# HG changeset patch
# User Alpar Juttner <alpar@cs.elte.hu>
# Date 2008-10-28 19:39:53
# Node ID 2f64c4a692a87056623c6fffafd76432806ee593
# Parent  956a29f3088780b83149718f6ae7756cb187d5fe

Port Suurballe algorithm from svn -r3512

diff --git a/lemon/Makefile.am b/lemon/Makefile.am
--- a/lemon/Makefile.am
+++ b/lemon/Makefile.am
@@ -40,6 +40,7 @@
 	lemon/path.h \
         lemon/random.h \
 	lemon/smart_graph.h \
+	lemon/suurballe.h \
         lemon/time_measure.h \
         lemon/tolerance.h \
 	lemon/unionfind.h
diff --git a/lemon/suurballe.h b/lemon/suurballe.h
new file mode 100644
--- /dev/null
+++ b/lemon/suurballe.h
@@ -0,0 +1,499 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_SUURBALLE_H
+#define LEMON_SUURBALLE_H
+
+///\ingroup shortest_path
+///\file
+///\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.
+  ///
+  /// \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.
+  ///
+  /// 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 LengthMap The type of the length (cost) map.
+  ///
+  /// \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, 
+             typename LengthMap = typename Digraph::template ArcMap<int> >
+  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
+    /// 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
+      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
+      std::vector<Node> _proc_nodes;
+      
+      Node _s;
+      Node _t;
+
+    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
+      /// 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
+        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
+          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
+          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
+        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
+    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
+    Node _source;
+    // The target node
+    Node _target;
+
+    // Container to store the found paths
+    std::vector< SimplePath<Digraph> > paths;
+    int _path_num;
+
+    // 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 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.
+    ///
+    /// 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.
+    ///
+    /// 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.
+    ///
+    /// 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
+    /// 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.
+    ///
+    /// Initializes the algorithm.
+    void init() {
+      // Initializing 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
+    /// an optimal flow.
+    ///
+    /// 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
+    /// arc-disjoint paths found.
+    ///
+    /// \pre \ref init() must be called before using this function.
+    int findFlow(int k = 2) {
+      // Finding shortest paths
+      _path_num = 0;
+      while (_path_num < k) {
+        // Running Dijkstra
+        if (!_dijkstra->run()) break;
+        ++_path_num;
+
+        // Setting 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.
+    ///
+    /// 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)
+      FlowMap res_flow(_graph);
+      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
+    /// functions.
+    /// \n The algorithm should be executed before using them.
+
+    /// @{
+
+    /// \brief Returns 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.
+    ///
+    /// \pre \ref run() or 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
+    /// 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.
+    ///
+    /// \pre \ref run() or findFlow() must be called before using this
+    /// function.
+    const PotentialMap& potentialMap() const {
+      return *_potential;
+    }
+
+    /// \brief Returns the flow on the given arc.
+    ///
+    /// 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.
+    int flow(const Arc& arc) const {
+      return (*_flow)[arc];
+    }
+
+    /// \brief Returns the potential of the given node.
+    ///
+    /// Returns the potential of the given node.
+    ///
+    /// \pre \ref run() or 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).
+    ///
+    /// 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.
+    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.
+    ///
+    /// Returns the number of the found paths.
+    ///
+    /// \pre \ref run() or findFlow() must be called before using this
+    /// function.
+    int pathNum() const {
+      return _path_num;
+    }
+
+    /// \brief Returns a const reference to the specified path.
+    ///
+    /// 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.
+    Path path(int i) const {
+      return paths[i];
+    }
+
+    /// @}
+
+  }; //class Suurballe
+
+  ///@}
+
+} //namespace lemon
+
+#endif //LEMON_SUURBALLE_H
diff --git a/test/Makefile.am b/test/Makefile.am
--- a/test/Makefile.am
+++ b/test/Makefile.am
@@ -1,5 +1,6 @@
 EXTRA_DIST += \
-	test/CMakeLists.txt
+	test/CMakeLists.txt \
+        test/min_cost_flow_test.lgf
 
 noinst_HEADERS += \
 	test/graph_test.h \
@@ -22,6 +23,7 @@
 	test/max_matching_test \
         test/random_test \
         test/path_test \
+        test/suurballe_test \
         test/test_tools_fail \
         test/test_tools_pass \
         test/time_measure_test \
@@ -45,6 +47,7 @@
 test_maps_test_SOURCES = test/maps_test.cc
 test_max_matching_test_SOURCES = test/max_matching_test.cc
 test_path_test_SOURCES = test/path_test.cc
+test_suurballe_test_SOURCES = test/suurballe_test.cc
 test_random_test_SOURCES = test/random_test.cc
 test_test_tools_fail_SOURCES = test/test_tools_fail.cc
 test_test_tools_pass_SOURCES = test/test_tools_pass.cc
diff --git a/test/min_cost_flow_test.lgf b/test/min_cost_flow_test.lgf
new file mode 100644
--- /dev/null
+++ b/test/min_cost_flow_test.lgf
@@ -0,0 +1,44 @@
+@nodes
+label	supply1	supply2	supply3
+1	0	20	27	
+2	0	-4	0		
+3	0	0	0	
+4	0	0	0	
+5	0	9	0	
+6	0	-6	0	
+7	0	0	0	
+8	0	0	0	
+9	0	3	0	
+10	0	-2	0	
+11	0	0	0		
+12	0	-20	-27	
+               
+@arcs
+		cost	capacity	lower1	lower2
+1	2	70	11		0	8
+1	3	150	3		0	1
+1	4	80	15		0	2
+2	8	80	12		0	0
+3	5	140	5		0	3
+4	6	60	10		0	1
+4	7	80	2		0	0
+4	8	110	3		0	0
+5	7	60	14		0	0
+5	11	120	12		0	0
+6	3	0	3		0	0
+6	9	140	4		0	0
+6	10	90	8		0	0
+7	1	30	5		0	0
+8	12	60	16		0	4
+9	12	50	6		0	0
+10	12	70	13		0	5
+10	2	100	7		0	0
+10	7	60	10		0	0
+11	10	20	14		0	6
+12	11	30	10		0	0
+
+@attributes
+source	1
+target	12
+
+@end
diff --git a/test/suurballe_test.cc b/test/suurballe_test.cc
new file mode 100644
--- /dev/null
+++ b/test/suurballe_test.cc
@@ -0,0 +1,160 @@
+/* -*- C++ -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library
+ *
+ * Copyright (C) 2003-2008
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#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
+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
+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
+  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 >
+bool checkPath( const Digraph& gr, const Path& path,
+                typename Digraph::Node s, typename Digraph::Node t)
+{
+  // Checking 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
+  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
+  {
+    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
+  {
+    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)
+  {
+    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");
+  }
+
+  return 0;
+}