# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 1258065045 -3600
# Node ID 22bb98ca010184543f08b8c072eaa13286422166
# Parent 9c428bb2b1056da486089cbcf6eee0c8e8ae4488
Entirely rework CostScaling (#180)
- Use the new interface similarly to NetworkSimplex.
- Rework the implementation using an efficient internal structure
for handling the residual network. This improvement made the
code much faster.
- Handle GEQ supply type (LEQ is not supported).
- Handle infinite upper bounds.
- Handle negative costs (for arcs of finite upper bound).
- Traits class + named parameter for the LargeCost type used in
internal computations.
- Extend the documentation.
diff -r 9c428bb2b105 -r 22bb98ca0101 lemon/cost_scaling.h
--- a/lemon/cost_scaling.h Thu Nov 12 23:29:42 2009 +0100
+++ b/lemon/cost_scaling.h Thu Nov 12 23:30:45 2009 +0100
@@ -30,548 +30,912 @@
#include <lemon/core.h>
#include <lemon/maps.h>
#include <lemon/math.h>
-#include <lemon/adaptors.h>
+#include <lemon/static_graph.h>
#include <lemon/circulation.h>
#include <lemon/bellman_ford.h>
namespace lemon {
+ /// \brief Default traits class of CostScaling algorithm.
+ ///
+ /// Default traits class of CostScaling algorithm.
+ /// \tparam GR Digraph type.
+ /// \tparam V The value type used for flow amounts, capacity bounds
+ /// and supply values. By default it is \c int.
+ /// \tparam C The value type used for costs and potentials.
+ /// By default it is the same as \c V.
+#ifdef DOXYGEN
+ template <typename GR, typename V = int, typename C = V>
+#else
+ template < typename GR, typename V = int, typename C = V,
+ bool integer = std::numeric_limits<C>::is_integer >
+#endif
+ struct CostScalingDefaultTraits
+ {
+ /// The type of the digraph
+ typedef GR Digraph;
+ /// The type of the flow amounts, capacity bounds and supply values
+ typedef V Value;
+ /// The type of the arc costs
+ typedef C Cost;
+
+ /// \brief The large cost type used for internal computations
+ ///
+ /// The large cost type used for internal computations.
+ /// It is \c long \c long if the \c Cost type is integer,
+ /// otherwise it is \c double.
+ /// \c Cost must be convertible to \c LargeCost.
+ typedef double LargeCost;
+ };
+
+ // Default traits class for integer cost types
+ template <typename GR, typename V, typename C>
+ struct CostScalingDefaultTraits<GR, V, C, true>
+ {
+ typedef GR Digraph;
+ typedef V Value;
+ typedef C Cost;
+#ifdef LEMON_HAVE_LONG_LONG
+ typedef long long LargeCost;
+#else
+ typedef long LargeCost;
+#endif
+ };
+
+
/// \addtogroup min_cost_flow_algs
/// @{
- /// \brief Implementation of the cost scaling algorithm for finding a
- /// minimum cost flow.
+ /// \brief Implementation of the Cost Scaling algorithm for
+ /// finding a \ref min_cost_flow "minimum cost flow".
///
- /// \ref CostScaling implements the cost scaling algorithm performing
- /// augment/push and relabel operations for finding a minimum cost
- /// flow.
+ /// \ref CostScaling implements a cost scaling algorithm that performs
+ /// push/augment and relabel operations for finding a minimum cost
+ /// flow. It is an efficient primal-dual solution method, which
+ /// can be viewed as the generalization of the \ref Preflow
+ /// "preflow push-relabel" algorithm for the maximum flow problem.
///
- /// \tparam Digraph The digraph type the algorithm runs on.
- /// \tparam LowerMap The type of the lower bound map.
- /// \tparam CapacityMap The type of the capacity (upper bound) map.
- /// \tparam CostMap The type of the cost (length) map.
- /// \tparam SupplyMap The type of the supply map.
+ /// Most of the parameters of the problem (except for the digraph)
+ /// can be given using separate functions, and the algorithm can be
+ /// executed using the \ref run() function. If some parameters are not
+ /// specified, then default values will be used.
///
- /// \warning
- /// - Arc capacities and costs should be \e non-negative \e integers.
- /// - Supply values should be \e signed \e integers.
- /// - The value types of the maps should be convertible to each other.
- /// - \c CostMap::Value must be signed type.
+ /// \tparam GR The digraph type the algorithm runs on.
+ /// \tparam V The value type used for flow amounts, capacity bounds
+ /// and supply values in the algorithm. By default it is \c int.
+ /// \tparam C The value type used for costs and potentials in the
+ /// algorithm. By default it is the same as \c V.
///
- /// \note Arc costs are multiplied with the number of nodes during
- /// the algorithm so overflow problems may arise more easily than with
- /// other minimum cost flow algorithms.
- /// If it is available, <tt>long long int</tt> type is used instead of
- /// <tt>long int</tt> in the inside computations.
- ///
- /// \author Peter Kovacs
- template < typename Digraph,
- typename LowerMap = typename Digraph::template ArcMap<int>,
- typename CapacityMap = typename Digraph::template ArcMap<int>,
- typename CostMap = typename Digraph::template ArcMap<int>,
- typename SupplyMap = typename Digraph::template NodeMap<int> >
+ /// \warning Both value types must be signed and all input data must
+ /// be integer.
+ /// \warning This algorithm does not support negative costs for such
+ /// arcs that have infinite upper bound.
+#ifdef DOXYGEN
+ template <typename GR, typename V, typename C, typename TR>
+#else
+ template < typename GR, typename V = int, typename C = V,
+ typename TR = CostScalingDefaultTraits<GR, V, C> >
+#endif
class CostScaling
{
- TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
+ public:
- typedef typename CapacityMap::Value Capacity;
- typedef typename CostMap::Value Cost;
- typedef typename SupplyMap::Value Supply;
- typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
- typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
+ /// The type of the digraph
+ typedef typename TR::Digraph Digraph;
+ /// The type of the flow amounts, capacity bounds and supply values
+ typedef typename TR::Value Value;
+ /// The type of the arc costs
+ typedef typename TR::Cost Cost;
- typedef ResidualDigraph< const Digraph,
- CapacityArcMap, CapacityArcMap > ResDigraph;
- typedef typename ResDigraph::Arc ResArc;
+ /// \brief The large cost type
+ ///
+ /// The large cost type used for internal computations.
+ /// Using the \ref CostScalingDefaultTraits "default traits class",
+ /// it is \c long \c long if the \c Cost type is integer,
+ /// otherwise it is \c double.
+ typedef typename TR::LargeCost LargeCost;
-#if defined __GNUC__ && !defined __STRICT_ANSI__
- typedef long long int LCost;
-#else
- typedef long int LCost;
-#endif
- typedef typename Digraph::template ArcMap<LCost> LargeCostMap;
+ /// The \ref CostScalingDefaultTraits "traits class" of the algorithm
+ typedef TR Traits;
public:
- /// The type of the flow map.
- typedef typename Digraph::template ArcMap<Capacity> FlowMap;
- /// The type of the potential map.
- typedef typename Digraph::template NodeMap<LCost> PotentialMap;
+ /// \brief Problem type constants for the \c run() function.
+ ///
+ /// Enum type containing the problem type constants that can be
+ /// returned by the \ref run() function of the algorithm.
+ enum ProblemType {
+ /// The problem has no feasible solution (flow).
+ INFEASIBLE,
+ /// The problem has optimal solution (i.e. it is feasible and
+ /// bounded), and the algorithm has found optimal flow and node
+ /// potentials (primal and dual solutions).
+ OPTIMAL,
+ /// The digraph contains an arc of negative cost and infinite
+ /// upper bound. It means that the objective function is unbounded
+ /// on that arc, however note that it could actually be bounded
+ /// over the feasible flows, but this algroithm cannot handle
+ /// these cases.
+ UNBOUNDED
+ };
private:
- /// \brief Map adaptor class for handling residual arc costs.
- ///
- /// Map adaptor class for handling residual arc costs.
- template <typename Map>
- class ResidualCostMap : public MapBase<ResArc, typename Map::Value>
- {
- private:
+ TEMPLATE_DIGRAPH_TYPEDEFS(GR);
- const Map &_cost_map;
+ typedef std::vector<int> IntVector;
+ typedef std::vector<char> BoolVector;
+ typedef std::vector<Value> ValueVector;
+ typedef std::vector<Cost> CostVector;
+ typedef std::vector<LargeCost> LargeCostVector;
+ private:
+
+ template <typename KT, typename VT>
+ class VectorMap {
public:
-
- ///\e
- ResidualCostMap(const Map &cost_map) :
- _cost_map(cost_map) {}
-
- ///\e
- inline typename Map::Value operator[](const ResArc &e) const {
- return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
+ typedef KT Key;
+ typedef VT Value;
+
+ VectorMap(std::vector<Value>& v) : _v(v) {}
+
+ const Value& operator[](const Key& key) const {
+ return _v[StaticDigraph::id(key)];
}
- }; //class ResidualCostMap
-
- /// \brief Map adaptor class for handling reduced arc costs.
- ///
- /// Map adaptor class for handling reduced arc costs.
- class ReducedCostMap : public MapBase<Arc, LCost>
- {
- private:
-
- const Digraph &_gr;
- const LargeCostMap &_cost_map;
- const PotentialMap &_pot_map;
-
- public:
-
- ///\e
- ReducedCostMap( const Digraph &gr,
- const LargeCostMap &cost_map,
- const PotentialMap &pot_map ) :
- _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}
-
- ///\e
- inline LCost operator[](const Arc &e) const {
- return _cost_map[e] + _pot_map[_gr.source(e)]
- - _pot_map[_gr.target(e)];
+ Value& operator[](const Key& key) {
+ return _v[StaticDigraph::id(key)];
+ }
+
+ void set(const Key& key, const Value& val) {
+ _v[StaticDigraph::id(key)] = val;
}
- }; //class ReducedCostMap
+ private:
+ std::vector<Value>& _v;
+ };
+
+ typedef VectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;
+ typedef VectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
private:
- // The digraph the algorithm runs on
- const Digraph &_graph;
- // The original lower bound map
- const LowerMap *_lower;
- // The modified capacity map
- CapacityArcMap _capacity;
- // The original cost map
- const CostMap &_orig_cost;
- // The scaled cost map
- LargeCostMap _cost;
- // The modified supply map
- SupplyNodeMap _supply;
- bool _valid_supply;
+ // Data related to the underlying digraph
+ const GR &_graph;
+ int _node_num;
+ int _arc_num;
+ int _res_node_num;
+ int _res_arc_num;
+ int _root;
- // Arc map of the current flow
- FlowMap *_flow;
- bool _local_flow;
- // Node map of the current potentials
- PotentialMap *_potential;
- bool _local_potential;
+ // Parameters of the problem
+ bool _have_lower;
+ Value _sum_supply;
- // The residual cost map
- ResidualCostMap<LargeCostMap> _res_cost;
- // The residual digraph
- ResDigraph *_res_graph;
- // The reduced cost map
- ReducedCostMap *_red_cost;
- // The excess map
- SupplyNodeMap _excess;
- // The epsilon parameter used for cost scaling
- LCost _epsilon;
- // The scaling factor
+ // Data structures for storing the digraph
+ IntNodeMap _node_id;
+ IntArcMap _arc_idf;
+ IntArcMap _arc_idb;
+ IntVector _first_out;
+ BoolVector _forward;
+ IntVector _source;
+ IntVector _target;
+ IntVector _reverse;
+
+ // Node and arc data
+ ValueVector _lower;
+ ValueVector _upper;
+ CostVector _scost;
+ ValueVector _supply;
+
+ ValueVector _res_cap;
+ LargeCostVector _cost;
+ LargeCostVector _pi;
+ ValueVector _excess;
+ IntVector _next_out;
+ std::deque<int> _active_nodes;
+
+ // Data for scaling
+ LargeCost _epsilon;
int _alpha;
+ // Data for a StaticDigraph structure
+ typedef std::pair<int, int> IntPair;
+ StaticDigraph _sgr;
+ std::vector<IntPair> _arc_vec;
+ std::vector<LargeCost> _cost_vec;
+ LargeCostArcMap _cost_map;
+ LargeCostNodeMap _pi_map;
+
+ public:
+
+ /// \brief Constant for infinite upper bounds (capacities).
+ ///
+ /// Constant for infinite upper bounds (capacities).
+ /// It is \c std::numeric_limits<Value>::infinity() if available,
+ /// \c std::numeric_limits<Value>::max() otherwise.
+ const Value INF;
+
public:
- /// \brief General constructor (with lower bounds).
+ /// \name Named Template Parameters
+ /// @{
+
+ template <typename T>
+ struct SetLargeCostTraits : public Traits {
+ typedef T LargeCost;
+ };
+
+ /// \brief \ref named-templ-param "Named parameter" for setting
+ /// \c LargeCost type.
///
- /// General constructor (with lower bounds).
+ /// \ref named-templ-param "Named parameter" for setting \c LargeCost
+ /// type, which is used for internal computations in the algorithm.
+ /// \c Cost must be convertible to \c LargeCost.
+ template <typename T>
+ struct SetLargeCost
+ : public CostScaling<GR, V, C, SetLargeCostTraits<T> > {
+ typedef CostScaling<GR, V, C, SetLargeCostTraits<T> > Create;
+ };
+
+ /// @}
+
+ public:
+
+ /// \brief Constructor.
///
- /// \param digraph The digraph the algorithm runs on.
- /// \param lower The lower bounds of the arcs.
- /// \param capacity The capacities (upper bounds) of the arcs.
- /// \param cost The cost (length) values of the arcs.
- /// \param supply The supply values of the nodes (signed).
- CostScaling( const Digraph &digraph,
- const LowerMap &lower,
- const CapacityMap &capacity,
- const CostMap &cost,
- const SupplyMap &supply ) :
- _graph(digraph), _lower(&lower), _capacity(digraph), _orig_cost(cost),
- _cost(digraph), _supply(digraph), _flow(NULL), _local_flow(false),
- _potential(NULL), _local_potential(false), _res_cost(_cost),
- _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
+ /// The constructor of the class.
+ ///
+ /// \param graph The digraph the algorithm runs on.
+ CostScaling(const GR& graph) :
+ _graph(graph), _node_id(graph), _arc_idf(graph), _arc_idb(graph),
+ _cost_map(_cost_vec), _pi_map(_pi),
+ INF(std::numeric_limits<Value>::has_infinity ?
+ std::numeric_limits<Value>::infinity() :
+ std::numeric_limits<Value>::max())
{
- // Check the sum of supply values
- Supply sum = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
- _valid_supply = sum == 0;
+ // Check the value types
+ LEMON_ASSERT(std::numeric_limits<Value>::is_signed,
+ "The flow type of CostScaling must be signed");
+ LEMON_ASSERT(std::numeric_limits<Cost>::is_signed,
+ "The cost type of CostScaling must be signed");
+
+ // Resize vectors
+ _node_num = countNodes(_graph);
+ _arc_num = countArcs(_graph);
+ _res_node_num = _node_num + 1;
+ _res_arc_num = 2 * (_arc_num + _node_num);
+ _root = _node_num;
+
+ _first_out.resize(_res_node_num + 1);
+ _forward.resize(_res_arc_num);
+ _source.resize(_res_arc_num);
+ _target.resize(_res_arc_num);
+ _reverse.resize(_res_arc_num);
+
+ _lower.resize(_res_arc_num);
+ _upper.resize(_res_arc_num);
+ _scost.resize(_res_arc_num);
+ _supply.resize(_res_node_num);
- for (ArcIt e(_graph); e != INVALID; ++e) _capacity[e] = capacity[e];
- for (NodeIt n(_graph); n != INVALID; ++n) _supply[n] = supply[n];
+ _res_cap.resize(_res_arc_num);
+ _cost.resize(_res_arc_num);
+ _pi.resize(_res_node_num);
+ _excess.resize(_res_node_num);
+ _next_out.resize(_res_node_num);
- // Remove non-zero lower bounds
- for (ArcIt e(_graph); e != INVALID; ++e) {
- if (lower[e] != 0) {
- _capacity[e] -= lower[e];
- _supply[_graph.source(e)] -= lower[e];
- _supply[_graph.target(e)] += lower[e];
+ _arc_vec.reserve(_res_arc_num);
+ _cost_vec.reserve(_res_arc_num);
+
+ // Copy the graph
+ int i = 0, j = 0, k = 2 * _arc_num + _node_num;
+ for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
+ _node_id[n] = i;
+ }
+ i = 0;
+ for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
+ _first_out[i] = j;
+ for (OutArcIt a(_graph, n); a != INVALID; ++a, ++j) {
+ _arc_idf[a] = j;
+ _forward[j] = true;
+ _source[j] = i;
+ _target[j] = _node_id[_graph.runningNode(a)];
}
+ for (InArcIt a(_graph, n); a != INVALID; ++a, ++j) {
+ _arc_idb[a] = j;
+ _forward[j] = false;
+ _source[j] = i;
+ _target[j] = _node_id[_graph.runningNode(a)];
+ }
+ _forward[j] = false;
+ _source[j] = i;
+ _target[j] = _root;
+ _reverse[j] = k;
+ _forward[k] = true;
+ _source[k] = _root;
+ _target[k] = i;
+ _reverse[k] = j;
+ ++j; ++k;
}
- }
-/*
- /// \brief General constructor (without lower bounds).
- ///
- /// General constructor (without lower bounds).
- ///
- /// \param digraph The digraph the algorithm runs on.
- /// \param capacity The capacities (upper bounds) of the arcs.
- /// \param cost The cost (length) values of the arcs.
- /// \param supply The supply values of the nodes (signed).
- CostScaling( const Digraph &digraph,
- const CapacityMap &capacity,
- const CostMap &cost,
- const SupplyMap &supply ) :
- _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
- _cost(digraph), _supply(supply), _flow(NULL), _local_flow(false),
- _potential(NULL), _local_potential(false), _res_cost(_cost),
- _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
- {
- // Check the sum of supply values
- Supply sum = 0;
- for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
- _valid_supply = sum == 0;
+ _first_out[i] = j;
+ _first_out[_res_node_num] = k;
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ int fi = _arc_idf[a];
+ int bi = _arc_idb[a];
+ _reverse[fi] = bi;
+ _reverse[bi] = fi;
+ }
+
+ // Reset parameters
+ reset();
}
- /// \brief Simple constructor (with lower bounds).
+ /// \name Parameters
+ /// The parameters of the algorithm can be specified using these
+ /// functions.
+
+ /// @{
+
+ /// \brief Set the lower bounds on the arcs.
///
- /// Simple constructor (with lower bounds).
+ /// This function sets the lower bounds on the arcs.
+ /// If it is not used before calling \ref run(), the lower bounds
+ /// will be set to zero on all arcs.
///
- /// \param digraph The digraph the algorithm runs on.
- /// \param lower The lower bounds of the arcs.
- /// \param capacity The capacities (upper bounds) of the arcs.
- /// \param cost The cost (length) values of the arcs.
- /// \param s The source node.
- /// \param t The target node.
- /// \param flow_value The required amount of flow from node \c s
- /// to node \c t (i.e. the supply of \c s and the demand of \c t).
- CostScaling( const Digraph &digraph,
- const LowerMap &lower,
- const CapacityMap &capacity,
- const CostMap &cost,
- Node s, Node t,
- Supply flow_value ) :
- _graph(digraph), _lower(&lower), _capacity(capacity), _orig_cost(cost),
- _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false),
- _potential(NULL), _local_potential(false), _res_cost(_cost),
- _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
- {
- // Remove non-zero lower bounds
- _supply[s] = flow_value;
- _supply[t] = -flow_value;
- for (ArcIt e(_graph); e != INVALID; ++e) {
- if (lower[e] != 0) {
- _capacity[e] -= lower[e];
- _supply[_graph.source(e)] -= lower[e];
- _supply[_graph.target(e)] += lower[e];
- }
+ /// \param map An arc map storing the lower bounds.
+ /// Its \c Value type must be convertible to the \c Value type
+ /// of the algorithm.
+ ///
+ /// \return <tt>(*this)</tt>
+ template <typename LowerMap>
+ CostScaling& lowerMap(const LowerMap& map) {
+ _have_lower = true;
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ _lower[_arc_idf[a]] = map[a];
+ _lower[_arc_idb[a]] = map[a];
}
- _valid_supply = true;
- }
-
- /// \brief Simple constructor (without lower bounds).
- ///
- /// Simple constructor (without lower bounds).
- ///
- /// \param digraph The digraph the algorithm runs on.
- /// \param capacity The capacities (upper bounds) of the arcs.
- /// \param cost The cost (length) values of the arcs.
- /// \param s The source node.
- /// \param t The target node.
- /// \param flow_value The required amount of flow from node \c s
- /// to node \c t (i.e. the supply of \c s and the demand of \c t).
- CostScaling( const Digraph &digraph,
- const CapacityMap &capacity,
- const CostMap &cost,
- Node s, Node t,
- Supply flow_value ) :
- _graph(digraph), _lower(NULL), _capacity(capacity), _orig_cost(cost),
- _cost(digraph), _supply(digraph, 0), _flow(NULL), _local_flow(false),
- _potential(NULL), _local_potential(false), _res_cost(_cost),
- _res_graph(NULL), _red_cost(NULL), _excess(digraph, 0)
- {
- _supply[s] = flow_value;
- _supply[t] = -flow_value;
- _valid_supply = true;
- }
-*/
- /// Destructor.
- ~CostScaling() {
- if (_local_flow) delete _flow;
- if (_local_potential) delete _potential;
- delete _res_graph;
- delete _red_cost;
- }
-
- /// \brief Set the flow map.
- ///
- /// Set the flow map.
- ///
- /// \return \c (*this)
- CostScaling& flowMap(FlowMap &map) {
- if (_local_flow) {
- delete _flow;
- _local_flow = false;
- }
- _flow = ↦
return *this;
}
- /// \brief Set the potential map.
+ /// \brief Set the upper bounds (capacities) on the arcs.
///
- /// Set the potential map.
+ /// This function sets the upper bounds (capacities) on the arcs.
+ /// If it is not used before calling \ref run(), the upper bounds
+ /// will be set to \ref INF on all arcs (i.e. the flow value will be
+ /// unbounded from above on each arc).
///
- /// \return \c (*this)
- CostScaling& potentialMap(PotentialMap &map) {
- if (_local_potential) {
- delete _potential;
- _local_potential = false;
+ /// \param map An arc map storing the upper bounds.
+ /// Its \c Value type must be convertible to the \c Value type
+ /// of the algorithm.
+ ///
+ /// \return <tt>(*this)</tt>
+ template<typename UpperMap>
+ CostScaling& upperMap(const UpperMap& map) {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ _upper[_arc_idf[a]] = map[a];
}
- _potential = ↦
return *this;
}
+ /// \brief Set the costs of the arcs.
+ ///
+ /// This function sets the costs of the arcs.
+ /// If it is not used before calling \ref run(), the costs
+ /// will be set to \c 1 on all arcs.
+ ///
+ /// \param map An arc map storing the costs.
+ /// Its \c Value type must be convertible to the \c Cost type
+ /// of the algorithm.
+ ///
+ /// \return <tt>(*this)</tt>
+ template<typename CostMap>
+ CostScaling& costMap(const CostMap& map) {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ _scost[_arc_idf[a]] = map[a];
+ _scost[_arc_idb[a]] = -map[a];
+ }
+ return *this;
+ }
+
+ /// \brief Set the supply values of the nodes.
+ ///
+ /// This function sets the supply values of the nodes.
+ /// If neither this function nor \ref stSupply() is used before
+ /// calling \ref run(), the supply of each node will be set to zero.
+ ///
+ /// \param map A node map storing the supply values.
+ /// Its \c Value type must be convertible to the \c Value type
+ /// of the algorithm.
+ ///
+ /// \return <tt>(*this)</tt>
+ template<typename SupplyMap>
+ CostScaling& supplyMap(const SupplyMap& map) {
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ _supply[_node_id[n]] = map[n];
+ }
+ return *this;
+ }
+
+ /// \brief Set single source and target nodes and a supply value.
+ ///
+ /// This function sets a single source node and a single target node
+ /// and the required flow value.
+ /// If neither this function nor \ref supplyMap() is used before
+ /// calling \ref run(), the supply of each node will be set to zero.
+ ///
+ /// Using this function has the same effect as using \ref supplyMap()
+ /// with such a map in which \c k is assigned to \c s, \c -k is
+ /// assigned to \c t and all other nodes have zero supply value.
+ ///
+ /// \param s The source node.
+ /// \param t The target node.
+ /// \param k The required amount of flow from node \c s to node \c t
+ /// (i.e. the supply of \c s and the demand of \c t).
+ ///
+ /// \return <tt>(*this)</tt>
+ CostScaling& stSupply(const Node& s, const Node& t, Value k) {
+ for (int i = 0; i != _res_node_num; ++i) {
+ _supply[i] = 0;
+ }
+ _supply[_node_id[s]] = k;
+ _supply[_node_id[t]] = -k;
+ return *this;
+ }
+
+ /// @}
+
/// \name Execution control
+ /// The algorithm can be executed using \ref run().
/// @{
/// \brief Run the algorithm.
///
- /// Run the algorithm.
+ /// This function runs the algorithm.
+ /// The paramters can be specified using functions \ref lowerMap(),
+ /// \ref upperMap(), \ref costMap(), \ref supplyMap(), \ref stSupply().
+ /// For example,
+ /// \code
+ /// CostScaling<ListDigraph> cs(graph);
+ /// cs.lowerMap(lower).upperMap(upper).costMap(cost)
+ /// .supplyMap(sup).run();
+ /// \endcode
+ ///
+ /// This function can be called more than once. All the parameters
+ /// that have been given are kept for the next call, unless
+ /// \ref reset() is called, thus only the modified parameters
+ /// have to be set again. See \ref reset() for examples.
+ /// However the underlying digraph must not be modified after this
+ /// class have been constructed, since it copies the digraph.
///
/// \param partial_augment By default the algorithm performs
/// partial augment and relabel operations in the cost scaling
/// phases. Set this parameter to \c false for using local push and
/// relabel operations instead.
///
- /// \return \c true if a feasible flow can be found.
- bool run(bool partial_augment = true) {
- if (partial_augment) {
- return init() && startPartialAugment();
- } else {
- return init() && startPushRelabel();
+ /// \return \c INFEASIBLE if no feasible flow exists,
+ /// \n \c OPTIMAL if the problem has optimal solution
+ /// (i.e. it is feasible and bounded), and the algorithm has found
+ /// optimal flow and node potentials (primal and dual solutions),
+ /// \n \c UNBOUNDED if the digraph contains an arc of negative cost
+ /// and infinite upper bound. It means that the objective function
+ /// is unbounded on that arc, however note that it could actually be
+ /// bounded over the feasible flows, but this algroithm cannot handle
+ /// these cases.
+ ///
+ /// \see ProblemType
+ ProblemType run(bool partial_augment = true) {
+ ProblemType pt = init();
+ if (pt != OPTIMAL) return pt;
+ start(partial_augment);
+ return OPTIMAL;
+ }
+
+ /// \brief Reset all the parameters that have been given before.
+ ///
+ /// This function resets all the paramaters that have been given
+ /// before using functions \ref lowerMap(), \ref upperMap(),
+ /// \ref costMap(), \ref supplyMap(), \ref stSupply().
+ ///
+ /// It is useful for multiple run() calls. If this function is not
+ /// used, all the parameters given before are kept for the next
+ /// \ref run() call.
+ /// However the underlying digraph must not be modified after this
+ /// class have been constructed, since it copies and extends the graph.
+ ///
+ /// For example,
+ /// \code
+ /// CostScaling<ListDigraph> cs(graph);
+ ///
+ /// // First run
+ /// cs.lowerMap(lower).upperMap(upper).costMap(cost)
+ /// .supplyMap(sup).run();
+ ///
+ /// // Run again with modified cost map (reset() is not called,
+ /// // so only the cost map have to be set again)
+ /// cost[e] += 100;
+ /// cs.costMap(cost).run();
+ ///
+ /// // Run again from scratch using reset()
+ /// // (the lower bounds will be set to zero on all arcs)
+ /// cs.reset();
+ /// cs.upperMap(capacity).costMap(cost)
+ /// .supplyMap(sup).run();
+ /// \endcode
+ ///
+ /// \return <tt>(*this)</tt>
+ CostScaling& reset() {
+ for (int i = 0; i != _res_node_num; ++i) {
+ _supply[i] = 0;
}
+ int limit = _first_out[_root];
+ for (int j = 0; j != limit; ++j) {
+ _lower[j] = 0;
+ _upper[j] = INF;
+ _scost[j] = _forward[j] ? 1 : -1;
+ }
+ for (int j = limit; j != _res_arc_num; ++j) {
+ _lower[j] = 0;
+ _upper[j] = INF;
+ _scost[j] = 0;
+ _scost[_reverse[j]] = 0;
+ }
+ _have_lower = false;
+ return *this;
}
/// @}
/// \name Query Functions
- /// The result of the algorithm can be obtained using these
+ /// The results of the algorithm can be obtained using these
/// functions.\n
- /// \ref lemon::CostScaling::run() "run()" must be called before
- /// using them.
+ /// The \ref run() function must be called before using them.
/// @{
- /// \brief Return a const reference to the arc map storing the
- /// found flow.
+ /// \brief Return the total cost of the found flow.
///
- /// Return a const reference to the arc map storing the found flow.
+ /// This function returns the total cost of the found flow.
+ /// Its complexity is O(e).
+ ///
+ /// \note The return type of the function can be specified as a
+ /// template parameter. For example,
+ /// \code
+ /// cs.totalCost<double>();
+ /// \endcode
+ /// It is useful if the total cost cannot be stored in the \c Cost
+ /// type of the algorithm, which is the default return type of the
+ /// function.
///
/// \pre \ref run() must be called before using this function.
- const FlowMap& flowMap() const {
- return *_flow;
+ template <typename Number>
+ Number totalCost() const {
+ Number c = 0;
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ int i = _arc_idb[a];
+ c += static_cast<Number>(_res_cap[i]) *
+ (-static_cast<Number>(_scost[i]));
+ }
+ return c;
}
- /// \brief Return a const reference to the node map storing the
- /// found potentials (the dual solution).
- ///
- /// Return a const reference to the node map storing the found
- /// potentials (the dual solution).
- ///
- /// \pre \ref run() must be called before using this function.
- const PotentialMap& potentialMap() const {
- return *_potential;
+#ifndef DOXYGEN
+ Cost totalCost() const {
+ return totalCost<Cost>();
}
+#endif
/// \brief Return the flow on the given arc.
///
- /// Return the flow on the given arc.
+ /// This function returns the flow on the given arc.
///
/// \pre \ref run() must be called before using this function.
- Capacity flow(const Arc& arc) const {
- return (*_flow)[arc];
+ Value flow(const Arc& a) const {
+ return _res_cap[_arc_idb[a]];
}
- /// \brief Return the potential of the given node.
+ /// \brief Return the flow map (the primal solution).
///
- /// Return the potential of the given node.
+ /// This function copies the flow value on each arc into the given
+ /// map. The \c Value type of the algorithm must be convertible to
+ /// the \c Value type of the map.
///
/// \pre \ref run() must be called before using this function.
- Cost potential(const Node& node) const {
- return (*_potential)[node];
+ template <typename FlowMap>
+ void flowMap(FlowMap &map) const {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ map.set(a, _res_cap[_arc_idb[a]]);
+ }
}
- /// \brief Return the total cost of the found flow.
+ /// \brief Return the potential (dual value) of the given node.
///
- /// Return the total cost of the found flow. The complexity of the
- /// function is \f$ O(e) \f$.
+ /// This function returns the potential (dual value) of the
+ /// given node.
///
/// \pre \ref run() must be called before using this function.
- Cost totalCost() const {
- Cost c = 0;
- for (ArcIt e(_graph); e != INVALID; ++e)
- c += (*_flow)[e] * _orig_cost[e];
- return c;
+ Cost potential(const Node& n) const {
+ return static_cast<Cost>(_pi[_node_id[n]]);
+ }
+
+ /// \brief Return the potential map (the dual solution).
+ ///
+ /// This function copies the potential (dual value) of each node
+ /// into the given map.
+ /// The \c Cost type of the algorithm must be convertible to the
+ /// \c Value type of the map.
+ ///
+ /// \pre \ref run() must be called before using this function.
+ template <typename PotentialMap>
+ void potentialMap(PotentialMap &map) const {
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ map.set(n, static_cast<Cost>(_pi[_node_id[n]]));
+ }
}
/// @}
private:
- /// Initialize the algorithm.
- bool init() {
- if (!_valid_supply) return false;
- // The scaling factor
+ // Initialize the algorithm
+ ProblemType init() {
+ if (_res_node_num == 0) return INFEASIBLE;
+
+ // Scaling factor
_alpha = 8;
- // Initialize flow and potential maps
- if (!_flow) {
- _flow = new FlowMap(_graph);
- _local_flow = true;
+ // Check the sum of supply values
+ _sum_supply = 0;
+ for (int i = 0; i != _root; ++i) {
+ _sum_supply += _supply[i];
}
- if (!_potential) {
- _potential = new PotentialMap(_graph);
- _local_potential = true;
+ if (_sum_supply > 0) return INFEASIBLE;
+
+
+ // Initialize vectors
+ for (int i = 0; i != _res_node_num; ++i) {
+ _pi[i] = 0;
+ _excess[i] = _supply[i];
+ }
+
+ // Remove infinite upper bounds and check negative arcs
+ const Value MAX = std::numeric_limits<Value>::max();
+ int last_out;
+ if (_have_lower) {
+ for (int i = 0; i != _root; ++i) {
+ last_out = _first_out[i+1];
+ for (int j = _first_out[i]; j != last_out; ++j) {
+ if (_forward[j]) {
+ Value c = _scost[j] < 0 ? _upper[j] : _lower[j];
+ if (c >= MAX) return UNBOUNDED;
+ _excess[i] -= c;
+ _excess[_target[j]] += c;
+ }
+ }
+ }
+ } else {
+ for (int i = 0; i != _root; ++i) {
+ last_out = _first_out[i+1];
+ for (int j = _first_out[i]; j != last_out; ++j) {
+ if (_forward[j] && _scost[j] < 0) {
+ Value c = _upper[j];
+ if (c >= MAX) return UNBOUNDED;
+ _excess[i] -= c;
+ _excess[_target[j]] += c;
+ }
+ }
+ }
+ }
+ Value ex, max_cap = 0;
+ for (int i = 0; i != _res_node_num; ++i) {
+ ex = _excess[i];
+ _excess[i] = 0;
+ if (ex < 0) max_cap -= ex;
+ }
+ for (int j = 0; j != _res_arc_num; ++j) {
+ if (_upper[j] >= MAX) _upper[j] = max_cap;
}
- _red_cost = new ReducedCostMap(_graph, _cost, *_potential);
- _res_graph = new ResDigraph(_graph, _capacity, *_flow);
+ // Initialize the large cost vector and the epsilon parameter
+ _epsilon = 0;
+ LargeCost lc;
+ for (int i = 0; i != _root; ++i) {
+ last_out = _first_out[i+1];
+ for (int j = _first_out[i]; j != last_out; ++j) {
+ lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;
+ _cost[j] = lc;
+ if (lc > _epsilon) _epsilon = lc;
+ }
+ }
+ _epsilon /= _alpha;
- // Initialize the scaled cost map and the epsilon parameter
- Cost max_cost = 0;
- int node_num = countNodes(_graph);
- for (ArcIt e(_graph); e != INVALID; ++e) {
- _cost[e] = LCost(_orig_cost[e]) * node_num * _alpha;
- if (_orig_cost[e] > max_cost) max_cost = _orig_cost[e];
+ // Initialize maps for Circulation and remove non-zero lower bounds
+ ConstMap<Arc, Value> low(0);
+ typedef typename Digraph::template ArcMap<Value> ValueArcMap;
+ typedef typename Digraph::template NodeMap<Value> ValueNodeMap;
+ ValueArcMap cap(_graph), flow(_graph);
+ ValueNodeMap sup(_graph);
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ sup[n] = _supply[_node_id[n]];
}
- _epsilon = max_cost * node_num;
+ if (_have_lower) {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ int j = _arc_idf[a];
+ Value c = _lower[j];
+ cap[a] = _upper[j] - c;
+ sup[_graph.source(a)] -= c;
+ sup[_graph.target(a)] += c;
+ }
+ } else {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ cap[a] = _upper[_arc_idf[a]];
+ }
+ }
// Find a feasible flow using Circulation
- Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap,
- SupplyMap >
- circulation( _graph, constMap<Arc>(Capacity(0)), _capacity,
- _supply );
- return circulation.flowMap(*_flow).run();
+ Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>
+ circ(_graph, low, cap, sup);
+ if (!circ.flowMap(flow).run()) return INFEASIBLE;
+
+ // Set residual capacities and handle GEQ supply type
+ if (_sum_supply < 0) {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ Value fa = flow[a];
+ _res_cap[_arc_idf[a]] = cap[a] - fa;
+ _res_cap[_arc_idb[a]] = fa;
+ sup[_graph.source(a)] -= fa;
+ sup[_graph.target(a)] += fa;
+ }
+ for (NodeIt n(_graph); n != INVALID; ++n) {
+ _excess[_node_id[n]] = sup[n];
+ }
+ for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
+ int u = _target[a];
+ int ra = _reverse[a];
+ _res_cap[a] = -_sum_supply + 1;
+ _res_cap[ra] = -_excess[u];
+ _cost[a] = 0;
+ _cost[ra] = 0;
+ _excess[u] = 0;
+ }
+ } else {
+ for (ArcIt a(_graph); a != INVALID; ++a) {
+ Value fa = flow[a];
+ _res_cap[_arc_idf[a]] = cap[a] - fa;
+ _res_cap[_arc_idb[a]] = fa;
+ }
+ for (int a = _first_out[_root]; a != _res_arc_num; ++a) {
+ int ra = _reverse[a];
+ _res_cap[a] = 1;
+ _res_cap[ra] = 0;
+ _cost[a] = 0;
+ _cost[ra] = 0;
+ }
+ }
+
+ return OPTIMAL;
+ }
+
+ // Execute the algorithm and transform the results
+ void start(bool partial_augment) {
+ // Execute the algorithm
+ if (partial_augment) {
+ startPartialAugment();
+ } else {
+ startPushRelabel();
+ }
+
+ // Compute node potentials for the original costs
+ _arc_vec.clear();
+ _cost_vec.clear();
+ for (int j = 0; j != _res_arc_num; ++j) {
+ if (_res_cap[j] > 0) {
+ _arc_vec.push_back(IntPair(_source[j], _target[j]));
+ _cost_vec.push_back(_scost[j]);
+ }
+ }
+ _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+
+ typename BellmanFord<StaticDigraph, LargeCostArcMap>
+ ::template SetDistMap<LargeCostNodeMap>::Create bf(_sgr, _cost_map);
+ bf.distMap(_pi_map);
+ bf.init(0);
+ bf.start();
+
+ // Handle non-zero lower bounds
+ if (_have_lower) {
+ int limit = _first_out[_root];
+ for (int j = 0; j != limit; ++j) {
+ if (!_forward[j]) _res_cap[j] += _lower[j];
+ }
+ }
}
/// Execute the algorithm performing partial augmentation and
- /// relabel operations.
- bool startPartialAugment() {
+ /// relabel operations
+ void startPartialAugment() {
// Paramters for heuristics
-// const int BF_HEURISTIC_EPSILON_BOUND = 1000;
-// const int BF_HEURISTIC_BOUND_FACTOR = 3;
+ const int BF_HEURISTIC_EPSILON_BOUND = 1000;
+ const int BF_HEURISTIC_BOUND_FACTOR = 3;
// Maximum augment path length
const int MAX_PATH_LENGTH = 4;
- // Variables
- typename Digraph::template NodeMap<Arc> pred_arc(_graph);
- typename Digraph::template NodeMap<bool> forward(_graph);
- typename Digraph::template NodeMap<OutArcIt> next_out(_graph);
- typename Digraph::template NodeMap<InArcIt> next_in(_graph);
- typename Digraph::template NodeMap<bool> next_dir(_graph);
- std::deque<Node> active_nodes;
- std::vector<Node> path_nodes;
-
-// int node_num = countNodes(_graph);
+ // Perform cost scaling phases
+ IntVector pred_arc(_res_node_num);
+ std::vector<int> path_nodes;
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
1 : _epsilon / _alpha )
{
-/*
// "Early Termination" heuristic: use Bellman-Ford algorithm
// to check if the current flow is optimal
if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
- typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
- ShiftCostMap shift_cost(_res_cost, 1);
- BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost);
+ _arc_vec.clear();
+ _cost_vec.clear();
+ for (int j = 0; j != _res_arc_num; ++j) {
+ if (_res_cap[j] > 0) {
+ _arc_vec.push_back(IntPair(_source[j], _target[j]));
+ _cost_vec.push_back(_cost[j] + 1);
+ }
+ }
+ _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+
+ BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
bf.init(0);
bool done = false;
- int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
+ int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num));
for (int i = 0; i < K && !done; ++i)
done = bf.processNextWeakRound();
if (done) break;
}
-*/
+
// Saturate arcs not satisfying the optimality condition
- Capacity delta;
- for (ArcIt e(_graph); e != INVALID; ++e) {
- if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
- delta = _capacity[e] - (*_flow)[e];
- _excess[_graph.source(e)] -= delta;
- _excess[_graph.target(e)] += delta;
- (*_flow)[e] = _capacity[e];
- }
- if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
- _excess[_graph.target(e)] -= (*_flow)[e];
- _excess[_graph.source(e)] += (*_flow)[e];
- (*_flow)[e] = 0;
+ for (int a = 0; a != _res_arc_num; ++a) {
+ if (_res_cap[a] > 0 &&
+ _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+ Value delta = _res_cap[a];
+ _excess[_source[a]] -= delta;
+ _excess[_target[a]] += delta;
+ _res_cap[a] = 0;
+ _res_cap[_reverse[a]] += delta;
}
}
-
+
// Find active nodes (i.e. nodes with positive excess)
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if (_excess[n] > 0) active_nodes.push_back(n);
+ for (int u = 0; u != _res_node_num; ++u) {
+ if (_excess[u] > 0) _active_nodes.push_back(u);
}
- // Initialize the next arc maps
- for (NodeIt n(_graph); n != INVALID; ++n) {
- next_out[n] = OutArcIt(_graph, n);
- next_in[n] = InArcIt(_graph, n);
- next_dir[n] = true;
+ // Initialize the next arcs
+ for (int u = 0; u != _res_node_num; ++u) {
+ _next_out[u] = _first_out[u];
}
// Perform partial augment and relabel operations
- while (active_nodes.size() > 0) {
+ while (true) {
// Select an active node (FIFO selection)
- if (_excess[active_nodes[0]] <= 0) {
- active_nodes.pop_front();
- continue;
+ while (_active_nodes.size() > 0 &&
+ _excess[_active_nodes.front()] <= 0) {
+ _active_nodes.pop_front();
}
- Node start = active_nodes[0];
+ if (_active_nodes.size() == 0) break;
+ int start = _active_nodes.front();
path_nodes.clear();
path_nodes.push_back(start);
// Find an augmenting path from the start node
- Node u, tip = start;
- LCost min_red_cost;
- while ( _excess[tip] >= 0 &&
- int(path_nodes.size()) <= MAX_PATH_LENGTH )
- {
- if (next_dir[tip]) {
- for (OutArcIt e = next_out[tip]; e != INVALID; ++e) {
- if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
- u = _graph.target(e);
- pred_arc[u] = e;
- forward[u] = true;
- next_out[tip] = e;
- tip = u;
- path_nodes.push_back(tip);
- goto next_step;
- }
- }
- next_dir[tip] = false;
- }
- for (InArcIt e = next_in[tip]; e != INVALID; ++e) {
- if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
- u = _graph.source(e);
- pred_arc[u] = e;
- forward[u] = false;
- next_in[tip] = e;
+ int tip = start;
+ while (_excess[tip] >= 0 &&
+ int(path_nodes.size()) <= MAX_PATH_LENGTH) {
+ int u;
+ LargeCost min_red_cost, rc;
+ int last_out = _sum_supply < 0 ?
+ _first_out[tip+1] : _first_out[tip+1] - 1;
+ for (int a = _next_out[tip]; a != last_out; ++a) {
+ if (_res_cap[a] > 0 &&
+ _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+ u = _target[a];
+ pred_arc[u] = a;
+ _next_out[tip] = a;
tip = u;
path_nodes.push_back(tip);
goto next_step;
@@ -579,266 +943,186 @@
}
// Relabel tip node
- min_red_cost = std::numeric_limits<LCost>::max() / 2;
- for (OutArcIt oe(_graph, tip); oe != INVALID; ++oe) {
- if ( _capacity[oe] - (*_flow)[oe] > 0 &&
- (*_red_cost)[oe] < min_red_cost )
- min_red_cost = (*_red_cost)[oe];
+ min_red_cost = std::numeric_limits<LargeCost>::max() / 2;
+ for (int a = _first_out[tip]; a != last_out; ++a) {
+ rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]];
+ if (_res_cap[a] > 0 && rc < min_red_cost) {
+ min_red_cost = rc;
+ }
}
- for (InArcIt ie(_graph, tip); ie != INVALID; ++ie) {
- if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
- min_red_cost = -(*_red_cost)[ie];
- }
- (*_potential)[tip] -= min_red_cost + _epsilon;
+ _pi[tip] -= min_red_cost + _epsilon;
- // Reset the next arc maps
- next_out[tip] = OutArcIt(_graph, tip);
- next_in[tip] = InArcIt(_graph, tip);
- next_dir[tip] = true;
+ // Reset the next arc of tip
+ _next_out[tip] = _first_out[tip];
// Step back
if (tip != start) {
path_nodes.pop_back();
- tip = path_nodes[path_nodes.size()-1];
+ tip = path_nodes.back();
}
- next_step:
- continue;
+ next_step: ;
}
// Augment along the found path (as much flow as possible)
- Capacity delta;
+ Value delta;
+ int u, v = path_nodes.front(), pa;
for (int i = 1; i < int(path_nodes.size()); ++i) {
- u = path_nodes[i];
- delta = forward[u] ?
- _capacity[pred_arc[u]] - (*_flow)[pred_arc[u]] :
- (*_flow)[pred_arc[u]];
- delta = std::min(delta, _excess[path_nodes[i-1]]);
- (*_flow)[pred_arc[u]] += forward[u] ? delta : -delta;
- _excess[path_nodes[i-1]] -= delta;
- _excess[u] += delta;
- if (_excess[u] > 0 && _excess[u] <= delta) active_nodes.push_back(u);
+ u = v;
+ v = path_nodes[i];
+ pa = pred_arc[v];
+ delta = std::min(_res_cap[pa], _excess[u]);
+ _res_cap[pa] -= delta;
+ _res_cap[_reverse[pa]] += delta;
+ _excess[u] -= delta;
+ _excess[v] += delta;
+ if (_excess[v] > 0 && _excess[v] <= delta)
+ _active_nodes.push_back(v);
}
}
}
-
- // Compute node potentials for the original costs
- ResidualCostMap<CostMap> res_cost(_orig_cost);
- BellmanFord< ResDigraph, ResidualCostMap<CostMap> >
- bf(*_res_graph, res_cost);
- bf.init(0); bf.start();
- for (NodeIt n(_graph); n != INVALID; ++n)
- (*_potential)[n] = bf.dist(n);
-
- // Handle non-zero lower bounds
- if (_lower) {
- for (ArcIt e(_graph); e != INVALID; ++e)
- (*_flow)[e] += (*_lower)[e];
- }
- return true;
}
- /// Execute the algorithm performing push and relabel operations.
- bool startPushRelabel() {
+ /// Execute the algorithm performing push and relabel operations
+ void startPushRelabel() {
// Paramters for heuristics
-// const int BF_HEURISTIC_EPSILON_BOUND = 1000;
-// const int BF_HEURISTIC_BOUND_FACTOR = 3;
+ const int BF_HEURISTIC_EPSILON_BOUND = 1000;
+ const int BF_HEURISTIC_BOUND_FACTOR = 3;
- typename Digraph::template NodeMap<bool> hyper(_graph, false);
- typename Digraph::template NodeMap<Arc> pred_arc(_graph);
- typename Digraph::template NodeMap<bool> forward(_graph);
- typename Digraph::template NodeMap<OutArcIt> next_out(_graph);
- typename Digraph::template NodeMap<InArcIt> next_in(_graph);
- typename Digraph::template NodeMap<bool> next_dir(_graph);
- std::deque<Node> active_nodes;
-
-// int node_num = countNodes(_graph);
+ // Perform cost scaling phases
+ BoolVector hyper(_res_node_num, false);
for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
1 : _epsilon / _alpha )
{
-/*
// "Early Termination" heuristic: use Bellman-Ford algorithm
// to check if the current flow is optimal
if (_epsilon <= BF_HEURISTIC_EPSILON_BOUND) {
- typedef ShiftMap< ResidualCostMap<LargeCostMap> > ShiftCostMap;
- ShiftCostMap shift_cost(_res_cost, 1);
- BellmanFord<ResDigraph, ShiftCostMap> bf(*_res_graph, shift_cost);
+ _arc_vec.clear();
+ _cost_vec.clear();
+ for (int j = 0; j != _res_arc_num; ++j) {
+ if (_res_cap[j] > 0) {
+ _arc_vec.push_back(IntPair(_source[j], _target[j]));
+ _cost_vec.push_back(_cost[j] + 1);
+ }
+ }
+ _sgr.build(_res_node_num, _arc_vec.begin(), _arc_vec.end());
+
+ BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
bf.init(0);
bool done = false;
- int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(node_num));
+ int K = int(BF_HEURISTIC_BOUND_FACTOR * sqrt(_res_node_num));
for (int i = 0; i < K && !done; ++i)
done = bf.processNextWeakRound();
if (done) break;
}
-*/
// Saturate arcs not satisfying the optimality condition
- Capacity delta;
- for (ArcIt e(_graph); e != INVALID; ++e) {
- if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
- delta = _capacity[e] - (*_flow)[e];
- _excess[_graph.source(e)] -= delta;
- _excess[_graph.target(e)] += delta;
- (*_flow)[e] = _capacity[e];
- }
- if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
- _excess[_graph.target(e)] -= (*_flow)[e];
- _excess[_graph.source(e)] += (*_flow)[e];
- (*_flow)[e] = 0;
+ for (int a = 0; a != _res_arc_num; ++a) {
+ if (_res_cap[a] > 0 &&
+ _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+ Value delta = _res_cap[a];
+ _excess[_source[a]] -= delta;
+ _excess[_target[a]] += delta;
+ _res_cap[a] = 0;
+ _res_cap[_reverse[a]] += delta;
}
}
// Find active nodes (i.e. nodes with positive excess)
- for (NodeIt n(_graph); n != INVALID; ++n) {
- if (_excess[n] > 0) active_nodes.push_back(n);
+ for (int u = 0; u != _res_node_num; ++u) {
+ if (_excess[u] > 0) _active_nodes.push_back(u);
}
- // Initialize the next arc maps
- for (NodeIt n(_graph); n != INVALID; ++n) {
- next_out[n] = OutArcIt(_graph, n);
- next_in[n] = InArcIt(_graph, n);
- next_dir[n] = true;
+ // Initialize the next arcs
+ for (int u = 0; u != _res_node_num; ++u) {
+ _next_out[u] = _first_out[u];
}
// Perform push and relabel operations
- while (active_nodes.size() > 0) {
+ while (_active_nodes.size() > 0) {
+ LargeCost min_red_cost, rc;
+ Value delta;
+ int n, t, a, last_out = _res_arc_num;
+
// Select an active node (FIFO selection)
- Node n = active_nodes[0], t;
- bool relabel_enabled = true;
+ next_node:
+ n = _active_nodes.front();
+ last_out = _sum_supply < 0 ?
+ _first_out[n+1] : _first_out[n+1] - 1;
// Perform push operations if there are admissible arcs
- if (_excess[n] > 0 && next_dir[n]) {
- OutArcIt e = next_out[n];
- for ( ; e != INVALID; ++e) {
- if (_capacity[e] - (*_flow)[e] > 0 && (*_red_cost)[e] < 0) {
- delta = std::min(_capacity[e] - (*_flow)[e], _excess[n]);
- t = _graph.target(e);
+ if (_excess[n] > 0) {
+ for (a = _next_out[n]; a != last_out; ++a) {
+ if (_res_cap[a] > 0 &&
+ _cost[a] + _pi[_source[a]] - _pi[_target[a]] < 0) {
+ delta = std::min(_res_cap[a], _excess[n]);
+ t = _target[a];
// Push-look-ahead heuristic
- Capacity ahead = -_excess[t];
- for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) {
- if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
- ahead += _capacity[oe] - (*_flow)[oe];
- }
- for (InArcIt ie(_graph, t); ie != INVALID; ++ie) {
- if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
- ahead += (*_flow)[ie];
+ Value ahead = -_excess[t];
+ int last_out_t = _sum_supply < 0 ?
+ _first_out[t+1] : _first_out[t+1] - 1;
+ for (int ta = _next_out[t]; ta != last_out_t; ++ta) {
+ if (_res_cap[ta] > 0 &&
+ _cost[ta] + _pi[_source[ta]] - _pi[_target[ta]] < 0)
+ ahead += _res_cap[ta];
+ if (ahead >= delta) break;
}
if (ahead < 0) ahead = 0;
// Push flow along the arc
if (ahead < delta) {
- (*_flow)[e] += ahead;
+ _res_cap[a] -= ahead;
+ _res_cap[_reverse[a]] += ahead;
_excess[n] -= ahead;
_excess[t] += ahead;
- active_nodes.push_front(t);
+ _active_nodes.push_front(t);
hyper[t] = true;
- relabel_enabled = false;
- break;
+ _next_out[n] = a;
+ goto next_node;
} else {
- (*_flow)[e] += delta;
+ _res_cap[a] -= delta;
+ _res_cap[_reverse[a]] += delta;
_excess[n] -= delta;
_excess[t] += delta;
if (_excess[t] > 0 && _excess[t] <= delta)
- active_nodes.push_back(t);
+ _active_nodes.push_back(t);
}
- if (_excess[n] == 0) break;
+ if (_excess[n] == 0) {
+ _next_out[n] = a;
+ goto remove_nodes;
+ }
}
}
- if (e != INVALID) {
- next_out[n] = e;
- } else {
- next_dir[n] = false;
- }
- }
-
- if (_excess[n] > 0 && !next_dir[n]) {
- InArcIt e = next_in[n];
- for ( ; e != INVALID; ++e) {
- if ((*_flow)[e] > 0 && -(*_red_cost)[e] < 0) {
- delta = std::min((*_flow)[e], _excess[n]);
- t = _graph.source(e);
-
- // Push-look-ahead heuristic
- Capacity ahead = -_excess[t];
- for (OutArcIt oe(_graph, t); oe != INVALID; ++oe) {
- if (_capacity[oe] - (*_flow)[oe] > 0 && (*_red_cost)[oe] < 0)
- ahead += _capacity[oe] - (*_flow)[oe];
- }
- for (InArcIt ie(_graph, t); ie != INVALID; ++ie) {
- if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < 0)
- ahead += (*_flow)[ie];
- }
- if (ahead < 0) ahead = 0;
-
- // Push flow along the arc
- if (ahead < delta) {
- (*_flow)[e] -= ahead;
- _excess[n] -= ahead;
- _excess[t] += ahead;
- active_nodes.push_front(t);
- hyper[t] = true;
- relabel_enabled = false;
- break;
- } else {
- (*_flow)[e] -= delta;
- _excess[n] -= delta;
- _excess[t] += delta;
- if (_excess[t] > 0 && _excess[t] <= delta)
- active_nodes.push_back(t);
- }
-
- if (_excess[n] == 0) break;
- }
- }
- next_in[n] = e;
+ _next_out[n] = a;
}
// Relabel the node if it is still active (or hyper)
- if (relabel_enabled && (_excess[n] > 0 || hyper[n])) {
- LCost min_red_cost = std::numeric_limits<LCost>::max() / 2;
- for (OutArcIt oe(_graph, n); oe != INVALID; ++oe) {
- if ( _capacity[oe] - (*_flow)[oe] > 0 &&
- (*_red_cost)[oe] < min_red_cost )
- min_red_cost = (*_red_cost)[oe];
+ if (_excess[n] > 0 || hyper[n]) {
+ min_red_cost = std::numeric_limits<LargeCost>::max() / 2;
+ for (int a = _first_out[n]; a != last_out; ++a) {
+ rc = _cost[a] + _pi[_source[a]] - _pi[_target[a]];
+ if (_res_cap[a] > 0 && rc < min_red_cost) {
+ min_red_cost = rc;
+ }
}
- for (InArcIt ie(_graph, n); ie != INVALID; ++ie) {
- if ((*_flow)[ie] > 0 && -(*_red_cost)[ie] < min_red_cost)
- min_red_cost = -(*_red_cost)[ie];
- }
- (*_potential)[n] -= min_red_cost + _epsilon;
+ _pi[n] -= min_red_cost + _epsilon;
hyper[n] = false;
- // Reset the next arc maps
- next_out[n] = OutArcIt(_graph, n);
- next_in[n] = InArcIt(_graph, n);
- next_dir[n] = true;
+ // Reset the next arc
+ _next_out[n] = _first_out[n];
}
-
+
// Remove nodes that are not active nor hyper
- while ( active_nodes.size() > 0 &&
- _excess[active_nodes[0]] <= 0 &&
- !hyper[active_nodes[0]] ) {
- active_nodes.pop_front();
+ remove_nodes:
+ while ( _active_nodes.size() > 0 &&
+ _excess[_active_nodes.front()] <= 0 &&
+ !hyper[_active_nodes.front()] ) {
+ _active_nodes.pop_front();
}
}
}
-
- // Compute node potentials for the original costs
- ResidualCostMap<CostMap> res_cost(_orig_cost);
- BellmanFord< ResDigraph, ResidualCostMap<CostMap> >
- bf(*_res_graph, res_cost);
- bf.init(0); bf.start();
- for (NodeIt n(_graph); n != INVALID; ++n)
- (*_potential)[n] = bf.dist(n);
-
- // Handle non-zero lower bounds
- if (_lower) {
- for (ArcIt e(_graph); e != INVALID; ++e)
- (*_flow)[e] += (*_lower)[e];
- }
- return true;
}
}; //class CostScaling