LEMON/LEMON-official Changeset - r358:7f26c4b32651

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Changeset - r358:7f26c4b32651

« 357:2f64c4

359:85820a »

r358:7f26c4b32651

Tue, 28 Oct 2008 23:10:27

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Minor doc improvements related to Suurballe (#47)

0 2 0

default

2 files changed with 87 insertions and 85 deletions:

lemon/suurballe.h

test/suurballe_test.cc

↑ Collapse diff ↑

lemon/suurballe.h

Show inline comments

@@ -24,82 +24,84 @@
 		///\brief An algorithm for finding arc-disjoint paths between two
 		/// nodes having minimum total length.
 		#include <vector>
 		#include <lemon/bin_heap.h>
 		#include <lemon/path.h>
 		namespace lemon {
 		  /// \addtogroup shortest_path
 		  /// @{
 		  /// \brief Implementation of an algorithm for finding arc-disjoint
 		  /// paths between two nodes having minimum total length.
 		  /// \brief Algorithm for finding arc-disjoint paths between two nodes
 		  /// having minimum total length.
 		  ///
 		  /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
 		  /// finding arc-disjoint paths having minimum total length (cost)
 		  /// from a given source node to a given target node in a directed
 		  /// digraph.
 		  /// from a given source node to a given target node in a digraph.
 		  ///
 		  /// In fact, this implementation is the specialization of the
 		  /// \ref CapacityScaling "successive shortest path" algorithm.
 		  ///
-		  /// \tparam Digraph The directed digraph type the algorithm runs on.
 		  /// \tparam Digraph The digraph type the algorithm runs on.
 		  /// The default value is \c ListDigraph.
 		  /// \tparam LengthMap The type of the length (cost) map.
 		  /// The default value is <tt>Digraph::ArcMap<int></tt>.
 		  ///
 		  /// \warning Length values should be \e non-negative \e integers.
 		  ///
 		  /// \note For finding node-disjoint paths this algorithm can be used
 		  /// with \ref SplitDigraphAdaptor.
 		  ///
 		  /// \author Attila Bernath and Peter Kovacs
 		  template < typename Digraph,
 		#ifdef DOXYGEN
 		  template <typename Digraph, typename LengthMap>
 		#else
 		  template < typename Digraph = ListDigraph,
 		             typename LengthMap = typename Digraph::template ArcMap<int> >
 		#endif
 		  class Suurballe
+		  {
 		    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		    typedef typename LengthMap::Value Length;
 		    typedef ConstMap<Arc, int> ConstArcMap;
 		    typedef typename Digraph::template NodeMap<Arc> PredMap;
 		  public:
 		    /// The type of the flow map.
 		    typedef typename Digraph::template ArcMap<int> FlowMap;
 		    /// The type of the potential map.
 		    typedef typename Digraph::template NodeMap<Length> PotentialMap;
 		    /// The type of the path structures.
 		    typedef SimplePath<Digraph> Path;
 		  private:
-		    /// \brief Special implementation of the \ref Dijkstra algorithm
 		    /// \brief Special implementation of the Dijkstra algorithm
 		    /// for finding shortest paths in the residual network.
 		    ///
 		    /// \ref ResidualDijkstra is a special implementation of the
 		    /// \ref Dijkstra algorithm for finding shortest paths in the
 		    /// residual network of the digraph with respect to the reduced arc
 		    /// lengths and modifying the node potentials according to the
 		    /// distance of the nodes.
 		    class ResidualDijkstra
+		    {
 		      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
 		      typedef BinHeap<Length, HeapCrossRef> Heap;
 		    private:
-		      // The directed digraph the algorithm runs on
 		      // The digraph the algorithm runs on
 		      const Digraph &_graph;
 		      // The main maps
 		      const FlowMap &_flow;
 		      const LengthMap &_length;
 		      PotentialMap &_potential;
 		      // The distance map
 		      PotentialMap _dist;
 		      // The pred arc map
 		      PredMap &_pred;
 		      // The processed (i.e. permanently labeled) nodes
@@ -111,99 +113,99 @@
 		    public:
 		      /// Constructor.
 		      ResidualDijkstra( const Digraph &digraph,
 		                        const FlowMap &flow,
 		                        const LengthMap &length,
 		                        PotentialMap &potential,
 		                        PredMap &pred,
 		                        Node s, Node t ) :
 		        _graph(digraph), _flow(flow), _length(length), _potential(potential),
 		        _dist(digraph), _pred(pred), _s(s), _t(t) {}
-		      /// \brief Runs the algorithm. Returns \c true if a path is found
+		      /// \brief Run the algorithm. It returns \c true if a path is found
 		      /// from the source node to the target node.
 		      bool run() {
 		        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
 		        Heap heap(heap_cross_ref);
 		        heap.push(_s, 0);
 		        _pred[_s] = INVALID;
 		        _proc_nodes.clear();
-		        // Processing nodes
+		        // Process nodes
 		        while (!heap.empty() && heap.top() != _t) {
 		          Node u = heap.top(), v;
 		          Length d = heap.prio() + _potential[u], nd;
 		          _dist[u] = heap.prio();
 		          heap.pop();
 		          _proc_nodes.push_back(u);
-		          // Traversing outgoing arcs
+		          // Traverse outgoing arcs
 		          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
 		            if (_flow[e] == 0) {
 		              v = _graph.target(e);
 		              switch(heap.state(v)) {
 		              case Heap::PRE_HEAP:
 		                heap.push(v, d + _length[e] - _potential[v]);
 		                _pred[v] = e;
 		                break;
 		              case Heap::IN_HEAP:
 		                nd = d + _length[e] - _potential[v];
 		                if (nd < heap[v]) {
 		                  heap.decrease(v, nd);
 		                  _pred[v] = e;
+		                }
 		                break;
 		              case Heap::POST_HEAP:
 		                break;
+		              }
+		            }
+		          }
-		          // Traversing incoming arcs
+		          // Traverse incoming arcs
 		          for (InArcIt e(_graph, u); e != INVALID; ++e) {
 		            if (_flow[e] == 1) {
 		              v = _graph.source(e);
 		              switch(heap.state(v)) {
 		              case Heap::PRE_HEAP:
 		                heap.push(v, d - _length[e] - _potential[v]);
 		                _pred[v] = e;
 		                break;
 		              case Heap::IN_HEAP:
 		                nd = d - _length[e] - _potential[v];
 		                if (nd < heap[v]) {
 		                  heap.decrease(v, nd);
 		                  _pred[v] = e;
+		                }
 		                break;
 		              case Heap::POST_HEAP:
 		                break;
+		              }
+		            }
+		          }
+		        }
 		        if (heap.empty()) return false;
-		        // Updating potentials of processed nodes
+		        // Update potentials of processed nodes
 		        Length t_dist = heap.prio();
 		        for (int i = 0; i < int(_proc_nodes.size()); ++i)
 		          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
 		        return true;
+		      }
 		    }; //class ResidualDijkstra
 		  private:
-		    // The directed digraph the algorithm runs on
 		    // The digraph the algorithm runs on
 		    const Digraph &_graph;
 		    // The length map
 		    const LengthMap &_length;
 		    // Arc map of the current flow
 		    FlowMap *_flow;
 		    bool _local_flow;
 		    // Node map of the current potentials
 		    PotentialMap *_potential;
 		    bool _local_potential;
 		    // The source node
@@ -218,281 +220,281 @@
 		    // The pred arc map
 		    PredMap _pred;
 		    // Implementation of the Dijkstra algorithm for finding augmenting
 		    // shortest paths in the residual network
 		    ResidualDijkstra *_dijkstra;
 		  public:
 		    /// \brief Constructor.
 		    ///
 		    /// Constructor.
 		    ///
-		    /// \param digraph The directed digraph the algorithm runs on.
 		    /// \param digraph The digraph the algorithm runs on.
 		    /// \param length The length (cost) values of the arcs.
 		    /// \param s The source node.
 		    /// \param t The target node.
 		    Suurballe( const Digraph &digraph,
 		               const LengthMap &length,
 		               Node s, Node t ) :
 		      _graph(digraph), _length(length), _flow(0), _local_flow(false),
 		      _potential(0), _local_potential(false), _source(s), _target(t),
 		      _pred(digraph) {}
 		    /// Destructor.
 		    ~Suurballe() {
 		      if (_local_flow) delete _flow;
 		      if (_local_potential) delete _potential;
 		      delete _dijkstra;
+		    }
-		    /// \brief Sets the flow map.
+		    /// \brief Set the flow map.
 		    ///
-		    /// Sets the flow map.
+		    /// This function sets the flow map.
 		    ///
 		    /// The found flow contains only 0 and 1 values. It is the union of
 		    /// the found arc-disjoint paths.
 		    ///
 		    /// \return \c (*this)
 		    Suurballe& flowMap(FlowMap &map) {
 		      if (_local_flow) {
 		        delete _flow;
 		        _local_flow = false;
+		      }
 		      _flow = &map;
 		      return *this;
+		    }
-		    /// \brief Sets the potential map.
+		    /// \brief Set the potential map.
 		    ///
-		    /// Sets the potential map.
+		    /// This function sets the potential map.
 		    ///
 		    /// The potentials provide the dual solution of the underlying
 		    /// minimum cost flow problem.
 		    ///
 		    /// \return \c (*this)
 		    Suurballe& potentialMap(PotentialMap &map) {
 		      if (_local_potential) {
 		        delete _potential;
 		        _local_potential = false;
+		      }
 		      _potential = &map;
 		      return *this;
+		    }
 		    /// \name Execution control
 		    /// The simplest way to execute the algorithm is to call the run()
 		    /// function.
 		    /// \n
 		    /// If you only need the flow that is the union of the found
 		    /// arc-disjoint paths, you may call init() and findFlow().
 		    /// @{
-		    /// \brief Runs the algorithm.
+		    /// \brief Run the algorithm.
 		    ///
-		    /// Runs the algorithm.
+		    /// This function runs the algorithm.
 		    ///
 		    /// \param k The number of paths to be found.
 		    ///
 		    /// \return \c k if there are at least \c k arc-disjoint paths
 		    /// from \c s to \c t. Otherwise it returns the number of
 		    /// \return \c k if there are at least \c k arc-disjoint paths from
 		    /// \c s to \c t in the digraph. Otherwise it returns the number of
 		    /// arc-disjoint paths found.
 		    ///
 		    /// \note Apart from the return value, <tt>s.run(k)</tt> is just a
 		    /// shortcut of the following code.
 		    /// \code
 		    ///   s.init();
 		    ///   s.findFlow(k);
 		    ///   s.findPaths();
 		    /// \endcode
 		    int run(int k = 2) {
 		      init();
 		      findFlow(k);
 		      findPaths();
 		      return _path_num;
+		    }
-		    /// \brief Initializes the algorithm.
+		    /// \brief Initialize the algorithm.
 		    ///
-		    /// Initializes the algorithm.
+		    /// This function initializes the algorithm.
 		    void init() {
-		      // Initializing maps
+		      // Initialize maps
 		      if (!_flow) {
 		        _flow = new FlowMap(_graph);
 		        _local_flow = true;
+		      }
 		      if (!_potential) {
 		        _potential = new PotentialMap(_graph);
 		        _local_potential = true;
+		      }
 		      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
 		      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
 		      _dijkstra = new ResidualDijkstra( _graph, *_flow, _length,
 		                                        *_potential, _pred,
 		                                        _source, _target );
+		    }
-		    /// \brief Executes the successive shortest path algorithm to find
+		    /// \brief Execute the successive shortest path algorithm to find
 		    /// an optimal flow.
 		    ///
 		    /// Executes the successive shortest path algorithm to find a
 		    /// minimum cost flow, which is the union of \c k or less
 		    /// This function executes the successive shortest path algorithm to
 		    /// find a minimum cost flow, which is the union of \c k or less
 		    /// arc-disjoint paths.
 		    ///
 		    /// \return \c k if there are at least \c k arc-disjoint paths
 		    /// from \c s to \c t. Otherwise it returns the number of
 		    /// \return \c k if there are at least \c k arc-disjoint paths from
 		    /// \c s to \c t in the digraph. Otherwise it returns the number of
 		    /// arc-disjoint paths found.
 		    ///
 		    /// \pre \ref init() must be called before using this function.
 		    int findFlow(int k = 2) {
-		      // Finding shortest paths
+		      // Find shortest paths
 		      _path_num = 0;
 		      while (_path_num < k) {
-		        // Running Dijkstra
+		        // Run Dijkstra
 		        if (!_dijkstra->run()) break;
 		        ++_path_num;
-		        // Setting the flow along the found shortest path
+		        // Set the flow along the found shortest path
 		        Node u = _target;
 		        Arc e;
 		        while ((e = _pred[u]) != INVALID) {
 		          if (u == _graph.target(e)) {
 		            (*_flow)[e] = 1;
 		            u = _graph.source(e);
 		          } else {
 		            (*_flow)[e] = 0;
 		            u = _graph.target(e);
+		          }
+		        }
+		      }
 		      return _path_num;
+		    }
-		    /// \brief Computes the paths from the flow.
+		    /// \brief Compute the paths from the flow.
 		    ///
-		    /// Computes the paths from the flow.
+		    /// This function computes the paths from the flow.
 		    ///
 		    /// \pre \ref init() and \ref findFlow() must be called before using
 		    /// this function.
 		    void findPaths() {
 		      // Creating the residual flow map (the union of the paths not
 		      // found so far)
 		      // Create the residual flow map (the union of the paths not found
 		      // so far)
 		      FlowMap res_flow(_graph);
 		      for(ArcIt a(_graph);a!=INVALID;++a) res_flow[a]=(*_flow)[a];
+		      for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
 		      paths.clear();
 		      paths.resize(_path_num);
 		      for (int i = 0; i < _path_num; ++i) {
 		        Node n = _source;
 		        while (n != _target) {
 		          OutArcIt e(_graph, n);
 		          for ( ; res_flow[e] == 0; ++e) ;
 		          n = _graph.target(e);
 		          paths[i].addBack(e);
 		          res_flow[e] = 0;
+		        }
+		      }
+		    }
 		    /// @}
 		    /// \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 The algorithm should be executed before using them.
 		    /// @{
-		    /// \brief Returns a const reference to the arc map storing the
+		    /// \brief Return a const reference to the arc map storing the
 		    /// found flow.
 		    ///
 		    /// Returns a const reference to the arc map storing the flow that
 		    /// is the union of the found arc-disjoint paths.
 		    /// This function returns a const reference to the arc map storing
 		    /// the flow that is the union of the found arc-disjoint paths.
 		    ///
 		    /// \pre \ref run() or findFlow() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findFlow() must be called before using
 		    /// this function.
 		    const FlowMap& flowMap() const {
 		      return *_flow;
+		    }
-		    /// \brief Returns a const reference to the node map storing the
+		    /// \brief Return a const reference to the node map storing the
 		    /// found potentials (the dual solution).
 		    ///
 		    /// Returns a const reference to the node map storing the found
 		    /// potentials that provide the dual solution of the underlying
-		    /// minimum cost flow problem.
+		    /// This function returns a const reference to the node map storing
 		    /// the found potentials that provide the dual solution of the
 		    /// underlying minimum cost flow problem.
 		    ///
 		    /// \pre \ref run() or findFlow() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findFlow() must be called before using
 		    /// this function.
 		    const PotentialMap& potentialMap() const {
 		      return *_potential;
+		    }
-		    /// \brief Returns the flow on the given arc.
+		    /// \brief Return the flow on the given arc.
 		    ///
-		    /// Returns the flow on the given arc.
+		    /// This function returns the flow on the given arc.
 		    /// It is \c 1 if the arc is involved in one of the found paths,
 		    /// otherwise it is \c 0.
 		    ///
 		    /// \pre \ref run() or findFlow() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findFlow() must be called before using
 		    /// this function.
 		    int flow(const Arc& arc) const {
 		      return (*_flow)[arc];
+		    }
-		    /// \brief Returns the potential of the given node.
+		    /// \brief Return the potential of the given node.
 		    ///
-		    /// Returns the potential of the given node.
+		    /// This function returns the potential of the given node.
 		    ///
 		    /// \pre \ref run() or findFlow() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findFlow() must be called before using
 		    /// this function.
 		    Length potential(const Node& node) const {
 		      return (*_potential)[node];
+		    }
-		    /// \brief Returns the total length (cost) of the found paths (flow).
+		    /// \brief Return the total length (cost) of the found paths (flow).
 		    ///
 		    /// Returns the total length (cost) of the found paths (flow).
 		    /// The complexity of the function is \f$ O(e) \f$.
 		    /// This function returns the total length (cost) of the found paths
 		    /// (flow). The complexity of the function is \f$ O(e) \f$.
 		    ///
 		    /// \pre \ref run() or findFlow() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findFlow() must be called before using
 		    /// this function.
 		    Length totalLength() const {
 		      Length c = 0;
 		      for (ArcIt e(_graph); e != INVALID; ++e)
 		        c += (*_flow)[e] * _length[e];
 		      return c;
+		    }
-		    /// \brief Returns the number of the found paths.
+		    /// \brief Return the number of the found paths.
 		    ///
-		    /// Returns the number of the found paths.
+		    /// This function returns the number of the found paths.
 		    ///
 		    /// \pre \ref run() or findFlow() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findFlow() must be called before using
 		    /// this function.
 		    int pathNum() const {
 		      return _path_num;
+		    }
-		    /// \brief Returns a const reference to the specified path.
+		    /// \brief Return a const reference to the specified path.
 		    ///
-		    /// Returns a const reference to the specified path.
+		    /// This function returns a const reference to the specified path.
 		    ///
 		    /// \param i The function returns the \c i-th path.
 		    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
 		    ///
 		    /// \pre \ref run() or findPaths() must be called before using this
 		    /// function.
 		    /// \pre \ref run() or \ref findPaths() must be called before using
 		    /// this function.
 		    Path path(int i) const {
 		      return paths[i];
+		    }
 		    /// @}
 		  }; //class Suurballe
 		  ///@}
 		} //namespace lemon

test/suurballe_test.cc

Show inline comments

@@ -19,138 +19,138 @@
 		#include <iostream>
 		#include <fstream>
 		#include <lemon/list_graph.h>
 		#include <lemon/lgf_reader.h>
 		#include <lemon/path.h>
 		#include <lemon/suurballe.h>
 		#include "test_tools.h"
 		using namespace lemon;
-		// Checks the feasibility of the flow
+		// Check the feasibility of the flow
 		template <typename Digraph, typename FlowMap>
 		bool checkFlow( const Digraph& gr, const FlowMap& flow,
 		                typename Digraph::Node s, typename Digraph::Node t,
 		                int value )
+		{
 		  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		  for (ArcIt e(gr); e != INVALID; ++e)
 		    if (!(flow[e] == 0 || flow[e] == 1)) return false;
 		  for (NodeIt n(gr); n != INVALID; ++n) {
 		    int sum = 0;
 		    for (OutArcIt e(gr, n); e != INVALID; ++e)
 		      sum += flow[e];
 		    for (InArcIt e(gr, n); e != INVALID; ++e)
 		      sum -= flow[e];
 		    if (n == s && sum != value) return false;
 		    if (n == t && sum != -value) return false;
 		    if (n != s && n != t && sum != 0) return false;
+		  }
 		  return true;
+		}
-		// Checks the optimalitiy of the flow
+		// Check the optimalitiy of the flow
 		template < typename Digraph, typename CostMap,
 		           typename FlowMap, typename PotentialMap >
 		bool checkOptimality( const Digraph& gr, const CostMap& cost,
 		                      const FlowMap& flow, const PotentialMap& pi )
+		{
-		  // Checking the Complementary Slackness optimality condition
+		  // Check the "Complementary Slackness" optimality condition
 		  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		  bool opt = true;
 		  for (ArcIt e(gr); e != INVALID; ++e) {
 		    typename CostMap::Value red_cost =
 		      cost[e] + pi[gr.source(e)] - pi[gr.target(e)];
 		    opt = (flow[e] == 0 && red_cost >= 0) ||
 		          (flow[e] == 1 && red_cost <= 0);
 		    if (!opt) break;
+		  }
 		  return opt;
+		}
 		// Checks a path
 		template < typename Digraph, typename Path >
 		// Check a path
 		template <typename Digraph, typename Path>
 		bool checkPath( const Digraph& gr, const Path& path,
 		                typename Digraph::Node s, typename Digraph::Node t)
+		{
-		  // Checking the Complementary Slackness optimality condition
+		  // Check the "Complementary Slackness" optimality condition
 		  TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
 		  Node n = s;
 		  for (int i = 0; i < path.length(); ++i) {
 		    if (gr.source(path.nth(i)) != n) return false;
 		    n = gr.target(path.nth(i));
+		  }
 		  return n == t;
+		}
 		int main()
+		{
 		  DIGRAPH_TYPEDEFS(ListDigraph);
-		  // Reading the test digraph
+		  // Read the test digraph
 		  ListDigraph digraph;
 		  ListDigraph::ArcMap<int> length(digraph);
 		  Node source, target;
 		  std::string fname;
 		  if(getenv("srcdir"))
 		    fname = std::string(getenv("srcdir"));
 		  else fname = ".";
 		  fname += "/test/min_cost_flow_test.lgf";
 		  std::ifstream input(fname.c_str());
 		  check(input, "Input file '" << fname << "' not found");
 		  DigraphReader<ListDigraph>(digraph, input).
 		    arcMap("cost", length).
 		    node("source", source).
 		    node("target", target).
 		    run();
 		  input.close();
-		  // Finding 2 paths
+		  // Find 2 paths
+		  {
 		    Suurballe<ListDigraph> suurballe(digraph, length, source, target);
 		    check(suurballe.run(2) == 2, "Wrong number of paths");
 		    check(checkFlow(digraph, suurballe.flowMap(), source, target, 2),
 		          "The flow is not feasible");
 		    check(suurballe.totalLength() == 510, "The flow is not optimal");
 		    check(checkOptimality(digraph, length, suurballe.flowMap(),
 		                          suurballe.potentialMap()),
 		          "Wrong potentials");
 		    for (int i = 0; i < suurballe.pathNum(); ++i)
 		      check(checkPath(digraph, suurballe.path(i), source, target),
 		            "Wrong path");
+		  }
-		  // Finding 3 paths
+		  // Find 3 paths
+		  {
 		    Suurballe<ListDigraph> suurballe(digraph, length, source, target);
 		    check(suurballe.run(3) == 3, "Wrong number of paths");
 		    check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),
 		          "The flow is not feasible");
 		    check(suurballe.totalLength() == 1040, "The flow is not optimal");
 		    check(checkOptimality(digraph, length, suurballe.flowMap(),
 		                          suurballe.potentialMap()),
 		          "Wrong potentials");
 		    for (int i = 0; i < suurballe.pathNum(); ++i)
 		      check(checkPath(digraph, suurballe.path(i), source, target),
 		            "Wrong path");
+		  }
-		  // Finding 5 paths (only 3 can be found)
+		  // Find 5 paths (only 3 can be found)
+		  {
 		    Suurballe<ListDigraph> suurballe(digraph, length, source, target);
 		    check(suurballe.run(5) == 3, "Wrong number of paths");
 		    check(checkFlow(digraph, suurballe.flowMap(), source, target, 3),
 		          "The flow is not feasible");
 		    check(suurballe.totalLength() == 1040, "The flow is not optimal");
 		    check(checkOptimality(digraph, length, suurballe.flowMap(),
 		                          suurballe.potentialMap()),
 		          "Wrong potentials");
 		    for (int i = 0; i < suurballe.pathNum(); ++i)
 		      check(checkPath(digraph, suurballe.path(i), source, target),
 		            "Wrong path");

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