAPACITY_SCALING_H
1.24 +
1.25 +/// \ingroup min_cost_flow_algs
1.26 +///
1.27 +/// \file
1.28 +/// \brief Capacity Scaling algorithm for finding a minimum cost flow.
1.29 +
1.30 +#include <vector>
1.31 +#include <limits>
1.32 +#include <lemon/core.h>
1.33 +#include <lemon/bin_heap.h>
1.34 +
1.35 +namespace lemon {
1.36 +
1.37 + /// \brief Default traits class of CapacityScaling algorithm.
1.38 + ///
1.39 + /// Default traits class of CapacityScaling algorithm.
1.40 + /// \tparam GR Digraph type.
1.41 + /// \tparam V The number type used for flow amounts, capacity bounds
1.42 + /// and supply values. By default it is \c int.
1.43 + /// \tparam C The number type used for costs and potentials.
1.44 + /// By default it is the same as \c V.
1.45 + template <typename GR, typename V = int, typename C = V>
1.46 + struct CapacityScalingDefaultTraits
1.47 + {
1.48 + /// The type of the digraph
1.49 + typedef GR Digraph;
1.50 + /// The type of the flow amounts, capacity bounds and supply values
1.51 + typedef V Value;
1.52 + /// The type of the arc costs
1.53 + typedef C Cost;
1.54 +
1.55 + /// \brief The type of the heap used for internal Dijkstra computations.
1.56 + ///
1.57 + /// The type of the heap used for internal Dijkstra computations.
1.58 + /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
1.59 + /// its priority type must be \c Cost and its cross reference type
1.60 + /// must be \ref RangeMap "RangeMap<int>".
1.61 + typedef BinHeap<Cost, RangeMap<int> > Heap;
1.62 + };
1.63 +
1.64 + /// \addtogroup min_cost_flow_algs
1.65 + /// @{
1.66 +
1.67 + /// \brief Implementation of the Capacity Scaling algorithm for
1.68 + /// finding a \ref min_cost_flow "minimum cost flow".
1.69 + ///
1.70 + /// \ref CapacityScaling implements the capacity scaling version
1.71 + /// of the successive shortest path algorithm for finding a
1.72 + /// \ref min_cost_flow "minimum cost flow" \ref amo93networkflows,
1.73 + /// \ref edmondskarp72theoretical. It is an efficient dual
1.74 + /// solution method.
1.75 + ///
1.76 + /// Most of the parameters of the problem (except for the digraph)
1.77 + /// can be given using separate functions, and the algorithm can be
1.78 + /// executed using the \ref run() function. If some parameters are not
1.79 + /// specified, then default values will be used.
1.80 + ///
1.81 + /// \tparam GR The digraph type the algorithm runs on.
1.82 + /// \tparam V The number type used for flow amounts, capacity bounds
1.83 + /// and supply values in the algorithm. By default, it is \c int.
1.84 + /// \tparam C The number type used for costs and potentials in the
1.85 + /// algorithm. By default, it is the same as \c V.
1.86 + /// \tparam TR The traits class that defines various types used by the
1.87 + /// algorithm. By default, it is \ref CapacityScalingDefaultTraits
1.88 + /// "CapacityScalingDefaultTraits<GR, V, C>".
1.89 + /// In most cases, this parameter should not be set directly,
1.90 + /// consider to use the named template parameters instead.
1.91 + ///
1.92 + /// \warning Both number types must be signed and all input data must
1.93 + /// be integer.
1.94 + /// \warning This algorithm does not support negative costs for such
1.95 + /// arcs that have infinite upper bound.
1.96 +#ifdef DOXYGEN
1.97 + template <typename GR, typename V, typename C, typename TR>
1.98 +#else
1.99 + template < typename GR, typename V = int, typename C = V,
1.100 + typename TR = CapacityScalingDefaultTraits<GR, V, C> >
1.101 +#endif
1.102 + class CapacityScaling
1.103 + {
1.104 + public:
1.105 +
1.106 + /// The type of the digraph
1.107 + typedef typename TR::Digraph Digraph;
1.108 + /// The type of the flow amounts, capacity bounds and supply values
1.109 + typedef typename TR::Value Value;
1.110 + /// The type of the arc costs
1.111 + typedef typename TR::Cost Cost;
1.112 +
1.113 + /// The type of the heap used for internal Dijkstra computations
1.114 + typedef typename TR::Heap Heap;
1.115 +
1.116 + /// The \ref CapacityScalingDefaultTraits "traits class" of the algorithm
1.117 + typedef TR Traits;
1.118 +
1.119 + public:
1.120 +
1.121 + /// \brief Problem type constants for the \c run() function.
1.122 + ///
1.123 + /// Enum type containing the problem type constants that can be
1.124 + /// returned by the \ref run() function of the algorithm.
1.125 + enum ProblemType {
1.126 + /// The problem has no feasible solution (flow).
1.127 + INFEASIBLE,
1.128 + /// The problem has optimal solution (i.e. it is feasible and
1.129 + /// bounded), and the algorithm has found optimal flow and node
1.130 + /// potentials (primal and dual solutions).
1.131 + OPTIMAL,
1.132 + /// The digraph contains an arc of negative cost and infinite
1.133 + /// upper bound. It means that the objective function is unbounded
1.134 + /// on that arc, however, note that it could actually be bounded
1.135 + /// over the feasible flows, but this algroithm cannot handle
1.136 + /// these cases.
1.137 + UNBOUNDED
1.138 + };
1.139 +
1.140 + private:
1.141 +
1.142 + TEMPLATE_DIGRAPH_TYPEDEFS(GR);
1.143 +
1.144 + typedef std::vector<int> IntVector;
1.145 + typedef std::vector<Value> ValueVector;
1.146 + typedef std::vector<Cost> CostVector;
1.147 + typedef std::vector<char> BoolVector;
1.148 + // Note: vector<char> is used instead of vector<bool> for efficiency reasons
1.149 +
1.150 + private:
1.151 +
1.152 + // Data related to the underlying digraph
1.153 + const GR &_graph;
1.154 + int _node_num;
1.155 + int _arc_num;
1.156 + int _res_arc_num;
1.157 + int _root;
1.158 +
1.159 + // Parameters of the problem
1.160 + bool _have_lower;
1.161 + Value _sum_supply;
1.162 +
1.163 + // Data structures for storing the digraph
1.164 + IntNodeMap _node_id;
1.165 + IntArcMap _arc_idf;
1.166 + IntArcMap _arc_idb;
1.167 + IntVector _first_out;
1.168 + BoolVector _forward;
1.169 + IntVector _source;
1.170 + IntVector _target;
1.171 + IntVector _reverse;
1.172 +
1.173 + // Node and arc data
1.174 + ValueVector _lower;
1.175 + ValueVector _upper;
1.176 + CostVector _cost;
1.177 + ValueVector _supply;
1.178 +
1.179 + ValueVector _res_cap;
1.180 + CostVector _pi;
1.181 + ValueVector _excess;
1.182 + IntVector _excess_nodes;
1.183 + IntVector _deficit_nodes;
1.184 +
1.185 + Value _delta;
1.186 + int _factor;
1.187 + IntVector _pred;
1.188 +
1.189 + public:
1.190 +
1.191 + /// \brief Constant for infinite upper bounds (capacities).
1.192 + ///
1.193 + /// Constant for infinite upper bounds (capacities).
1.194 + /// It is \c std::numeric_limits<Value>::infinity() if available,
1.195 + /// \c std::numeric_limits<Value>::max() otherwise.
1.196 + const Value INF;
1.197 +
1.198 + private:
1.199 +
1.200 + // Special implementation of the Dijkstra algorithm for finding
1.201 + // shortest paths in the residual network of the digraph with
1.202 + // respect to the reduced arc costs and modifying the node
1.203 + // potentials according to the found distance labels.
1.204 + class ResidualDijkstra
1.205 + {
1.206 + private:
1.207 +
1.208 + int _node_num;
1.209 + bool _geq;
1.210 + const IntVector &_first_out;
1.211 + const IntVector &_target;
1.212 + const CostVector &_cost;
1.213 + const ValueVector &_res_cap;
1.214 + const ValueVector &_excess;
1.215 + CostVector &_pi;
1.216 + IntVector &_pred;
1.217 +
1.218 + IntVector _proc_nodes;
1.219 + CostVector _dist;
1.220 +
1.221 + public:
1.222 +
1.223 + ResidualDijkstra(CapacityScaling& cs) :
1.224 + _node_num(cs._node_num), _geq(cs._sum_supply < 0),
1.225 + _first_out(cs._first_out), _target(cs._target), _cost(cs._cost),
1.226 + _res_cap(cs._res_cap), _excess(cs._excess), _pi(cs._pi),
1.227 + _pred(cs._pred), _dist(cs._node_num)
1.228 + {}
1.229 +
1.230 + int run(int s, Value delta = 1) {
1.231 + RangeMap<int> heap_cross_ref(_node_num, Heap::PRE_HEAP);
1.232 + Heap heap(heap_cross_ref);
1.233 + heap.push(s, 0);
1.234 + _pred[s] = -1;
1.235 + _proc_nodes.clear();
1.236 +
1.237 + // Process nodes
1.238 + while (!heap.empty() && _excess[heap.top()] > -delta) {
1.239 + int u = heap.top(), v;
1.240 + Cost d = heap.prio() + _pi[u], dn;
1.241 + _dist[u] = heap.prio();
1.242 + _proc_nodes.push_back(u);
1.243 + heap.pop();
1.244 +
1.245 + // Traverse outgoing residual arcs
1.246 + int last_out = _geq ? _first_out[u+1] : _first_out[u+1] - 1;
1.247 + for (int a = _first_out[u]; a != last_out; ++a) {
1.248 + if (_res_cap[a] < delta) continue;
1.249 + v = _target[a];
1.250 + switch (heap.state(v)) {
1.251 + case Heap::PRE_HEAP:
1.252 + heap.push(v, d + _cost[a] - _pi[v]);
1.253 + _pred[v] = a;
1.254 + break;
1.255 + case Heap::IN_HEAP:
1.256 + dn = d + _cost[a] - _pi[v];
1.257 + if (dn < heap[v]) {
1.258 + heap.decrease(v, dn);
1.259 + _pred[v] = a;
1.260 + }
1.261 + break;
1.262 + case Heap::POST_HEAP:
1.263 + break;
1.264 + }
1.265 + }
1.266 + }
1.267 + if (heap.empty()) return -1;
1.268 +
1.269 + // Update potentials of processed nodes
1.270 + int t = heap.top();
1.271 + Cost dt = heap.prio();
1.272 + for (int i = 0; i < int(_proc_nodes.size()); ++i) {
1.273 + _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - dt;
1.274 + }
1.275 +
1.276 + return t;
1.277 + }
1.278 +
1.279 + }; //class ResidualDijkstra
1.280 +
1.281 + public:
1.282 +
1.283 + /// \name Named Template Parameters
1.284 + /// @{
1.285 +
1.286 + template <typename T>
1.287 + struct SetHeapTraits : public Traits {
1.288 + typedef T Heap;
1.289 + };
1.290 +
1.291 + /// \brief \ref named-templ-param "Named parameter" for setting
1.292 + /// \c Heap type.
1.293 + ///
1.294 + /// \ref named-templ-param "Named parameter" for setting \c Heap
1.295 + /// type, which is used for internal Dijkstra computations.
1.296 + /// It must conform to the \ref lemon::concepts::Heap "Heap" concept,
1.297 + /// its priority type must be \c Cost and its cross reference type
1.298 + /// must be \ref RangeMap "RangeMap<int>".
1.299 + template <typename T>
1.300 + struct SetHeap
1.301 + : public CapacityScaling<GR, V, C, SetHeapTraits<T> > {
1.302 + typedef CapacityScaling<GR, V, C, SetHeapTraits<T> > Create;
1.303 + };
1.304 +
1.305 + /// @}
1.306 +
1.307 + protected:
1.308 +
1.309 + CapacityScaling() {}
1.310 +
1.311 + public:
1.312 +
1.313 + /// \brief Constructor.
1.314 + ///
1.315 + /// The constructor of the class.
1.316 + ///
1.317 + /// \param graph The digraph the algorithm runs on.
1.318 + CapacityScaling(const GR& graph) :
1.319 + _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
1.320 + INF(std::numeric_limits<Value>::has_infinity ?
1.321 + std::numeric_limits<Value>::infinity() :
1.322 + std::numeric_limits<Value>::max())
1.323 + {
1.324 + // Check the number types
1.325 + LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
1.326 + "The flow type of CapacityScaling must be signed");
1.327 + LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
1.328 + "The cost type of CapacityScaling must be signed");
1.329 +
1.330 + // Reset data structures
1.331 + reset();
1.332 + }
1.333 +
1.334 + /// \name Parameters
1.335 + /// The parameters of the algorithm can be specified using these
1.336 + /// functions.
1.337 +
1.338 + /// @{
1.339 +
1.340 + /// \brief Set the lower bounds on the arcs.
1.341 + ///
1.342 + /// This function sets the lower bounds on the arcs.
1.343 + /// If it is not used before calling \ref run(), the lower bounds
1.344 + /// will be set to zero on all arcs.
1.345 + ///
1.346 + /// \param map An arc map storing the lower bounds.
1.347 + /// Its \c Value type must be convertible to the \c Value type
1.348 + /// of the algorithm.
1.349 + ///
1.350 + /// \return <tt>(*this)</tt>
1.351 + template <typename LowerMap>
1.352 + CapacityScaling& lowerMap(const LowerMap& map) {
1.353 + _have_lower = true;
1.354 + for (ArcIt a(_graph); a != INVALID; ++a) {
1.355 + _lower[_arc_idf[a]] = map[a];
1.356 + _lower[_arc_idb[a]] = map[a];
1.357 + }
1.358 + return *this;
1.359 + }
1.360 +
1.361 + /// \brief Set the upper bounds (capacities) on the arcs.
1.362 + ///
1.363 + /// This function sets the upper bounds (capacities) on the arcs.
1.364 + /// If it is not used before calling \ref run(), the upper bounds
1.365 + /// will be set to \ref INF on all arcs (i.e. the flow value will be
1.366 + /// unbounded from above).
1.367 + ///
1.368 + /// \param map An arc map storing the upper bounds.
1.369 + /// Its \c Value type must be convertible to the \c Value type
1.370 + /// of the algorithm.
1.371 + ///
1.372 + /// \return <tt>(*this)</tt>
1.373 + template<typename UpperMap>
1.374 + CapacityScaling& upperMap(const UpperMap& map) {
1.375 + for (ArcIt a(_graph); a != INVALID; ++a) {
1.376 + _upper[_arc_idf[a]] = map[a];
1.377 + }
1.378 + return *this;
1.379 + }
1.380 +
1.381 + /// \brief Set the costs of the arcs.
1.382 + ///
1.383 + /// This function sets the costs of the arcs.
1.384 + /// If it is not used before calling \ref run(), the costs
1.385 + /// will be set to \c 1 on all arcs.
1.386 + ///
1.387 + /// \param map An arc map storing the costs.
1.388 + /// Its \c Value type must be convertible to the \c Cost type
1.389 + /// of the algorithm.
1.390 + ///
1.391 + /// \return <tt>(*this)</tt>
1.392 + template<typename CostMap>
1.393 + CapacityScaling& costMap(const CostMap& map) {
1.394 + for (ArcIt a(_graph); a != INVALID; ++a) {
1.395 + _cost[_arc_idf[a]] = map[a];
1.396 + _cost[_arc_idb[a]] = -map[a];
1.397 + }
1.398 + return *this;
1.399 + }
1.400 +
1.401 + /// \brief Set the supply values of the nodes.
1.402 + ///
1.403 + /// This function sets the supply values of the nodes.
1.404 + /// If neither this function nor \ref stSupply() is used before
1.405 + /// calling \ref run(), the supply of each node will be set to zero.
1.406 + ///
1.407 + /// \param map A node map storing the supply values.
1.408 + /// Its \c Value type must be convertible to the \c Value type
1.409 + /// of the algorithm.
1.410 + ///
1.411 + /// \return <tt>(*this)</tt>
1.412 + template<typename SupplyMap>
1.413 + CapacityScaling& supplyMap(const SupplyMap& map) {
1.414 + for (NodeIt n(_graph); n != INVALID; ++n) {
1.415 + _supply[_node_id[n]] = map[n];
1.416 + }
1.417 + return *this;
1.418 + }
1.419 +
1.420 + /// \brief Set single source and target nodes and a supply value.
1.421 + ///
1.422 + /// This function sets a single source node and a single target node
1.423 + /// and the required flow value.
1.424 + /// If neither this function nor \ref supplyMap() is used before
1.425 + /// calling \ref run(), the supply of each node will be set to zero.
1.426 + ///
1.427 + /// Using this function has the same effect as using \ref supplyMap()
1.428 + /// with such a map in which \c k is assigned to \c s, \c -k is
1.429 + /// assigned to \c t and all other nodes have zero supply value.
1.430 + ///
1.431 + /// \param s The source node.
1.432 + /// \param t The target node.
1.433 + /// \param k The required amount of flow from node \c s to node \c t
1.434 + /// (i.e. the supply of \c s and the demand of \c t).
1.435 + ///
1.436 + /// \return <tt>(*this)</tt>
1.437 + CapacityScaling& stSupply(const Node& s, const Node& t, Value k) {
1.438 + for (int i = 0; i != _node_num; ++i) {
1.439 + _supply[i] = 0;
1.440 + }
1.441 + _supply[_node_id[s]] = k;
1.442 + _supply[_node_id[t]] = -k;
1.443 + return *this;
1.444 + }
1.445 +
1.446 + /// @}
1.447 +
1.448 + /// \name Execution control
1.449 + /// The algorithm can be executed using \ref run().
1.450 +
1.451 + /// @{
1.452 +
1.453 + /// \brief Run the algorithm.
1.454 + ///
1.455 + /// This function runs the algorithm.
1.456 + /// The paramters can be specified using functions \ref lowerMap(),
1.457 + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
1.458 + /// For example,
1.459 + /// \code
1.460 + /// CapacityScaling<ListDigraph> cs(graph);
1.461 + /// cs.lowerMap(lower).upperMap(upper).costMap(cost)
1.462 + /// .supplyMap(sup).run();
1.463 + /// \endcode
1.464 + ///
1.465 + /// This function can be called more than once. All the given parameters
1.466 + /// are kept for the next call, unless \ref resetParams() or \ref reset()
1.467 + /// is used, thus only the modified parameters have to be set again.
1.468 + /// If the underlying digraph was also modified after the construction
1.469 + /// of the class (or the last \ref reset() call), then the \ref reset()
1.470 + /// function must be called.
1.471 + ///
1.472 + /// \param factor The capacity scaling factor. It must be larger than
1.473 + /// one to use scaling. If it is less or equal to one, then scaling
1.474 + /// will be disabled.
1.475 + ///
1.476 + /// \return \c INFEASIBLE if no feasible flow exists,
1.477 + /// \n \c OPTIMAL if the problem has optimal solution
1.478 + /// (i.e. it is feasible and bounded), and the algorithm has found
1.479 + /// optimal flow and node potentials (primal and dual solutions),
1.480 + /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
1.481 + /// and infinite upper bound. It means that the objective function
1.482 + /// is unbounded on that arc, however, note that it could actually be
1.483 + /// bounded over the feasible flows, but this algroithm cannot handle
1.484 + /// these cases.
1.485 + ///
1.486 + /// \see ProblemType
1.487 + /// \see resetParams(), reset()
1.488 + ProblemType run(int factor = 4) {
1.489 + _factor = factor;
1.490 + ProblemType pt = init();
1.491 + if (pt != OPTIMAL) return pt;
1.492 + return start();
1.493 + }
1.494 +
1.495 + /// \brief Reset all the parameters that have been given before.
1.496 + ///
1.497 + /// This function resets all the paramaters that have been given
1.498 + /// before using functions \ref lowerMap(), \ref upperMap(),
1.499 + /// \ref costMap(), \ref supplyMap(), \ref stSupply().
1.500 + ///
1.501 + /// It is useful for multiple \ref run() calls. Basically, all the given
1.502 + /// parameters are kept for the next \ref run() call, unless
1.503 + /// \ref resetParams() or \ref reset() is used.
1.504 + /// If the underlying digraph was also modified after the construction
1.505 + /// of the class or the last \ref reset() call, then the \ref reset()
1.506 + /// function must be used, otherwise \ref resetParams() is sufficient.
1.507 + ///
1.508 + /// For example,
1.509 + /// \code
1.510 + /// CapacityScaling<ListDigraph> cs(graph);
1.511 + ///
1.512 + /// // First run
1.513 + /// cs.lowerMap(lower).upperMap(upper).costMap(cost)
1.514 + /// .supplyMap(sup).run();
1.515 + ///
1.516 + /// // Run again with modified cost map (resetParams() is not called,
1.517 + /// // so only the cost map have to be set again)
1.518 + /// cost[e] += 100;
1.519 + /// cs.costMap(cost).run();
1.520 + ///
1.521 + /// // Run again from scratch using resetParams()
1.522 + /// // (the lower bounds will be set to zero on all arcs)
1.523 + /// cs.resetParams();
1.524 + /// cs.upperMap(capacity).costMap(cost)
1.525 + /// .supplyMap(sup).run();
1.526 + /// \endcode
1.527 + ///
1.528 + /// \return <tt>(*this)</tt>
1.529 + ///
1.530 + /// \see reset(), run()
1.531 + CapacityScaling& resetParams() {
1.532 + for (int i = 0; i != _node_num; ++i) {
1.533 + _supply[i] = 0;
1.534 + }
1.535 + for (int j = 0; j != _res_arc_num; ++j) {
1.536 + _lower[j] = 0;
1.537 + _upper[j] = INF;
1.538 + _cost[j] = _forward[j] ? 1 : -1;
1.539 + }
1.540 + _have_lower = false;
1.541 + return *this;
1.542 + }
1.543 +
1.544 + /// \brief Reset the internal data structures and all the parameters
1.545 + /// that have been given before.
1.546 + ///
1.547 + /// This function resets the internal data structures and all the
1.548 + /// paramaters that have been given before using functions \ref lowerMap(),
1.549 + /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
1.550 + ///
1.551 + /// It is useful for multiple \ref run() calls. Basically, all the given
1.552 + /// parameters are kept for the next \ref run() call, unless
1.553 + /// \ref resetParams() or \ref reset() is used.
1.554 + /// If the underlying digraph was also modified after the construction
1.555 + /// of the class or the last \ref reset() call, then the \ref reset()
1.556 + /// function must be used, otherwise \ref resetParams() is sufficient.
1.557 + ///
1.558 + /// See \ref resetParams() for examples.
1.559 + ///
1.560 + /// \return <tt>(*this)</tt>
1.561 + ///
1.562 + /// \see resetParams(), run()
1.563 + CapacityScaling& reset() {
1.564 + // Resize vectors
1.565 + _node_num = countNodes(_graph);
1.566 + _arc_num = countArcs(_graph);
1.567 + _res_arc_num = 2 * (_arc_num + _node_num);
1.568 + _root = _node_num;
1.569 + ++_node_num;
1.570 +
1.571 + _first_out.resize(_node_num + 1);
1.572 + _forward.resize(_res_arc_num);
1.573 + _source.resize(_res_arc_num);
1.574 + _target.resize(_res_arc_num);
1.575 + _reverse.resize(_res_arc_num);
1.576 +
1.577 + _lower.resize(_res_arc_num);
1.578 + _upper.resize(_res_arc_num);
1.579 + _cost.resize(_res_arc_num);
1.580 + _supply.resize(_node_num);
1.581 +
1.582 + _res_cap.resize(_res_arc_num);
1.583 + _pi.resize(_node_num);
1.584 + _excess.resize(_node_num);
1.585 + _pred.resize(_node_num);
1.586 +
1.587 + // Copy the graph
1.588 + int i = 0, j = 0, k = 2 * _arc_num + _node_num - 1;
1.589 + for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
1.590 + _node_id[n] = i;
1.591 + }
1.592 + i = 0;
1.593 + for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
1.594 + _first_out[i] = j;
1.595 + for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
1.596 + _arc_idf[a] = j;
1.597 + _forward[j] = true;
1.598 + _source[j] = i;
1.599 + _target[j] = _node_id[_graph.runningNode(a)];
1.600 + }
1.601 + for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
1.602 + _arc_idb[a] = j;
1.603 + _forward[j] = false;
1.604 + _source[j] = i;
1.605 + _target[j] = _node_id[_graph.runningNode(a)];
1.606 + }
1.607 + _forward[j] = false;
1.608 + _source[j] = i;
1.609 + _target[j] = _root;
1.610 + _reverse[j] = k;
1.611 + _forward[k] = true;
1.612 + _source[k] = _root;
1.613 + _target[k] = i;
1.614 + _reverse[k] = j;
1.615 + ++j; ++k;
1.616 + }
1.617 + _first_out[i] = j;
1.618 + _first_out[_node_num] = k;
1.619 + for (ArcIt a(_graph); a != INVALID; ++a) {
1.620 + int fi = _arc_idf[a];
1.621 + int bi = _arc_idb[a];
1.622 + _reverse[fi] = bi;
1.623 + _reverse[bi] = fi;
1.624 + }
1.625 +
1.626 + // Reset parameters
1.627 + resetParams();
1.628 + return *this;
1.629 + }
1.630 +
1.631 + /// @}
1.632 +
1.633 + /// \name Query Functions
1.634 + /// The results of the algorithm can be obtained using these
1.635 + /// functions.\n
1.636 + /// The \ref run() function must be called before using them.
1.637 +
1.638 + /// @{
1.639 +
1.640 + /// \brief Return the total cost of the found flow.
1.641 + ///
1.642 + /// This function returns the total cost of the found flow.
1.643 + /// Its complexity is O(e).
1.644 + ///
1.645 + /// \note The return type of the function can be specified as a
1.646 + /// template parameter. For example,
1.647 + /// \code
1.648 + /// cs.totalCost<double>();
1.649 + /// \endcode
1.650 + /// It is useful if the total cost cannot be stored in the \c Cost
1.651 + /// type of the algorithm, which is the default return type of the
1.652 + /// function.
1.653 + ///
1.654 + /// \pre \ref run() must be called before using this function.
1.655 + template <typename Number>
1.656 + Number totalCost() const {
1.657 + Number c = 0;
1.658 + for (ArcIt a(_graph); a != INVALID; ++a) {
1.659 + int i = _arc_idb[a];
1.660 + c += static_cast<Number>(_res_cap[i]) *
1.661 + (-static_cast<Number>(_cost[i]));
1.662 + }
1.663 + return c;
1.664 + }
1.665 +
1.666 +#ifndef DOXYGEN
1.667 + Cost totalCost() const {
1.668 + return totalCost<Cost>();
1.669 + }
1.670 +#endif
1.671 +
1.672 + /// \brief Return the flow on the given arc.
1.673 + ///
1.674 + /// This function returns the flow on the given arc.
1.675 + ///
1.676 + /// \pre \ref run() must be called before using this function.
1.677 + Value flow(const Arc& a) const {
1.678 + return _res_cap[_arc_idb[a]];
1.679 + }
1.680 +
1.681 + /// \brief Return the flow map (the primal solution).
1.682 + ///
1.683 + /// This function copies the flow value on each arc into the given
1.684 + /// map. The \c Value type of the algorithm must be convertible to
1.685 + /// the \c Value type of the map.
1.686 + ///
1.687 + /// \pre \ref run() must be called before using this function.
1.688 + template <typename FlowMap>
1.689 + void flowMap(FlowMap &map) const {
1.690 + for (ArcIt a(_graph); a != INVALID; ++a) {
1.691 + map.set(a, _res_cap[_arc_idb[a]]);
1.692 + }
1.693 + }
1.694 +
1.695 + /// \brief Return the potential (dual value) of the given node.
1.696 + ///
1.697 + /// This function returns the potential (dual value) of the
1.698 + /// given node.
1.699 + ///
1.700 + /// \pre \ref run() must be called before using this function.
1.701 + Cost potential(const Node& n) const {
1.702 + return _pi[_node_id[n]];
1.703 + }
1.704 +
1.705 + /// \brief Return the potential map (the dual solution).
1.706 + ///
1.707 + /// This function copies the potential (dual value) of each node
1.708 + /// into the given map.
1.709 + /// The \c Cost type of the algorithm must be convertible to the
1.710 + /// \c Value type of the map.
1.711 + ///
1.712 + /// \pre \ref run() must be called before using this function.
1.713 + template <typename PotentialMap>
1.714 + void potentialMap(PotentialMap &map) const {
1.715 + for (NodeIt n(_graph); n != INVALID; ++n) {
1.716 + map.set(n, _pi[_node_id[n]]);
1.717 + }
1.718 + }
1.719 +
1.720 + /// @}
1.721 +
1.722 + private:
1.723 +
1.724 + // Initialize the algorithm
1.725 + ProblemType init() {
1.726 + if (_node_num <= 1) return INFEASIBLE;
1.727 +
1.728 + // Check the sum of supply values
1.729 + _sum_supply = 0;
1.730 + for (int i = 0; i != _root; ++i) {
1.731 + _sum_supply += _supply[i];
1.732 + }
1.733 + if (_sum_supply > 0) return INFEASIBLE;
1.734 +
1.735 + // Initialize vectors
1.736 + for (int i = 0; i != _root; ++i) {
1.737 + _pi[i] = 0;
1.738 + _excess[i] = _supply[i];
1.739 + }
1.740 +
1.741 + // Remove non-zero lower bounds
1.742 + const Value MAX = std::numeric_limits<Value>::max();
1.743 + int last_out;
1.744 + if (_have_lower) {
1.745 + for (int i = 0; i != _root; ++i) {
1.746 + last_out = _first_out[i+1];
1.747 + for (int j = _first_out[i]; j != last_out; ++j) {
1.748 + if (_forward[j]) {
1.749 + Value c = _lower[j];
1.750 + if (c >= 0) {
1.751 + _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;
1.752 + } else {
1.753 + _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;
1.754 + }
1.755 + _excess[i] -= c;
1.756 + _excess[_target[j]] += c;
1.757 + } else {
1.758 + _res_cap[j] = 0;
1.759 + }
1.760 + }
1.761 + }
1.762 + } else {
1.763 + for (int j = 0; j != _res_arc_num; ++j) {
1.764 + _res_cap[j] = _forward[j] ? _upper[j] : 0;
1.765 + }
1.766 + }
1.767 +
1.768 + // Handle negative costs
1.769 + for (int i = 0; i != _root; ++i) {
1.770 + last_out = _first_out[i+1] - 1;
1.771 + for (int j = _first_out[i]; j != last_out; ++j) {
1.772 + Value rc = _res_cap[j];
1.773 + if (_cost[j] < 0 && rc > 0) {
1.774 + if (rc >= MAX) return UNBOUNDED;
1.775 + _excess[i] -= rc;
1.776 + _excess[_target[j]] += rc;
1.777 + _res_cap[j] = 0;
1.778 + _res_cap[_reverse[j]] += rc;
1.779 + }
1.780 + }
1.781 + }
1.782 +
1.783 + // Handle GEQ supply type
1.784 + if (_sum_supply < 0) {
1.785 + _pi[_root] = 0;
1.786 + _excess[_root] = -_sum_supply;
1.787 + for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
1.788 + int ra = _reverse[a];
1.789 + _res_cap[a] = -_sum_supply + 1;
1.790 + _res_cap[ra] = 0;
1.791 + _cost[a] = 0;
1.792 + _cost[ra] = 0;
1.793 + }
1.794 + } else {
1.795 + _pi[_root] = 0;
1.796 + _excess[_root] = 0;
1.797 + for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
1.798 + int ra = _reverse[a];
1.799 + _res_cap[a] = 1;
1.800 + _res_cap[ra] = 0;
1.801 + _cost[a] = 0;
1.802 + _cost[ra] = 0;
1.803 + }
1.804 + }
1.805 +
1.806 + // Initialize delta value
1.807 + if (_factor > 1) {
1.808 + // With scaling
1.809 + Value max_sup = 0, max_dem = 0, max_cap = 0;
1.810 + for (int i = 0; i != _root; ++i) {
1.811 + Value ex = _excess[i];
1.812 + if ( ex > max_sup) max_sup = ex;
1.813 + if (-ex > max_dem) max_dem = -ex;
1.814 + int last_out = _first_out[i+1] - 1;
1.815 + for (int j = _first_out[i]; j != last_out; ++j) {
1.816 + if (_res_cap[j] > max_cap) max_cap = _res_cap[j];
1.817 + }
1.818 + }
1.819 + max_sup = std::min(std::min(max_sup, max_dem), max_cap);
1.820 + for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;
1.821 + } else {
1.822 + // Without scaling
1.823 + _delta = 1;
1.824 + }
1.825 +
1.826 + return OPTIMAL;
1.827 + }
1.828 +
1.829 + ProblemType start() {
1.830 + // Execute the algorithm
1.831 + ProblemType pt;
1.832 + if (_delta > 1)
1.833 + pt = startWithScaling();
1.834 + else
1.835 + pt = startWithoutScaling();
1.836 +
1.837 + // Handle non-zero lower bounds
1.838 + if (_have_lower) {
1.839 + int limit = _first_out[_root];
1.840 + for (int j = 0; j != limit; ++j) {
1.841 + if (!_forward[j]) _res_cap[j] += _lower[j];
1.842 + }
1.843 + }
1.844 +
1.845 + // Shift potentials if necessary
1.846 + Cost pr = _pi[_root];
1.847 + if (_sum_supply < 0 || pr > 0) {
1.848 + for (int i = 0; i != _node_num; ++i) {
1.849 + _pi[i] -= pr;
1.850 + }
1.851 + }
1.852 +
1.853 + return pt;
1.854 + }
1.855 +
1.856 + // Execute the capacity scaling algorithm
1.857 + ProblemType startWithScaling() {
1.858 + // Perform capacity scaling phases
1.859 + int s, t;
1.860 + ResidualDijkstra _dijkstra(*this);
1.861 + while (true) {
1.862 + // Saturate all arcs not satisfying the optimality condition
1.863 + int last_out;
1.864 + for (int u = 0; u != _node_num; ++u) {
1.865 + last_out = _sum_supply < 0 ?
1.866 + _first_out[u+1] : _first_out[u+1] - 1;
1.867 + for (int a = _first_out[u]; a != last_out; ++a) {
1.868 + int v = _target[a];
1.869 + Cost c = _cost[a] + _pi[u] - _pi[v];
1.870 + Value rc = _res_cap[a];
1.871 + if (c < 0 && rc >= _delta) {
1.872 + _excess[u] -= rc;
1.873 + _excess[v] += rc;
1.874 + _res_cap[a] = 0;
1.875 + _res_cap[_reverse[a]] += rc;
1.876 + }
1.877 + }
1.878 + }
1.879 +
1.880 + // Find excess nodes and deficit nodes
1.881 + _excess_nodes.clear();
1.882 + _deficit_nodes.clear();
1.883 + for (int u = 0; u != _node_num; ++u) {
1.884 + Value ex = _excess[u];
1.885 + if (ex >= _delta) _excess_nodes.push_back(u);
1.886 + if (ex <= -_delta) _deficit_nodes.push_back(u);
1.887 + }
1.888 + int next_node = 0, next_def_node = 0;
1.889 +
1.890 + // Find augmenting shortest paths
1.891 + while (next_node < int(_excess_nodes.size())) {
1.892 + // Check deficit nodes
1.893 + if (_delta > 1) {
1.894 + bool delta_deficit = false;
1.895 + for ( ; next_def_node < int(_deficit_nodes.size());
1.896 + ++next_def_node ) {
1.897 + if (_excess[_deficit_nodes[next_def_node]] <= -_delta) {
1.898 + delta_deficit = true;
1.899 + break;
1.900 + }
1.901 + }
1.902 + if (!delta_deficit) break;
1.903 + }
1.904 +
1.905 + // Run Dijkstra in the residual network
1.906 + s = _excess_nodes[next_node];
1.907 + if ((t = _dijkstra.run(s, _delta)) == -1) {
1.908 + if (_delta > 1) {
1.909 + ++next_node;
1.910 + continue;
1.911 + }
1.912 + return INFEASIBLE;
1.913 + }
1.914 +
1.915 + // Augment along a shortest path from s to t
1.916 + Value d = std::min(_excess[s], -_excess[t]);
1.917 + int u = t;
1.918 + int a;
1.919 + if (d > _delta) {
1.920 + while ((a = _pred[u]) != -1) {
1.921 + if (_res_cap[a] < d) d = _res_cap[a];
1.922 + u = _source[a];
1.923 + }
1.924 + }
1.925 + u = t;
1.926 + while ((a = _pred[u]) != -1) {
1.927 + _res_cap[a] -= d;
1.928 + _res_cap[_reverse[a]] += d;
1.929 + u = _source[a];
1.930 + }
1.931 + _excess[s] -= d;
1.932 + _excess[t] += d;
1.933 +
1.934 + if (_excess[s] < _delta) ++next_node;
1.935 + }
1.936 +
1.937 + if (_delta == 1) break;
1.938 + _delta = _delta <= _factor ? 1 : _delta / _factor;
1.939 + }
1.940 +
1.941 + return OPTIMAL;
1.942 + }
1.943 +
1.944 + // Execute the successive shortest path algorithm
1.945 + ProblemType startWithoutScaling() {
1.946 + // Find excess nodes
1.947 + _excess_nodes.clear();
1.948 + for (int i = 0; i != _node_num; ++i) {
1.949 + if (_excess[i] > 0) _excess_nodes.push_back(i);
1.950 + }
1.951 + if (_excess_nodes.size() == 0) return OPTIMAL;
1.952 + int next_node = 0;
1.953 +
1.954 + // Find shortest paths
1.955 + int s, t;
1.956 + ResidualDijkstra _dijkstra(*this);
1.957 + while ( _excess[_excess_nodes[next_node]] > 0 ||
1.958 + ++next_node < int(_excess_nodes.size()) )
1.959 + {
1.960 + // Run Dijkstra in the residual network
1.961 + s = _excess_nodes[next_node];
1.962 + if ((t = _dijkstra.run(s)) == -1) return INFEASIBLE;
1.963 +
1.964 + // Augment along a shortest path from s to t
1.965 + Value d = std::min(_excess[s], -_excess[t]);
1.966 + int u = t;
1.967 + int a;
1.968 + if (d > 1) {
1.969 + while ((a = _pred[u]) != -1) {
1.970 + if (_res_cap[a] < d) d = _res_cap[a];
1.971 + u = _source[a];
1.972 + }
1.973 + }
1.974 + u = t;
1.975 + while ((a = _pred[u]) != -1) {
1.976 + _res_cap[a] -= d;
1.977 + _res_cap[_reverse[a]] += d;
1.978 + u = _source[a];
1.979 + }
1.980 + _excess[s] -= d;
1.981 + _excess[t] += d;
1.982 + }
1.983 +
1.984 + return OPTIMAL;
1.985 + }
1.986 +
1.987 + }; //class CapacityScaling
1.988 +
1.989 + ///@}
1.990 +
1.991 +} //namespace lemon
1.992 +
1.993 +#endif //LEMON_CAPACITY_SCALING_H