lemon-main: comparison lemon/network

equal deleted inserted replaced

-:9cdbdb665726
+:2a9d8e31081e
 #include <limits>
 #include <algorithm>
 #include <lemon/core.h>
 #include <lemon/math.h>
+#include <lemon/maps.h>
+#include <lemon/circulation.h>
+#include <lemon/adaptors.h>
 namespace lemon {
 /// \addtogroup min_cost_flow
 /// @{
 /// simplex method directly for the minimum cost flow problem.
 /// It is one of the most efficient solution methods.
 ///
 /// In general this class is the fastest implementation available
 /// in LEMON for the minimum cost flow problem.
+/// Moreover it supports both direction of the supply/demand inequality
+/// constraints. For more information see \ref ProblemType.
 ///
 /// \tparam GR The digraph type the algorithm runs on.
 /// \tparam F 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
 ///
 /// \warning Both value types must be signed and all input data must
 /// be integer.
 ///
 /// \note %NetworkSimplex provides five different pivot rule
-/// implementations. For more information see \ref PivotRule.
+/// implementations, from which the most efficient one is used
+/// by default. For more information see \ref PivotRule.
 template <typename GR, typename F = int, typename C = F>
 class NetworkSimplex
 {
 public:
 /// The flow type of the algorithm
 typedef F Flow;
 /// The cost type of the algorithm
 typedef C Cost;
+#ifdef DOXYGEN
+/// The type of the flow map
+typedef GR::ArcMap<Flow> FlowMap;
+/// The type of the potential map
+typedef GR::NodeMap<Cost> PotentialMap;
+#else
 /// The type of the flow map
 typedef typename GR::template ArcMap<Flow> FlowMap;
 /// The type of the potential map
 typedef typename GR::template NodeMap<Cost> PotentialMap;
+#endif
 public:
 /// \brief Enum type for selecting the pivot rule.
 ///
 /// It is a modified version of the Candidate List method.
 /// It keeps only the several best eligible arcs from the former
 /// candidate list and extends this list in every iteration.
 ALTERING_LIST
 };
+/// \brief Enum type for selecting the problem type.
+///
+/// Enum type for selecting the problem type, i.e. the direction of
+/// the inequalities in the supply/demand constraints of the
+/// \ref min_cost_flow "minimum cost flow problem".
+///
+/// The default problem type is \c GEQ, since this form is supported
+/// by other minimum cost flow algorithms and the \ref Circulation
+/// algorithm as well.
+/// The \c LEQ problem type can be selected using the \ref problemType()
+/// function.
+///
+/// Note that the equality form is a special case of both problem type.
+enum ProblemType {
+/// This option means that there are "<em>greater or equal</em>"
+/// constraints in the defintion, i.e. the exact formulation of the
+/// problem is the following.
+/**
+\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
+\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
+sup(u) \quad \forall u\in V \f]
+\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
+*/
+/// It means that the total demand must be greater or equal to the
+/// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or
+/// negative) and all the supplies have to be carried out from
+/// the supply nodes, but there could be demands that are not
+/// satisfied.
+GEQ,
+/// It is just an alias for the \c GEQ option.
+CARRY_SUPPLIES = GEQ,
+/// This option means that there are "<em>less or equal</em>"
+/// constraints in the defintion, i.e. the exact formulation of the
+/// problem is the following.
+/**
+\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
+\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \leq
+sup(u) \quad \forall u\in V \f]
+\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
+*/
+/// It means that the total demand must be less or equal to the
+/// total supply (i.e. \f$\sum_{u\in V} sup(u)\f$ must be zero or
+/// positive) and all the demands have to be satisfied, but there
+/// could be supplies that are not carried out from the supply
+/// nodes.
+LEQ,
+/// It is just an alias for the \c LEQ option.
+SATISFY_DEMANDS = LEQ
+};
 private:
 TEMPLATE_DIGRAPH_TYPEDEFS(GR);
 CostArcMap *_pcost;
 FlowNodeMap *_psupply;
 bool _pstsup;
 Node _psource, _ptarget;
 Flow _pstflow;
+ProblemType _ptype;
 // Result maps
 FlowMap *_flow_map;
 PotentialMap *_potential_map;
 bool _local_flow;
 public:
 /// \brief Constructor.
 ///
-/// Constructor.
+/// The constructor of the class.
 ///
 /// \param graph The digraph the algorithm runs on.
 NetworkSimplex(const GR& graph) :
 _graph(graph),
 _plower(NULL), _pupper(NULL), _pcost(NULL),
-_psupply(NULL), _pstsup(false),
+_psupply(NULL), _pstsup(false), _ptype(GEQ),
 _flow_map(NULL), _potential_map(NULL),
 _local_flow(false), _local_potential(false),
 _node_id(graph)
 {
 LEMON_ASSERT(std::numeric_limits<Flow>::is_integer &&
 ~NetworkSimplex() {
 if (_local_flow) delete _flow_map;
 if (_local_potential) delete _potential_map;
 }
+/// \name Parameters
+/// The parameters of the algorithm can be specified using these
+/// functions.
+/// @{
 /// \brief Set the lower bounds on the arcs.
 ///
 /// This function sets the lower bounds on the arcs.
 /// If neither this function nor \ref boundMaps() is used before
 /// calling \ref run(), the lower bounds will be set to zero
 _psource = s;
 _ptarget = t;
 _pstflow = k;
 return *this;
 }
+/// \brief Set the problem type.
+///
+/// This function sets the problem type for the algorithm.
+/// If it is not used before calling \ref run(), the \ref GEQ problem
+/// type will be used.
+///
+/// For more information see \ref ProblemType.
+///
+/// \return <tt>(*this)</tt>
+NetworkSimplex& problemType(ProblemType problem_type) {
+_ptype = problem_type;
+return *this;
+}
 /// \brief Set the flow map.
 ///
 /// This function sets the flow map.
 /// If it is not used before calling \ref run(), an instance will
 _local_potential = false;
 }
 _potential_map = &map;
 return *this;
 }
+/// @}
 /// \name Execution Control
 /// The algorithm can be executed using \ref run().
 /// @{
 /// \brief Run the algorithm.
 ///
 /// This function runs the algorithm.
-/// The paramters can be specified using \ref lowerMap(),
+/// The paramters can be specified using functions \ref lowerMap(),
 /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(),
-/// \ref costMap(), \ref supplyMap() and \ref stSupply()
+/// \ref costMap(), \ref supplyMap(), \ref stSupply(),
-/// functions. For example,
+/// \ref problemType(), \ref flowMap() and \ref potentialMap().
+/// For example,
 /// \code
 ///   NetworkSimplex<ListDigraph> ns(graph);
 ///   ns.boundMaps(lower, upper).costMap(cost)
 ///     .supplyMap(sup).run();
 /// \endcode
 }
 /// \brief Reset all the parameters that have been given before.
 ///
 /// This function resets all the paramaters that have been given
-/// using \ref lowerMap(), \ref upperMap(), \ref capacityMap(),
+/// before using functions \ref lowerMap(), \ref upperMap(),
-/// \ref boundMaps(), \ref costMap(), \ref supplyMap() and
+/// \ref capacityMap(), \ref boundMaps(), \ref costMap(),
-/// \ref stSupply() functions before.
+/// \ref supplyMap(), \ref stSupply(), \ref problemType(),
+/// \ref flowMap() and \ref potentialMap().
 ///
 /// 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.
 ///
 _plower = NULL;
 _pupper = NULL;
 _pcost = NULL;
 _psupply = NULL;
 _pstsup = false;
+_ptype = GEQ;
+if (_local_flow) delete _flow_map;
+if (_local_potential) delete _potential_map;
+_flow_map = NULL;
+_potential_map = NULL;
+_local_flow = false;
+_local_potential = false;
 return *this;
 }
 /// @}
 _last_succ.resize(all_node_num);
 _state.resize(all_arc_num);
 // Initialize node related data
 bool valid_supply = true;
+Flow sum_supply = 0;
 if (!_pstsup && !_psupply) {
 _pstsup = true;
 _psource = _ptarget = NodeIt(_graph);
 _pstflow = 0;
 }
 if (_psupply) {
-Flow sum = 0;
 int i = 0;
 for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 _node_id[n] = i;
 _supply[i] = (*_psupply)[n];
-sum += _supply[i];
+sum_supply += _supply[i];
 }
-valid_supply = (sum == 0);
+valid_supply = (_ptype == GEQ && sum_supply <= 0) ||
+(_ptype == LEQ && sum_supply >= 0);
 } else {
 int i = 0;
 for (NodeIt n(_graph); n != INVALID; ++n, ++i) {
 _node_id[n] = i;
 _supply[i] = 0;
 }
 _supply[_node_id[_psource]] =  _pstflow;
-_supply[_node_id[_ptarget]]   = -_pstflow;
+_supply[_node_id[_ptarget]] = -_pstflow;
 }
 if (!valid_supply) return false;
+// Infinite capacity value
+Flow inf_cap =
+std::numeric_limits<Flow>::has_infinity ?
+std::numeric_limits<Flow>::infinity() :
+std::numeric_limits<Flow>::max();
+// Initialize artifical cost
+Cost art_cost;
+if (std::numeric_limits<Cost>::is_exact) {
+art_cost = std::numeric_limits<Cost>::max() / 4 + 1;
+} else {
+art_cost = std::numeric_limits<Cost>::min();
+for (int i = 0; i != _arc_num; ++i) {
+if (_cost[i] > art_cost) art_cost = _cost[i];
+}
+art_cost = (art_cost + 1) * _node_num;
+}
+// Run Circulation to check if a feasible solution exists
+typedef ConstMap<Arc, Flow> ConstArcMap;
+FlowNodeMap *csup = NULL;
+bool local_csup = false;
+if (_psupply) {
+csup = _psupply;
+} else {
+csup = new FlowNodeMap(_graph, 0);
+(*csup)[_psource] =  _pstflow;
+(*csup)[_ptarget] = -_pstflow;
+local_csup = true;
+}
+bool circ_result = false;
+if (_ptype == GEQ || (_ptype == LEQ && sum_supply == 0)) {
+// GEQ problem type
+if (_plower) {
+if (_pupper) {
+Circulation<GR, FlowArcMap, FlowArcMap, FlowNodeMap>
+circ(_graph, *_plower, *_pupper, *csup);
+circ_result = circ.run();
+} else {
+Circulation<GR, FlowArcMap, ConstArcMap, FlowNodeMap>
+circ(_graph, *_plower, ConstArcMap(inf_cap), *csup);
+circ_result = circ.run();
+}
+} else {
+if (_pupper) {
+Circulation<GR, ConstArcMap, FlowArcMap, FlowNodeMap>
+circ(_graph, ConstArcMap(0), *_pupper, *csup);
+circ_result = circ.run();
+} else {
+Circulation<GR, ConstArcMap, ConstArcMap, FlowNodeMap>
+circ(_graph, ConstArcMap(0), ConstArcMap(inf_cap), *csup);
+circ_result = circ.run();
+}
+}
+} else {
+// LEQ problem type
+typedef ReverseDigraph<const GR> RevGraph;
+typedef NegMap<FlowNodeMap> NegNodeMap;
+RevGraph rgraph(_graph);
+NegNodeMap neg_csup(*csup);
+if (_plower) {
+if (_pupper) {
+Circulation<RevGraph, FlowArcMap, FlowArcMap, NegNodeMap>
+circ(rgraph, *_plower, *_pupper, neg_csup);
+circ_result = circ.run();
+} else {
+Circulation<RevGraph, FlowArcMap, ConstArcMap, NegNodeMap>
+circ(rgraph, *_plower, ConstArcMap(inf_cap), neg_csup);
+circ_result = circ.run();
+}
+} else {
+if (_pupper) {
+Circulation<RevGraph, ConstArcMap, FlowArcMap, NegNodeMap>
+circ(rgraph, ConstArcMap(0), *_pupper, neg_csup);
+circ_result = circ.run();
+} else {
+Circulation<RevGraph, ConstArcMap, ConstArcMap, NegNodeMap>
+circ(rgraph, ConstArcMap(0), ConstArcMap(inf_cap), neg_csup);
+circ_result = circ.run();
+}
+}
+}
+if (local_csup) delete csup;
+if (!circ_result) return false;
 // Set data for the artificial root node
 _root = _node_num;
 _parent[_root] = -1;
 _pred[_root] = -1;
 _thread[_root] = 0;
 _rev_thread[0] = _root;
 _succ_num[_root] = all_node_num;
 _last_succ[_root] = _root - 1;
-_supply[_root] = 0;
+_supply[_root] = -sum_supply;
-_pi[_root] = 0;
+if (sum_supply < 0) {
+_pi[_root] = -art_cost;
+} else {
+_pi[_root] = art_cost;
+}
 // Store the arcs in a mixed order
 int k = std::max(int(sqrt(_arc_num)), 10);
 int i = 0;
 for (ArcIt e(_graph); e != INVALID; ++e) {
 _arc_ref[i] = e;
 if ((i += k) >= _arc_num) i = (i % k) + 1;
 }
 // Initialize arc maps
-Flow inf_cap =
-std::numeric_limits<Flow>::has_infinity ?
-std::numeric_limits<Flow>::infinity() :
-std::numeric_limits<Flow>::max();
 if (_pupper && _pcost) {
 for (int i = 0; i != _arc_num; ++i) {
 Arc e = _arc_ref[i];
 _source[i] = _node_id[_graph.source(e)];
 _target[i] = _node_id[_graph.target(e)];
 for (int i = 0; i != _arc_num; ++i)
 _cost[i] = 1;
 }
 }
-// Initialize artifical cost
-Cost art_cost;
-if (std::numeric_limits<Cost>::is_exact) {
-art_cost = std::numeric_limits<Cost>::max() / 4 + 1;
-} else {
-art_cost = std::numeric_limits<Cost>::min();
-for (int i = 0; i != _arc_num; ++i) {
-if (_cost[i] > art_cost) art_cost = _cost[i];
-}
-art_cost = (art_cost + 1) * _node_num;
-}
 // Remove non-zero lower bounds
 if (_plower) {
 for (int i = 0; i != _arc_num; ++i) {
 Flow c = (*_plower)[_arc_ref[i]];
 if (c != 0) {
 _parent[u] = _root;
 _pred[u] = e;
 _cost[e] = art_cost;
 _cap[e] = inf_cap;
 _state[e] = STATE_TREE;
-if (_supply[u] >= 0) {
+if (_supply[u] > 0 || (_supply[u] == 0 && sum_supply <= 0)) {
 _flow[e] = _supply[u];
 _forward[u] = true;
-_pi[u] = -art_cost;
+_pi[u] = -art_cost + _pi[_root];
 } else {
 _flow[e] = -_supply[u];
 _forward[u] = false;
-_pi[u] = art_cost;
+_pi[u] = art_cost + _pi[_root];
 }
 }
 return true;
 }
 updateTreeStructure();
 updatePotential();
 }
 }
-// Check if the flow amount equals zero on all the artificial arcs
-for (int e = _arc_num; e != _arc_num + _node_num; ++e) {
-if (_flow[e] > 0) return false;
-}
 // Copy flow values to _flow_map
 if (_plower) {
 for (int i = 0; i != _arc_num; ++i) {
 Arc e = _arc_ref[i];
 _flow_map->set(e, (*_plower)[e] + _flow[i]);

changeset 611	85cb3aa71cce
parent 608	6ac5d9ae1d3d
child 612	0c8e5c688440
child 613	b1811c363299