# HG changeset patch
# User Peter Kovacs <kpeter@inf.elte.hu>
# Date 2009-10-16 01:06:16
# Node ID ec0b1b423b8b100883ab1ef766204eb978363c80
# Parent  30c77d1c0cba549cb3f5309642d576cfa9c16534

Rework and improve Suurballe (#323)

 - Improve the implementation: use a specific, faster variant of
   residual Dijkstra for the first search.
 - Some reorganizatiopn to make the code simpler.
 - Small doc improvements.

diff --git a/lemon/suurballe.h b/lemon/suurballe.h
--- a/lemon/suurballe.h
+++ b/lemon/suurballe.h
@@ -46,7 +46,7 @@
   /// Note that this problem is a special case of the \ref min_cost_flow
   /// "minimum cost flow problem". This implementation is actually an
   /// efficient specialized version of the \ref CapacityScaling
-  /// "Successive Shortest Path" algorithm directly for this problem.
+  /// "successive shortest path" algorithm directly for this problem.
   /// Therefore this class provides query functions for flow values and
   /// node potentials (the dual solution) just like the minimum cost flow
   /// algorithms.
@@ -57,7 +57,7 @@
   ///
   /// \warning Length values should be \e non-negative.
   ///
-  /// \note For finding node-disjoint paths this algorithm can be used
+  /// \note For finding \e node-disjoint paths, this algorithm can be used
   /// along with the \ref SplitNodes adaptor.
 #ifdef DOXYGEN
   template <typename GR, typename LEN>
@@ -109,39 +109,36 @@
 
     private:
 
-      // The digraph the algorithm runs on
       const Digraph &_graph;
-
-      // The main maps
+      const LengthMap &_length;
       const FlowMap &_flow;
-      const LengthMap &_length;
-      PotentialMap &_potential;
-
-      // The distance map
-      PotentialMap _dist;
-      // The pred arc map
+      PotentialMap &_pi;
       PredMap &_pred;
-      // The processed (i.e. permanently labeled) nodes
-      std::vector<Node> _proc_nodes;
-
       Node _s;
       Node _t;
+      
+      PotentialMap _dist;
+      std::vector<Node> _proc_nodes;
 
     public:
 
-      /// Constructor.
-      ResidualDijkstra( const Digraph &graph,
-                        const FlowMap &flow,
-                        const LengthMap &length,
-                        PotentialMap &potential,
-                        PredMap &pred,
-                        Node s, Node t ) :
-        _graph(graph), _flow(flow), _length(length), _potential(potential),
-        _dist(graph), _pred(pred), _s(s), _t(t) {}
+      // Constructor
+      ResidualDijkstra(Suurballe &srb) :
+        _graph(srb._graph), _length(srb._length),
+        _flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred), 
+        _s(srb._s), _t(srb._t), _dist(_graph) {}
+        
+      // Run the algorithm and return true if a path is found
+      // from the source node to the target node.
+      bool run(int cnt) {
+        return cnt == 0 ? startFirst() : start();
+      }
 
-      /// \brief Run the algorithm. It returns \c true if a path is found
-      /// from the source node to the target node.
-      bool run() {
+    private:
+    
+      // Execute the algorithm for the first time (the flow and potential
+      // functions have to be identically zero).
+      bool startFirst() {
         HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
         Heap heap(heap_cross_ref);
         heap.push(_s, 0);
@@ -151,29 +148,74 @@
         // Process nodes
         while (!heap.empty() && heap.top() != _t) {
           Node u = heap.top(), v;
-          Length d = heap.prio() + _potential[u], nd;
+          Length d = heap.prio(), dn;
           _dist[u] = heap.prio();
+          _proc_nodes.push_back(u);
           heap.pop();
+
+          // Traverse outgoing arcs
+          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
+            v = _graph.target(e);
+            switch(heap.state(v)) {
+              case Heap::PRE_HEAP:
+                heap.push(v, d + _length[e]);
+                _pred[v] = e;
+                break;
+              case Heap::IN_HEAP:
+                dn = d + _length[e];
+                if (dn < heap[v]) {
+                  heap.decrease(v, dn);
+                  _pred[v] = e;
+                }
+                break;
+              case Heap::POST_HEAP:
+                break;
+            }
+          }
+        }
+        if (heap.empty()) return false;
+
+        // Update potentials of processed nodes
+        Length t_dist = heap.prio();
+        for (int i = 0; i < int(_proc_nodes.size()); ++i)
+          _pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist;
+        return true;
+      }
+
+      // Execute the algorithm.
+      bool start() {
+        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
+        Heap heap(heap_cross_ref);
+        heap.push(_s, 0);
+        _pred[_s] = INVALID;
+        _proc_nodes.clear();
+
+        // Process nodes
+        while (!heap.empty() && heap.top() != _t) {
+          Node u = heap.top(), v;
+          Length d = heap.prio() + _pi[u], dn;
+          _dist[u] = heap.prio();
           _proc_nodes.push_back(u);
+          heap.pop();
 
           // 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);
+                case Heap::PRE_HEAP:
+                  heap.push(v, d + _length[e] - _pi[v]);
                   _pred[v] = e;
-                }
-                break;
-              case Heap::POST_HEAP:
-                break;
+                  break;
+                case Heap::IN_HEAP:
+                  dn = d + _length[e] - _pi[v];
+                  if (dn < heap[v]) {
+                    heap.decrease(v, dn);
+                    _pred[v] = e;
+                  }
+                  break;
+                case Heap::POST_HEAP:
+                  break;
               }
             }
           }
@@ -183,19 +225,19 @@
             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);
+                case Heap::PRE_HEAP:
+                  heap.push(v, d - _length[e] - _pi[v]);
                   _pred[v] = e;
-                }
-                break;
-              case Heap::POST_HEAP:
-                break;
+                  break;
+                case Heap::IN_HEAP:
+                  dn = d - _length[e] - _pi[v];
+                  if (dn < heap[v]) {
+                    heap.decrease(v, dn);
+                    _pred[v] = e;
+                  }
+                  break;
+                case Heap::POST_HEAP:
+                  break;
               }
             }
           }
@@ -205,7 +247,7 @@
         // 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;
+          _pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
         return true;
       }
 
@@ -226,19 +268,16 @@
     bool _local_potential;
 
     // The source node
-    Node _source;
+    Node _s;
     // The target node
-    Node _target;
+    Node _t;
 
     // Container to store the found paths
-    std::vector< SimplePath<Digraph> > paths;
+    std::vector<Path> _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:
 
@@ -258,7 +297,6 @@
     ~Suurballe() {
       if (_local_flow) delete _flow;
       if (_local_potential) delete _potential;
-      delete _dijkstra;
     }
 
     /// \brief Set the flow map.
@@ -342,7 +380,7 @@
     ///
     /// \param s The source node.
     void init(const Node& s) {
-      _source = s;
+      _s = s;
 
       // Initialize maps
       if (!_flow) {
@@ -372,20 +410,18 @@
     ///
     /// \pre \ref init() must be called before using this function.
     int findFlow(const Node& t, int k = 2) {
-      _target = t;
-      _dijkstra =
-        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
-                              _source, _target );
+      _t = t;
+      ResidualDijkstra dijkstra(*this);
 
       // Find shortest paths
       _path_num = 0;
       while (_path_num < k) {
         // Run Dijkstra
-        if (!_dijkstra->run()) break;
+        if (!dijkstra.run(_path_num)) break;
         ++_path_num;
 
         // Set the flow along the found shortest path
-        Node u = _target;
+        Node u = _t;
         Arc e;
         while ((e = _pred[u]) != INVALID) {
           if (u == _graph.target(e)) {
@@ -402,8 +438,8 @@
 
     /// \brief Compute the paths from the flow.
     ///
-    /// This function computes the paths from the found minimum cost flow,
-    /// which is the union of some arc-disjoint paths.
+    /// This function computes arc-disjoint paths from the found minimum
+    /// cost flow, which is the union of them.
     ///
     /// \pre \ref init() and \ref findFlow() must be called before using
     /// this function.
@@ -411,15 +447,15 @@
       FlowMap res_flow(_graph);
       for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
 
-      paths.clear();
-      paths.resize(_path_num);
+      _paths.clear();
+      _paths.resize(_path_num);
       for (int i = 0; i < _path_num; ++i) {
-        Node n = _source;
-        while (n != _target) {
+        Node n = _s;
+        while (n != _t) {
           OutArcIt e(_graph, n);
           for ( ; res_flow[e] == 0; ++e) ;
           n = _graph.target(e);
-          paths[i].addBack(e);
+          _paths[i].addBack(e);
           res_flow[e] = 0;
         }
       }
@@ -518,7 +554,7 @@
     /// \pre \ref run() or \ref findPaths() must be called before using
     /// this function.
     const Path& path(int i) const {
-      return paths[i];
+      return _paths[i];
     }
 
     /// @}