Changes in / [965:a1fd7008a052:966:c8fce9beb46a] in lemon-main

Files:

• CMakeLists.txt (modified) (2 diffs)
• contrib/CMakeLists.txt (added)
• doc/Doxyfile.in (modified) (1 diff)
• doc/coding_style.dox (modified) (1 diff)
• doc/dirs.dox (modified) (1 diff)
• doc/groups.dox (modified) (5 diffs)
• doc/references.bib (modified) (1 diff)
• lemon/Makefile.am (modified) (2 diffs)
• lemon/capacity_scaling.h (modified) (2 diffs)
• lemon/core.h (modified) (1 diff)
• lemon/cost_scaling.h (modified) (29 diffs)
• lemon/cycle_canceling.h (modified) (3 diffs)
• lemon/euler.h (modified) (1 diff)
• lemon/grosso_locatelli_pullan_mc.h (added)
• lemon/hao_orlin.h (modified) (7 diffs)
• lemon/kruskal.h (modified) (1 diff)
• lemon/max_cardinality_search.h (added)
• lemon/nagamochi_ibaraki.h (added)
• lemon/network_simplex.h (modified) (31 diffs)
• lemon/path.h (modified) (13 diffs)
• test/CMakeLists.txt (modified) (1 diff)
• test/Makefile.am (modified) (3 diffs)
• test/graph_copy_test.cc (modified) (8 diffs)
• test/max_cardinality_search_test.cc (added)
• test/max_clique_test.cc (added)
• test/nagamochi_ibaraki_test.cc (added)

CMakeLists.txt

@@ -115 +115 @@
 SET(LEMON_HAVE_LONG_LONG ${HAVE_LONG_LONG})
 
-INCLUDE(FindPythonInterp)
-
 ENABLE_TESTING()
 
@@ -127 +125 @@
 ADD_SUBDIRECTORY(lemon)
 IF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})
+  ADD_SUBDIRECTORY(contrib)
   ADD_SUBDIRECTORY(demo)
   ADD_SUBDIRECTORY(tools)

doc/Doxyfile.in

@@ -96 +96 @@
                          "@abs_top_srcdir@/lemon/concepts" \
                          "@abs_top_srcdir@/demo" \
+                         "@abs_top_srcdir@/contrib" \
                          "@abs_top_srcdir@/tools" \
                          "@abs_top_srcdir@/test/test_tools.h" \

doc/coding_style.dox

@@ -99 +99 @@
 \subsection pri-loc-var Private member variables
 
-Private member variables should start with underscore
+Private member variables should start with underscore.
 
 \code
-_start_with_underscores
+_start_with_underscore
 \endcode
 

doc/dirs.dox

@@ -32 +32 @@
 documentation.
 */
+
+/**
+\dir contrib
+\brief Directory for user contributed source codes.
+
+You can place your own C++ code using LEMON into this directory, which
+will compile to an executable along with LEMON when you build the
+library. This is probably the easiest way of compiling short to medium
+codes, for this does require neither a LEMON installed system-wide nor
+adding several paths to the compiler.
+
+Please have a look at <tt>contrib/CMakeLists.txt</tt> for
+instruction on how to add your own files into the build process.  */
 
 /**

doc/groups.dox

@@ -407 +407 @@
    strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
 
-In general NetworkSimplex is the most efficient implementation,
-but in special cases other algorithms could be faster.
+In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
+implementations, but the other two algorithms could be faster in special cases.
 For example, if the total supply and/or capacities are rather small,
-CapacityScaling is usually the fastest algorithm (without effective scaling).
+\ref CapacityScaling is usually the fastest algorithm (without effective scaling).
 */
 
@@ -472 +472 @@
   \ref dasdan98minmeancycle.
 
-In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
+In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
 most efficient one, though the best known theoretical bound on its running
 time is exponential.
@@ -540 +540 @@
 
 /**
-@defgroup planar Planarity Embedding and Drawing
+@defgroup planar Planar Embedding and Drawing
 @ingroup algs
 \brief Algorithms for planarity checking, embedding and drawing
@@ -552 +552 @@
 
 /**
-@defgroup approx Approximation Algorithms
+@defgroup approx_algs Approximation Algorithms
 @ingroup algs
 \brief Approximation algorithms.
@@ -558 +558 @@
 This group contains the approximation and heuristic algorithms
 implemented in LEMON.
+
+<b>Maximum Clique Problem</b>
+  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
+    Grosso, Locatelli, and Pullan.
 */
 

doc/references.bib

@@ -298 +298 @@
   address =      {Dublin, Ireland},
   year =         1991,
-  month =        sep,
-}
+  month =        sep
+}
+
+%%%%% Other algorithms %%%%%
+
+@article{grosso08maxclique,
+  author =       {Andrea Grosso and Marco Locatelli and Wayne Pullan},
+  title =        {Simple ingredients leading to very efficient
+                  heuristics for the maximum clique problem},
+  journal =      {Journal of Heuristics},
+  year =         2008,
+  volume =       14,
+  number =       6,
+  pages =        {587--612}
+}

lemon/Makefile.am

@@ -92 +92 @@
         lemon/graph_to_eps.h \
         lemon/grid_graph.h \
+        lemon/grosso_locatelli_pullan_mc.h \
         lemon/hartmann_orlin_mmc.h \
         lemon/howard_mmc.h \
@@ -108 +109 @@
         lemon/math.h \
         lemon/min_cost_arborescence.h \
+        lemon/max_cardinality_search.h \
+        lemon/nagamochi_ibaraki.h \
         lemon/nauty_reader.h \
         lemon/network_simplex.h \

lemon/capacity_scaling.h

@@ -87 +87 @@
   /// consider to use the named template parameters instead.
   ///
-  /// \warning Both number types must be signed and all input data must
+  /// \warning Both \c V and \c C must be signed number types.
+  /// \warning All input data (capacities, supply values, and costs) must
   /// be integer.
-  /// \warning This algorithm does not support negative costs for such
-  /// arcs that have infinite upper bound.
+  /// \warning This algorithm does not support negative costs for
+  /// arcs having infinite upper bound.
 #ifdef DOXYGEN
   template <typename GR, typename V, typename C, typename TR>
@@ -423 +424 @@
     ///
     /// 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
+    /// with 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.
     ///

lemon/core.h

@@ -447 +447 @@
 
   }
+
+  /// \brief Check whether a graph is undirected.
+  ///
+  /// This function returns \c true if the given graph is undirected.
+#ifdef DOXYGEN
+  template <typename GR>
+  bool undirected(const GR& g) { return false; }
+#else
+  template <typename GR>
+  typename enable_if<UndirectedTagIndicator<GR>, bool>::type
+  undirected(const GR&) {
+    return true;
+  }
+  template <typename GR>
+  typename disable_if<UndirectedTagIndicator<GR>, bool>::type
+  undirected(const GR&) {
+    return false;
+  }
+#endif
 
   /// \brief Class to copy a digraph.

lemon/cost_scaling.h

@@ -98 +98 @@
   /// "preflow push-relabel" algorithm for the maximum flow problem.
   ///
+  /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
+  /// implementations available in LEMON for this problem.
+  ///
   /// Most of the parameters of the problem (except for the digraph)
   /// can be given using separate functions, and the algorithm can be
@@ -114 +117 @@
   /// consider to use the named template parameters instead.
   ///
-  /// \warning Both number types must be signed and all input data must
+  /// \warning Both \c V and \c C must be signed number types.
+  /// \warning All input data (capacities, supply values, and costs) must
   /// be integer.
-  /// \warning This algorithm does not support negative costs for such
-  /// arcs that have infinite upper bound.
+  /// \warning This algorithm does not support negative costs for
+  /// arcs having infinite upper bound.
   ///
   /// \note %CostScaling provides three different internal methods,
@@ -179 +183 @@
     /// relabel operation.
     /// By default, the so called \ref PARTIAL_AUGMENT
-    /// "Partial Augment-Relabel" method is used, which proved to be
+    /// "Partial Augment-Relabel" method is used, which turned out to be
     /// the most efficient and the most robust on various test inputs.
     /// However, the other methods can be selected using the \ref run()
@@ -234 +238 @@
     };
 
-    typedef StaticVectorMap<StaticDigraph::Node, LargeCost> LargeCostNodeMap;
     typedef StaticVectorMap<StaticDigraph::Arc, LargeCost> LargeCostArcMap;
 
@@ -285 +288 @@
     int _max_rank;
 
-    // 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:
 
@@ -339 +334 @@
     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() :
@@ -448 +442 @@
     ///
     /// 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
+    /// with 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.
     ///
@@ -494 +488 @@
     /// \param method The internal method that will be used in the
     /// algorithm. For more information, see \ref Method.
-    /// \param factor The cost scaling factor. It must be larger than one.
+    /// \param factor The cost scaling factor. It must be at least two.
     ///
     /// \return \c INFEASIBLE if no feasible flow exists,
@@ -508 +502 @@
     /// \see ProblemType, Method
     /// \see resetParams(), reset()
-    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 8) {
+    ProblemType run(Method method = PARTIAL_AUGMENT, int factor = 16) {
+      LEMON_ASSERT(factor >= 2, "The scaling factor must be at least 2");
       _alpha = factor;
       ProblemType pt = init();
@@ -572 +567 @@
     }
 
-    /// \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.
+    /// \brief Reset the internal data structures and all the parameters
+    /// that have been given before.
+    ///
+    /// This function resets the internal data structures and 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 \ref run() calls. By default, all the given
+    /// parameters are kept for the next \ref run() call, unless
+    /// \ref resetParams() or \ref reset() is used.
+    /// If the underlying digraph was also modified after the construction
+    /// of the class or the last \ref reset() call, then the \ref reset()
+    /// function must be used, otherwise \ref resetParams() is sufficient.
+    ///
+    /// See \ref resetParams() for examples.
+    ///
     /// \return <tt>(*this)</tt>
+    ///
+    /// \see resetParams(), run()
     CostScaling& reset() {
       // Resize vectors
@@ -608 +610 @@
       _excess.resize(_res_node_num);
       _next_out.resize(_res_node_num);
-
-      _arc_vec.reserve(_res_arc_num);
-      _cost_vec.reserve(_res_arc_num);
 
       // Copy the graph
@@ -887 +886 @@
       }
 
-      return OPTIMAL;
-    }
-
-    // Execute the algorithm and transform the results
-    void start(Method method) {
-      // Maximum path length for partial augment
-      const int MAX_PATH_LENGTH = 4;
-
       // Initialize data structures for buckets
       _max_rank = _alpha * _res_node_num;
@@ -902 +893 @@
       _rank.resize(_res_node_num + 1);
 
-      // Execute the algorithm
+      return OPTIMAL;
+    }
+
+    // Execute the algorithm and transform the results
+    void start(Method method) {
+      const int MAX_PARTIAL_PATH_LENGTH = 4;
+
       switch (method) {
         case PUSH:
@@ -911 +908 @@
           break;
         case PARTIAL_AUGMENT:
-          startAugment(MAX_PATH_LENGTH);
+          startAugment(MAX_PARTIAL_PATH_LENGTH);
           break;
       }
 
-      // 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();
+      // Compute node potentials (dual solution)
+      for (int i = 0; i != _res_node_num; ++i) {
+        _pi[i] = static_cast<Cost>(_pi[i] / (_res_node_num * _alpha));
+      }
+      bool optimal = true;
+      for (int i = 0; optimal && i != _res_node_num; ++i) {
+        LargeCost pi_i = _pi[i];
+        int last_out = _first_out[i+1];
+        for (int j = _first_out[i]; j != last_out; ++j) {
+          if (_res_cap[j] > 0 && _scost[j] + pi_i - _pi[_target[j]] < 0) {
+            optimal = false;
+            break;
+          }
+        }
+      }
+
+      if (!optimal) {
+        // Compute node potentials for the original costs with BellmanFord
+        // (if it is necessary)
+        typedef std::pair<int, int> IntPair;
+        StaticDigraph sgr;
+        std::vector<IntPair> arc_vec;
+        std::vector<LargeCost> cost_vec;
+        LargeCostArcMap cost_map(cost_vec);
+
+        arc_vec.clear();
+        cost_vec.clear();
+        for (int j = 0; j != _res_arc_num; ++j) {
+          if (_res_cap[j] > 0) {
+            int u = _source[j], v = _target[j];
+            arc_vec.push_back(IntPair(u, v));
+            cost_vec.push_back(_scost[j] + _pi[u] - _pi[v]);
+          }
+        }
+        sgr.build(_res_node_num, arc_vec.begin(), arc_vec.end());
+
+        typename BellmanFord<StaticDigraph, LargeCostArcMap>::Create
+          bf(sgr, cost_map);
+        bf.init(0);
+        bf.start();
+
+        for (int i = 0; i != _res_node_num; ++i) {
+          _pi[i] += bf.dist(sgr.node(i));
+        }
+      }
+
+      // Shift potentials to meet the requirements of the GEQ type
+      // optimality conditions
+      LargeCost max_pot = _pi[_root];
+      for (int i = 0; i != _res_node_num; ++i) {
+        if (_pi[i] > max_pot) max_pot = _pi[i];
+      }
+      if (max_pot != 0) {
+        for (int i = 0; i != _res_node_num; ++i) {
+          _pi[i] -= max_pot;
+        }
+      }
 
       // Handle non-zero lower bounds
@@ -948 +986 @@
         LargeCost pi_u = _pi[u];
         for (int a = _first_out[u]; a != last_out; ++a) {
-          int v = _target[a];
-          if (_res_cap[a] > 0 && _cost[a] + pi_u - _pi[v] < 0) {
-            Value delta = _res_cap[a];
-            _excess[u] -= delta;
-            _excess[v] += delta;
-            _res_cap[a] = 0;
-            _res_cap[_reverse[a]] += delta;
+          Value delta = _res_cap[a];
+          if (delta > 0) {
+            int v = _target[a];
+            if (_cost[a] + pi_u - _pi[v] < 0) {
+              _excess[u] -= delta;
+              _excess[v] += delta;
+              _res_cap[a] = 0;
+              _res_cap[_reverse[a]] += delta;
+            }
           }
         }
@@ -970 +1010 @@
     }
 
-    // Early termination heuristic
-    bool earlyTermination() {
-      const double EARLY_TERM_FACTOR = 3.0;
-
-      // Build a static residual graph
-      _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());
-
-      // Run Bellman-Ford algorithm to check if the current flow is optimal
-      BellmanFord<StaticDigraph, LargeCostArcMap> bf(_sgr, _cost_map);
-      bf.init(0);
-      bool done = false;
-      int K = int(EARLY_TERM_FACTOR * std::sqrt(double(_res_node_num)));
-      for (int i = 0; i < K && !done; ++i) {
-        done = bf.processNextWeakRound();
-      }
-      return done;
+    // Price (potential) refinement heuristic
+    bool priceRefinement() {
+
+      // Stack for stroing the topological order
+      IntVector stack(_res_node_num);
+      int stack_top;
+
+      // Perform phases
+      while (topologicalSort(stack, stack_top)) {
+
+        // Compute node ranks in the acyclic admissible network and
+        // store the nodes in buckets
+        for (int i = 0; i != _res_node_num; ++i) {
+          _rank[i] = 0;
+        }
+        const int bucket_end = _root + 1;
+        for (int r = 0; r != _max_rank; ++r) {
+          _buckets[r] = bucket_end;
+        }
+        int top_rank = 0;
+        for ( ; stack_top >= 0; --stack_top) {
+          int u = stack[stack_top], v;
+          int rank_u = _rank[u];
+
+          LargeCost rc, pi_u = _pi[u];
+          int last_out = _first_out[u+1];
+          for (int a = _first_out[u]; a != last_out; ++a) {
+            if (_res_cap[a] > 0) {
+              v = _target[a];
+              rc = _cost[a] + pi_u - _pi[v];
+              if (rc < 0) {
+                LargeCost nrc = static_cast<LargeCost>((-rc - 0.5) / _epsilon);
+                if (nrc < LargeCost(_max_rank)) {
+                  int new_rank_v = rank_u + static_cast<int>(nrc);
+                  if (new_rank_v > _rank[v]) {
+                    _rank[v] = new_rank_v;
+                  }
+                }
+              }
+            }
+          }
+
+          if (rank_u > 0) {
+            top_rank = std::max(top_rank, rank_u);
+            int bfirst = _buckets[rank_u];
+            _bucket_next[u] = bfirst;
+            _bucket_prev[bfirst] = u;
+            _buckets[rank_u] = u;
+          }
+        }
+
+        // Check if the current flow is epsilon-optimal
+        if (top_rank == 0) {
+          return true;
+        }
+
+        // Process buckets in top-down order
+        for (int rank = top_rank; rank > 0; --rank) {
+          while (_buckets[rank] != bucket_end) {
+            // Remove the first node from the current bucket
+            int u = _buckets[rank];
+            _buckets[rank] = _bucket_next[u];
+
+            // Search the outgoing arcs of u
+            LargeCost rc, pi_u = _pi[u];
+            int last_out = _first_out[u+1];
+            int v, old_rank_v, new_rank_v;
+            for (int a = _first_out[u]; a != last_out; ++a) {
+              if (_res_cap[a] > 0) {
+                v = _target[a];
+                old_rank_v = _rank[v];
+
+                if (old_rank_v < rank) {
+
+                  // Compute the new rank of node v
+                  rc = _cost[a] + pi_u - _pi[v];
+                  if (rc < 0) {
+                    new_rank_v = rank;
+                  } else {
+                    LargeCost nrc = rc / _epsilon;
+                    new_rank_v = 0;
+                    if (nrc < LargeCost(_max_rank)) {
+                      new_rank_v = rank - 1 - static_cast<int>(nrc);
+                    }
+                  }
+
+                  // Change the rank of node v
+                  if (new_rank_v > old_rank_v) {
+                    _rank[v] = new_rank_v;
+
+                    // Remove v from its old bucket
+                    if (old_rank_v > 0) {
+                      if (_buckets[old_rank_v] == v) {
+                        _buckets[old_rank_v] = _bucket_next[v];
+                      } else {
+                        int pv = _bucket_prev[v], nv = _bucket_next[v];
+                        _bucket_next[pv] = nv;
+                        _bucket_prev[nv] = pv;
+                      }
+                    }
+
+                    // Insert v into its new bucket
+                    int nv = _buckets[new_rank_v];
+                    _bucket_next[v] = nv;
+                    _bucket_prev[nv] = v;
+                    _buckets[new_rank_v] = v;
+                  }
+                }
+              }
+            }
+
+            // Refine potential of node u
+            _pi[u] -= rank * _epsilon;
+          }
+        }
+
+      }
+
+      return false;
+    }
+
+    // Find and cancel cycles in the admissible network and
+    // determine topological order using DFS
+    bool topologicalSort(IntVector &stack, int &stack_top) {
+      const int MAX_CYCLE_CANCEL = 1;
+
+      BoolVector reached(_res_node_num, false);
+      BoolVector processed(_res_node_num, false);
+      IntVector pred(_res_node_num);
+      for (int i = 0; i != _res_node_num; ++i) {
+        _next_out[i] = _first_out[i];
+      }
+      stack_top = -1;
+
+      int cycle_cnt = 0;
+      for (int start = 0; start != _res_node_num; ++start) {
+        if (reached[start]) continue;
+
+        // Start DFS search from this start node
+        pred[start] = -1;
+        int tip = start, v;
+        while (true) {
+          // Check the outgoing arcs of the current tip node
+          reached[tip] = true;
+          LargeCost pi_tip = _pi[tip];
+          int a, last_out = _first_out[tip+1];
+          for (a = _next_out[tip]; a != last_out; ++a) {
+            if (_res_cap[a] > 0) {
+              v = _target[a];
+              if (_cost[a] + pi_tip - _pi[v] < 0) {
+                if (!reached[v]) {
+                  // A new node is reached
+                  reached[v] = true;
+                  pred[v] = tip;
+                  _next_out[tip] = a;
+                  tip = v;
+                  a = _next_out[tip];
+                  last_out = _first_out[tip+1];
+                  break;
+                }
+                else if (!processed[v]) {
+                  // A cycle is found
+                  ++cycle_cnt;
+                  _next_out[tip] = a;
+
+                  // Find the minimum residual capacity along the cycle
+                  Value d, delta = _res_cap[a];
+                  int u, delta_node = tip;
+                  for (u = tip; u != v; ) {
+                    u = pred[u];
+                    d = _res_cap[_next_out[u]];
+                    if (d <= delta) {
+                      delta = d;
+                      delta_node = u;
+                    }
+                  }
+
+                  // Augment along the cycle
+                  _res_cap[a] -= delta;
+                  _res_cap[_reverse[a]] += delta;
+                  for (u = tip; u != v; ) {
+                    u = pred[u];
+                    int ca = _next_out[u];
+                    _res_cap[ca] -= delta;
+                    _res_cap[_reverse[ca]] += delta;
+                  }
+
+                  // Check the maximum number of cycle canceling
+                  if (cycle_cnt >= MAX_CYCLE_CANCEL) {
+                    return false;
+                  }
+
+                  // Roll back search to delta_node
+                  if (delta_node != tip) {
+                    for (u = tip; u != delta_node; u = pred[u]) {
+                      reached[u] = false;
+                    }
+                    tip = delta_node;
+                    a = _next_out[tip] + 1;
+                    last_out = _first_out[tip+1];
+                    break;
+                  }
+                }
+              }
+            }
+          }
+
+          // Step back to the previous node
+          if (a == last_out) {
+            processed[tip] = true;
+            stack[++stack_top] = tip;
+            tip = pred[tip];
+            if (tip < 0) {
+              // Finish DFS from the current start node
+              break;
+            }
+            ++_next_out[tip];
+          }
+        }
+
+      }
+
+      return (cycle_cnt == 0);
     }
 
     // Global potential update heuristic
     void globalUpdate() {
-      int bucket_end = _root + 1;
+      const int bucket_end = _root + 1;
 
       // Initialize buckets
@@ -1005 +1244 @@
       }
       Value total_excess = 0;
+      int b0 = bucket_end;
       for (int i = 0; i != _res_node_num; ++i) {
         if (_excess[i] < 0) {
           _rank[i] = 0;
-          _bucket_next[i] = _buckets[0];
-          _bucket_prev[_buckets[0]] = i;
-          _buckets[0] = i;
+          _bucket_next[i] = b0;
+          _bucket_prev[b0] = i;
+          b0 = i;
         } else {
           total_excess += _excess[i];
@@ -1017 +1257 @@
       }
       if (total_excess == 0) return;
+      _buckets[0] = b0;
 
       // Search the buckets
@@ -1038 +1279 @@
                 LargeCost nrc = (_cost[ra] + _pi[v] - pi_u) / _epsilon;
                 int new_rank_v = old_rank_v;
-                if (nrc < LargeCost(_max_rank))
-                  new_rank_v = r + 1 + int(nrc);
+                if (nrc < LargeCost(_max_rank)) {
+                  new_rank_v = r + 1 + static_cast<int>(nrc);
+                }
 
                 // Change the rank of v
@@ -1051 +1293 @@
                       _buckets[old_rank_v] = _bucket_next[v];
                     } else {
-                      _bucket_next[_bucket_prev[v]] = _bucket_next[v];
-                      _bucket_prev[_bucket_next[v]] = _bucket_prev[v];
+                      int pv = _bucket_prev[v], nv = _bucket_next[v];
+                      _bucket_next[pv] = nv;
+                      _bucket_prev[nv] = pv;
                     }
                   }
 
-                  // Insert v to its new bucket
-                  _bucket_next[v] = _buckets[new_rank_v];
-                  _bucket_prev[_buckets[new_rank_v]] = v;
+                  // Insert v into its new bucket
+                  int nv = _buckets[new_rank_v];
+                  _bucket_next[v] = nv;
+                  _bucket_prev[nv] = v;
                   _buckets[new_rank_v] = v;
                 }
@@ -1087 +1331 @@
     void startAugment(int max_length) {
       // Paramters for heuristics
-      const int EARLY_TERM_EPSILON_LIMIT = 1000;
-      const double GLOBAL_UPDATE_FACTOR = 3.0;
-
-      const int global_update_freq = int(GLOBAL_UPDATE_FACTOR *
+      const int PRICE_REFINEMENT_LIMIT = 2;
+      const double GLOBAL_UPDATE_FACTOR = 1.0;
+      const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
         (_res_node_num + _sup_node_num * _sup_node_num));
-      int next_update_limit = global_update_freq;
-
+      int next_global_update_limit = global_update_skip;
+
+      // Perform cost scaling phases
+      IntVector path;
+      BoolVector path_arc(_res_arc_num, false);
       int relabel_cnt = 0;
-
-      // Perform cost scaling phases
-      std::vector<int> path;
+      int eps_phase_cnt = 0;
       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
                                         1 : _epsilon / _alpha )
       {
-        // Early termination heuristic
-        if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) {
-          if (earlyTermination()) break;
+        ++eps_phase_cnt;
+
+        // Price refinement heuristic
+        if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
+          if (priceRefinement()) continue;
         }
 
@@ -1120 +1366 @@
 
           // Find an augmenting path from the start node
-          path.clear();
           int tip = start;
-          while (_excess[tip] >= 0 && int(path.size()) < max_length) {
+          while (int(path.size()) < max_length && _excess[tip] >= 0) {
             int u;
-            LargeCost min_red_cost, rc, pi_tip = _pi[tip];
+            LargeCost rc, min_red_cost = std::numeric_limits<LargeCost>::max();
+            LargeCost pi_tip = _pi[tip];
             int last_out = _first_out[tip+1];
             for (int a = _next_out[tip]; a != last_out; ++a) {
-              u = _target[a];
-              if (_res_cap[a] > 0 && _cost[a] + pi_tip - _pi[u] < 0) {
-                path.push_back(a);
-                _next_out[tip] = a;
-                tip = u;
-                goto next_step;
+              if (_res_cap[a] > 0) {
+                u = _target[a];
+                rc = _cost[a] + pi_tip - _pi[u];
+                if (rc < 0) {
+                  path.push_back(a);
+                  _next_out[tip] = a;
+                  if (path_arc[a]) {
+                    goto augment;   // a cycle is found, stop path search
+                  }
+                  tip = u;
+                  path_arc[a] = true;
+                  goto next_step;
+                }
+                else if (rc < min_red_cost) {
+                  min_red_cost = rc;
+                }
               }
             }
 
             // Relabel tip node
-            min_red_cost = std::numeric_limits<LargeCost>::max();
             if (tip != start) {
               int ra = _reverse[path.back()];
-              min_red_cost = _cost[ra] + pi_tip - _pi[_target[ra]];
+              min_red_cost =
+                std::min(min_red_cost, _cost[ra] + pi_tip - _pi[_target[ra]]);
             }
+            last_out = _next_out[tip];
             for (int a = _first_out[tip]; a != last_out; ++a) {
-              rc = _cost[a] + pi_tip - _pi[_target[a]];
-              if (_res_cap[a] > 0 && rc < min_red_cost) {
-                min_red_cost = rc;
+              if (_res_cap[a] > 0) {
+                rc = _cost[a] + pi_tip - _pi[_target[a]];
+                if (rc < min_red_cost) {
+                  min_red_cost = rc;
+                }
               }
             }
@@ -1154 +1413 @@
             // Step back
             if (tip != start) {
-              tip = _source[path.back()];
+              int pa = path.back();
+              path_arc[pa] = false;
+              tip = _source[pa];
               path.pop_back();
             }
@@ -1162 +1423 @@
 
           // Augment along the found path (as much flow as possible)
+        augment:
           Value delta;
           int pa, u, v = start;
@@ -1168 +1430 @@
             u = v;
             v = _target[pa];
+            path_arc[pa] = false;
             delta = std::min(_res_cap[pa], _excess[u]);
             _res_cap[pa] -= delta;
@@ -1173 +1436 @@
             _excess[u] -= delta;
             _excess[v] += delta;
-            if (_excess[v] > 0 && _excess[v] <= delta)
+            if (_excess[v] > 0 && _excess[v] <= delta) {
               _active_nodes.push_back(v);
-          }
+            }
+          }
+          path.clear();
 
           // Global update heuristic
-          if (relabel_cnt >= next_update_limit) {
+          if (relabel_cnt >= next_global_update_limit) {
             globalUpdate();
-            next_update_limit += global_update_freq;
-          }
-        }
-      }
+            next_global_update_limit += global_update_skip;
+          }
+        }
+
+      }
+
     }
 
@@ -1189 +1456 @@
     void startPush() {
       // Paramters for heuristics
-      const int EARLY_TERM_EPSILON_LIMIT = 1000;
+      const int PRICE_REFINEMENT_LIMIT = 2;
       const double GLOBAL_UPDATE_FACTOR = 2.0;
 
-      const int global_update_freq = int(GLOBAL_UPDATE_FACTOR *
+      const int global_update_skip = static_cast<int>(GLOBAL_UPDATE_FACTOR *
         (_res_node_num + _sup_node_num * _sup_node_num));
-      int next_update_limit = global_update_freq;
-
-      int relabel_cnt = 0;
+      int next_global_update_limit = global_update_skip;
 
       // Perform cost scaling phases
       BoolVector hyper(_res_node_num, false);
       LargeCostVector hyper_cost(_res_node_num);
+      int relabel_cnt = 0;
+      int eps_phase_cnt = 0;
       for ( ; _epsilon >= 1; _epsilon = _epsilon < _alpha && _epsilon > 1 ?
                                         1 : _epsilon / _alpha )
       {
-        // Early termination heuristic
-        if (_epsilon <= EARLY_TERM_EPSILON_LIMIT) {
-          if (earlyTermination()) break;
+        ++eps_phase_cnt;
+
+        // Price refinement heuristic
+        if (eps_phase_cnt >= PRICE_REFINEMENT_LIMIT) {
+          if (priceRefinement()) continue;
         }
 
@@ -1278 +1547 @@
                std::numeric_limits<LargeCost>::max();
             for (int a = _first_out[n]; a != last_out; ++a) {
-              rc = _cost[a] + pi_n - _pi[_target[a]];
-              if (_res_cap[a] > 0 && rc < min_red_cost) {
-                min_red_cost = rc;
+              if (_res_cap[a] > 0) {
+                rc = _cost[a] + pi_n - _pi[_target[a]];
+                if (rc < min_red_cost) {
+                  min_red_cost = rc;
+                }
               }
             }
@@ -1298 +1569 @@
 
           // Global update heuristic
-          if (relabel_cnt >= next_update_limit) {
+          if (relabel_cnt >= next_global_update_limit) {
             globalUpdate();
             for (int u = 0; u != _res_node_num; ++u)
               hyper[u] = false;
-            next_update_limit += global_update_freq;
+            next_global_update_limit += global_update_skip;
           }
         }

lemon/cycle_canceling.h

@@ -66 +66 @@
   /// algorithm. By default, it is the same as \c V.
   ///
-  /// \warning Both number types must be signed and all input data must
+  /// \warning Both \c V and \c C must be signed number types.
+  /// \warning All input data (capacities, supply values, and costs) must
   /// be integer.
-  /// \warning This algorithm does not support negative costs for such
-  /// arcs that have infinite upper bound.
+  /// \warning This algorithm does not support negative costs for
+  /// arcs having infinite upper bound.
   ///
   /// \note For more information about the three available methods,
@@ -117 +118 @@
     /// \ref CycleCanceling provides three different cycle-canceling
     /// methods. By default, \ref CANCEL_AND_TIGHTEN "Cancel and Tighten"
-    /// is used, which proved to be the most efficient and the most robust
-    /// on various test inputs.
+    /// is used, which is by far the most efficient and the most robust.
     /// However, the other methods can be selected using the \ref run()
     /// function with the proper parameter.
@@ -350 +350 @@
     ///
     /// 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
+    /// with 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.
     ///

lemon/euler.h

@@ -37 +37 @@
   ///Euler tour iterator for digraphs.
 
-  /// \ingroup graph_prop
+  /// \ingroup graph_properties
   ///This iterator provides an Euler tour (Eulerian circuit) of a \e directed
   ///graph (if there exists) and it converts to the \c Arc type of the digraph.

lemon/hao_orlin.h

@@ -54 +54 @@
   /// preflow push-relabel algorithm. Our implementation calculates
   /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
-  /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The
-  /// purpose of such algorithm is e.g. testing network reliability.
+  /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. A notable
+  /// use of this algorithm is testing network reliability.
   ///
   /// For an undirected graph you can run just the first phase of the
@@ -913 +913 @@
     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with
     /// \f$ source \in X \f$ and minimal outgoing capacity).
+    /// It updates the stored cut if (and only if) the newly found one
+    /// is better.
     ///
     /// \pre \ref init() must be called before using this function.
@@ -925 +927 @@
     /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with
     /// \f$ source \notin X \f$ and minimal outgoing capacity).
+    /// It updates the stored cut if (and only if) the newly found one
+    /// is better.
     ///
     /// \pre \ref init() must be called before using this function.
@@ -934 +938 @@
     /// \brief Run the algorithm.
     ///
-    /// This function runs the algorithm. It finds nodes \c source and
-    /// \c target arbitrarily and then calls \ref init(), \ref calculateOut()
+    /// This function runs the algorithm. It chooses source node,
+    /// then calls \ref init(), \ref calculateOut()
     /// and \ref calculateIn().
     void run() {
@@ -945 +949 @@
     /// \brief Run the algorithm.
     ///
-    /// This function runs the algorithm. It uses the given \c source node,
-    /// finds a proper \c target node and then calls the \ref init(),
-    /// \ref calculateOut() and \ref calculateIn().
+    /// This function runs the algorithm. It calls \ref init(),
+    /// \ref calculateOut() and \ref calculateIn() with the given
+    /// source node.
     void run(const Node& s) {
       init(s);
@@ -966 +970 @@
     /// \brief Return the value of the minimum cut.
     ///
-    /// This function returns the value of the minimum cut.
+    /// This function returns the value of the best cut found by the
+    /// previously called \ref run(), \ref calculateOut() or \ref
+    /// calculateIn().
     ///
     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
@@ -977 +983 @@
     /// \brief Return a minimum cut.
     ///
-    /// This function sets \c cutMap to the characteristic vector of a
-    /// minimum value cut: it will give a non-empty set \f$ X\subsetneq V \f$
-    /// with minimal outgoing capacity (i.e. \c cutMap will be \c true exactly
+    /// This function gives the best cut found by the
+    /// previously called \ref run(), \ref calculateOut() or \ref
+    /// calculateIn().
+    ///
+    /// It sets \c cutMap to the characteristic vector of the found
+    /// minimum value cut - a non-empty set \f$ X\subsetneq V \f$
+    /// of minimum outgoing capacity (i.e. \c cutMap will be \c true exactly
     /// for the nodes of \f$ X \f$).
     ///

lemon/kruskal.h

@@ -31 +31 @@
 ///\file
 ///\brief Kruskal's algorithm to compute a minimum cost spanning tree
-///
-///Kruskal's algorithm to compute a minimum cost spanning tree.
-///
 
 namespace lemon {

lemon/network_simplex.h

@@ -48 +48 @@
   /// flow problem.
   ///
-  /// In general, %NetworkSimplex is the fastest implementation available
-  /// in LEMON for this problem.
-  /// Moreover, it supports both directions of the supply/demand inequality
-  /// constraints. For more information, see \ref SupplyType.
+  /// In general, \ref NetworkSimplex and \ref CostScaling are the fastest
+  /// implementations available in LEMON for this problem.
+  /// Furthermore, this class supports both directions of the supply/demand
+  /// inequality constraints. For more information, see \ref SupplyType.
   ///
   /// Most of the parameters of the problem (except for the digraph)
@@ -64 +64 @@
   /// algorithm. By default, it is the same as \c V.
   ///
-  /// \warning Both number types must be signed and all input data must
+  /// \warning Both \c V and \c C must be signed number types.
+  /// \warning All input data (capacities, supply values, and costs) must
   /// be integer.
   ///
@@ -126 +127 @@
     /// of the algorithm.
     /// By default, \ref BLOCK_SEARCH "Block Search" is used, which
-    /// proved to be the most efficient and the most robust on various
+    /// turend out to be the most efficient and the most robust on various
     /// test inputs.
     /// However, another pivot rule can be selected using the \ref run()
@@ -167 +168 @@
     typedef std::vector<Value> ValueVector;
     typedef std::vector<Cost> CostVector;
-    typedef std::vector<char> BoolVector;
-    // Note: vector<char> is used instead of vector<bool> for efficiency reasons
+    typedef std::vector<signed char> CharVector;
+    // Note: vector<signed char> is used instead of vector<ArcState> and
+    // vector<ArcDirection> for efficiency reasons
 
     // State constants for arcs
@@ -177 +179 @@
     };
 
-    typedef std::vector<signed char> StateVector;
-    // Note: vector<signed char> is used instead of vector<ArcState> for
-    // efficiency reasons
+    // Direction constants for tree arcs
+    enum ArcDirection {
+      DIR_DOWN = -1,
+      DIR_UP   =  1
+    };
 
   private:
@@ -218 +222 @@
     IntVector _succ_num;
     IntVector _last_succ;
+    CharVector _pred_dir;
+    CharVector _state;
     IntVector _dirty_revs;
-    BoolVector _forward;
-    StateVector _state;
     int _root;
 
     // Temporary data used in the current pivot iteration
     int in_arc, join, u_in, v_in, u_out, v_out;
-    int first, second, right, last;
-    int stem, par_stem, new_stem;
     Value delta;
 
@@ -251 +253 @@
       const IntVector  &_target;
       const CostVector &_cost;
-      const StateVector &_state;
+      const CharVector &_state;
       const CostVector &_pi;
       int &_in_arc;
@@ -303 +305 @@
       const IntVector  &_target;
       const CostVector &_cost;
-      const StateVector &_state;
+      const CharVector &_state;
       const CostVector &_pi;
       int &_in_arc;
@@ -342 +344 @@
       const IntVector  &_target;
       const CostVector &_cost;
-      const StateVector &_state;
+      const CharVector &_state;
       const CostVector &_pi;
       int &_in_arc;
@@ -415 +417 @@
       const IntVector  &_target;
       const CostVector &_cost;
-      const StateVector &_state;
+      const CharVector &_state;
       const CostVector &_pi;
       int &_in_arc;
@@ -518 +520 @@
       const IntVector  &_target;
       const CostVector &_cost;
-      const StateVector &_state;
+      const CharVector &_state;
       const CostVector &_pi;
       int &_in_arc;
@@ -571 +573 @@
         // Check the current candidate list
         int e;
+        Cost c;
         for (int i = 0; i != _curr_length; ++i) {
           e = _candidates[i];
-          _cand_cost[e] = _state[e] *
-            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
-          if (_cand_cost[e] >= 0) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < 0) {
+            _cand_cost[e] = c;
+          } else {
             _candidates[i--] = _candidates[--_curr_length];
           }
@@ -585 +589 @@
 
         for (e = _next_arc; e != _search_arc_num; ++e) {
-          _cand_cost[e] = _state[e] *
-            (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
-          if (_cand_cost[e] < 0) {
+          c = _state[e] * (_cost[e] + _pi[_source[e]] - _pi[_target[e]]);
+          if (c < 0) {
+            _cand_cost[e] = c;
             _candidates[_curr_length++] = e;
           }
@@ -634 +638 @@
     ///
     /// \param graph The digraph the algorithm runs on.
-    /// \param arc_mixing Indicate if the arcs have to be stored in a
+    /// \param arc_mixing Indicate if the arcs will be stored in a
     /// mixed order in the internal data structure.
-    /// In special cases, it could lead to better overall performance,
-    /// but it is usually slower. Therefore it is disabled by default.
-    NetworkSimplex(const GR& graph, bool arc_mixing = false) :
+    /// In general, it leads to similar performance as using the original
+    /// arc order, but it makes the algorithm more robust and in special
+    /// cases, even significantly faster. Therefore, it is enabled by default.
+    NetworkSimplex(const GR& graph, bool arc_mixing = true) :
       _graph(graph), _node_id(graph), _arc_id(graph),
       _arc_mixing(arc_mixing),
@@ -731 +736 @@
     ///
     /// \return <tt>(*this)</tt>
+    ///
+    /// \sa supplyType()
     template<typename SupplyMap>
     NetworkSimplex& supplyMap(const SupplyMap& map) {
@@ -747 +754 @@
     ///
     /// 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
+    /// with 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.
     ///
@@ -914 +921 @@
       _parent.resize(all_node_num);
       _pred.resize(all_node_num);
-      _forward.resize(all_node_num);
+      _pred_dir.resize(all_node_num);
       _thread.resize(all_node_num);
       _rev_thread.resize(all_node_num);
@@ -928 +935 @@
       if (_arc_mixing) {
         // Store the arcs in a mixed order
-        int k = std::max(int(std::sqrt(double(_arc_num))), 10);
+        const int skip = std::max(_arc_num / _node_num, 3);
         int i = 0, j = 0;
         for (ArcIt a(_graph); a != INVALID; ++a) {
@@ -934 +941 @@
           _source[i] = _node_id[_graph.source(a)];
           _target[i] = _node_id[_graph.target(a)];
-          if ((i += k) >= _arc_num) i = ++j;
+          if ((i += skip) >= _arc_num) i = ++j;
         }
       } else {
@@ -1117 +1124 @@
           _state[e] = STATE_TREE;
           if (_supply[u] >= 0) {
-            _forward[u] = true;
+            _pred_dir[u] = DIR_UP;
             _pi[u] = 0;
             _source[e] = u;
@@ -1124 +1131 @@
             _cost[e] = 0;
           } else {
-            _forward[u] = false;
+            _pred_dir[u] = DIR_DOWN;
             _pi[u] = ART_COST;
             _source[e] = _root;
@@ -1144 +1151 @@
           _last_succ[u] = u;
           if (_supply[u] >= 0) {
-            _forward[u] = true;
+            _pred_dir[u] = DIR_UP;
             _pi[u] = 0;
             _pred[u] = e;
@@ -1154 +1161 @@
             _state[e] = STATE_TREE;
           } else {
-            _forward[u] = false;
+            _pred_dir[u] = DIR_DOWN;
             _pi[u] = ART_COST;
             _pred[u] = f;
@@ -1185 +1192 @@
           _last_succ[u] = u;
           if (_supply[u] <= 0) {
-            _forward[u] = false;
+            _pred_dir[u] = DIR_DOWN;
             _pi[u] = 0;
             _pred[u] = e;
@@ -1195 +1202 @@
             _state[e] = STATE_TREE;
           } else {
-            _forward[u] = true;
+            _pred_dir[u] = DIR_UP;
             _pi[u] = -ART_COST;
             _pred[u] = f;
@@ -1238 +1245 @@
       // Initialize first and second nodes according to the direction
       // of the cycle
+      int first, second;
       if (_state[in_arc] == STATE_LOWER) {
         first  = _source[in_arc];
@@ -1247 +1255 @@
       delta = _cap[in_arc];
       int result = 0;
-      Value d;
+      Value c, d;
       int e;
 
-      // Search the cycle along the path form the first node to the root
+      // Search the cycle form the first node to the join node
       for (int u = first; u != join; u = _parent[u]) {
         e = _pred[u];
-        d = _forward[u] ?
-          _flow[e] : (_cap[e] >= MAX ? INF : _cap[e] - _flow[e]);
+        d = _flow[e];
+        if (_pred_dir[u] == DIR_DOWN) {
+          c = _cap[e];
+          d = c >= MAX ? INF : c - d;
+        }
         if (d < delta) {
           delta = d;
@@ -1261 +1272 @@
         }
       }
-      // Search the cycle along the path form the second node to the root
+
+      // Search the cycle form the second node to the join node
       for (int u = second; u != join; u = _parent[u]) {
         e = _pred[u];
-        d = _forward[u] ?
-          (_cap[e] >= MAX ? INF : _cap[e] - _flow[e]) : _flow[e];
+        d = _flow[e];
+        if (_pred_dir[u] == DIR_UP) {
+          c = _cap[e];
+          d = c >= MAX ? INF : c - d;
+        }
         if (d <= delta) {
           delta = d;
@@ -1290 +1305 @@
         _flow[in_arc] += val;
         for (int u = _source[in_arc]; u != join; u = _parent[u]) {
-          _flow[_pred[u]] += _forward[u] ? -val : val;
+          _flow[_pred[u]] -= _pred_dir[u] * val;
         }
         for (int u = _target[in_arc]; u != join; u = _parent[u]) {
-          _flow[_pred[u]] += _forward[u] ? val : -val;
+          _flow[_pred[u]] += _pred_dir[u] * val;
         }
       }
@@ -1308 +1323 @@
     // Update the tree structure
     void updateTreeStructure() {
-      int u, w;
       int old_rev_thread = _rev_thread[u_out];
       int old_succ_num = _succ_num[u_out];
@@ -1314 +1328 @@
       v_out = _parent[u_out];
 
-      u = _last_succ[u_in];  // the last successor of u_in
-      right = _thread[u];    // the node after it
-
-      // Handle the case when old_rev_thread equals to v_in
-      // (it also means that join and v_out coincide)
-      if (old_rev_thread == v_in) {
-        last = _thread[_last_succ[u_out]];
+      // Check if u_in and u_out coincide
+      if (u_in == u_out) {
+        // Update _parent, _pred, _pred_dir
+        _parent[u_in] = v_in;
+        _pred[u_in] = in_arc;
+        _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
+
+        // Update _thread and _rev_thread
+        if (_thread[v_in] != u_out) {
+          int after = _thread[old_last_succ];
+          _thread[old_rev_thread] = after;
+          _rev_thread[after] = old_rev_thread;
+          after = _thread[v_in];
+          _thread[v_in] = u_out;
+          _rev_thread[u_out] = v_in;
+          _thread[old_last_succ] = after;
+          _rev_thread[after] = old_last_succ;
+        }
       } else {
-        last = _thread[v_in];
-      }
-
-      // Update _thread and _parent along the stem nodes (i.e. the nodes
-      // between u_in and u_out, whose parent have to be changed)
-      _thread[v_in] = stem = u_in;
-      _dirty_revs.clear();
-      _dirty_revs.push_back(v_in);
-      par_stem = v_in;
-      while (stem != u_out) {
-        // Insert the next stem node into the thread list
-        new_stem = _parent[stem];
-        _thread[u] = new_stem;
-        _dirty_revs.push_back(u);
-
-        // Remove the subtree of stem from the thread list
-        w = _rev_thread[stem];
-        _thread[w] = right;
-        _rev_thread[right] = w;
-
-        // Change the parent node and shift stem nodes
-        _parent[stem] = par_stem;
-        par_stem = stem;
-        stem = new_stem;
-
-        // Update u and right
-        u = _last_succ[stem] == _last_succ[par_stem] ?
-          _rev_thread[par_stem] : _last_succ[stem];
-        right = _thread[u];
-      }
-      _parent[u_out] = par_stem;
-      _thread[u] = last;
-      _rev_thread[last] = u;
-      _last_succ[u_out] = u;
-
-      // Remove the subtree of u_out from the thread list except for
-      // the case when old_rev_thread equals to v_in
-      // (it also means that join and v_out coincide)
-      if (old_rev_thread != v_in) {
-        _thread[old_rev_thread] = right;
-        _rev_thread[right] = old_rev_thread;
-      }
-
-      // Update _rev_thread using the new _thread values
-      for (int i = 0; i != int(_dirty_revs.size()); ++i) {
-        u = _dirty_revs[i];
-        _rev_thread[_thread[u]] = u;
-      }
-
-      // Update _pred, _forward, _last_succ and _succ_num for the
-      // stem nodes from u_out to u_in
-      int tmp_sc = 0, tmp_ls = _last_succ[u_out];
-      u = u_out;
-      while (u != u_in) {
-        w = _parent[u];
-        _pred[u] = _pred[w];
-        _forward[u] = !_forward[w];
-        tmp_sc += _succ_num[u] - _succ_num[w];
-        _succ_num[u] = tmp_sc;
-        _last_succ[w] = tmp_ls;
-        u = w;
-      }
-      _pred[u_in] = in_arc;
-      _forward[u_in] = (u_in == _source[in_arc]);
-      _succ_num[u_in] = old_succ_num;
-
-      // Set limits for updating _last_succ form v_in and v_out
-      // towards the root
-      int up_limit_in = -1;
-      int up_limit_out = -1;
-      if (_last_succ[join] == v_in) {
-        up_limit_out = join;
-      } else {
-        up_limit_in = join;
+        // Handle the case when old_rev_thread equals to v_in
+        // (it also means that join and v_out coincide)
+        int thread_continue = old_rev_thread == v_in ?
+          _thread[old_last_succ] : _thread[v_in];
+
+        // Update _thread and _parent along the stem nodes (i.e. the nodes
+        // between u_in and u_out, whose parent have to be changed)
+        int stem = u_in;              // the current stem node
+        int par_stem = v_in;          // the new parent of stem
+        int next_stem;                // the next stem node
+        int last = _last_succ[u_in];  // the last successor of stem
+        int before, after = _thread[last];
+        _thread[v_in] = u_in;
+        _dirty_revs.clear();
+        _dirty_revs.push_back(v_in);
+        while (stem != u_out) {
+          // Insert the next stem node into the thread list
+          next_stem = _parent[stem];
+          _thread[last] = next_stem;
+          _dirty_revs.push_back(last);
+
+          // Remove the subtree of stem from the thread list
+          before = _rev_thread[stem];
+          _thread[before] = after;
+          _rev_thread[after] = before;
+
+          // Change the parent node and shift stem nodes
+          _parent[stem] = par_stem;
+          par_stem = stem;
+          stem = next_stem;
+
+          // Update last and after
+          last = _last_succ[stem] == _last_succ[par_stem] ?
+            _rev_thread[par_stem] : _last_succ[stem];
+          after = _thread[last];
+        }
+        _parent[u_out] = par_stem;
+        _thread[last] = thread_continue;
+        _rev_thread[thread_continue] = last;
+        _last_succ[u_out] = last;
+
+        // Remove the subtree of u_out from the thread list except for
+        // the case when old_rev_thread equals to v_in
+        if (old_rev_thread != v_in) {
+          _thread[old_rev_thread] = after;
+          _rev_thread[after] = old_rev_thread;
+        }
+
+        // Update _rev_thread using the new _thread values
+        for (int i = 0; i != int(_dirty_revs.size()); ++i) {
+          int u = _dirty_revs[i];
+          _rev_thread[_thread[u]] = u;
+        }
+
+        // Update _pred, _pred_dir, _last_succ and _succ_num for the
+        // stem nodes from u_out to u_in
+        int tmp_sc = 0, tmp_ls = _last_succ[u_out];
+        for (int u = u_out, p = _parent[u]; u != u_in; u = p, p = _parent[u]) {
+          _pred[u] = _pred[p];
+          _pred_dir[u] = -_pred_dir[p];
+          tmp_sc += _succ_num[u] - _succ_num[p];
+          _succ_num[u] = tmp_sc;
+          _last_succ[p] = tmp_ls;
+        }
+        _pred[u_in] = in_arc;
+        _pred_dir[u_in] = u_in == _source[in_arc] ? DIR_UP : DIR_DOWN;
+        _succ_num[u_in] = old_succ_num;
       }
 
       // Update _last_succ from v_in towards the root
-      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;
-           u = _parent[u]) {
-        _last_succ[u] = _last_succ[u_out];
-      }
+      int up_limit_out = _last_succ[join] == v_in ? join : -1;
+      int last_succ_out = _last_succ[u_out];
+      for (int u = v_in; u != -1 && _last_succ[u] == v_in; u = _parent[u]) {
+        _last_succ[u] = last_succ_out;
+      }
+
       // Update _last_succ from v_out towards the root
       if (join != old_rev_thread && v_in != old_rev_thread) {
-        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
+        for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
              u = _parent[u]) {
           _last_succ[u] = old_rev_thread;
         }
-      } else {
-        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
+      }
+      else if (last_succ_out != old_last_succ) {
+        for (int u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;
              u = _parent[u]) {
-          _last_succ[u] = _last_succ[u_out];
+          _last_succ[u] = last_succ_out;
         }
       }
 
       // Update _succ_num from v_in to join
-      for (u = v_in; u != join; u = _parent[u]) {
+      for (int u = v_in; u != join; u = _parent[u]) {
         _succ_num[u] += old_succ_num;
       }
       // Update _succ_num from v_out to join
-      for (u = v_out; u != join; u = _parent[u]) {
+      for (int u = v_out; u != join; u = _parent[u]) {
         _succ_num[u] -= old_succ_num;
       }
     }
 
-    // Update potentials
+    // Update potentials in the subtree that has been moved
     void updatePotential() {
-      Cost sigma = _forward[u_in] ?
-        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :
-        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];
-      // Update potentials in the subtree, which has been moved
+      Cost sigma = _pi[v_in] - _pi[u_in] -
+                   _pred_dir[u_in] * _cost[in_arc];
       int end = _thread[_last_succ[u_in]];
       for (int u = u_in; u != end; u = _thread[u]) {

lemon/path.h

@@ -44 +44 @@
   ///
   /// In a sense, the path can be treated as a list of arcs. The
-  /// lemon path type stores just this list. As a consequence, it
+  /// LEMON path type stores just this list. As a consequence, it
   /// cannot enumerate the nodes of the path and the source node of
   /// a zero length path is undefined.
@@ -136 +136 @@
     void clear() { head.clear(); tail.clear(); }
 
-    /// \brief The nth arc.
+    /// \brief The n-th arc.
     ///
     /// \pre \c n is in the <tt>[0..length() - 1]</tt> range.
@@ -144 +144 @@
     }
 
-    /// \brief Initialize arc iterator to point to the nth arc
+    /// \brief Initialize arc iterator to point to the n-th arc
     ///
     /// \pre \c n is in the <tt>[0..length() - 1]</tt> range.
@@ -232 +232 @@
   ///
   /// In a sense, the path can be treated as a list of arcs. The
-  /// lemon path type stores just this list. As a consequence it
+  /// LEMON path type stores just this list. As a consequence it
   /// cannot enumerate the nodes in the path and the zero length paths
   /// cannot store the source.
@@ -328 +328 @@
     void clear() { data.clear(); }
 
-    /// \brief The nth arc.
+    /// \brief The n-th arc.
     ///
     /// \pre \c n is in the <tt>[0..length() - 1]</tt> range.
@@ -335 +335 @@
     }
 
-    /// \brief  Initializes arc iterator to point to the nth arc.
+    /// \brief  Initializes arc iterator to point to the n-th arc.
     ArcIt nthIt(int n) const {
       return ArcIt(*this, n);
@@ -396 +396 @@
   ///
   /// In a sense, the path can be treated as a list of arcs. The
-  /// lemon path type stores just this list. As a consequence it
+  /// LEMON path type stores just this list. As a consequence it
   /// cannot enumerate the nodes in the path and the zero length paths
   /// cannot store the source.
@@ -505 +505 @@
     };
 
-    /// \brief The nth arc.
-    ///
-    /// This function looks for the nth arc in O(n) time.
+    /// \brief The n-th arc.
+    ///
+    /// This function looks for the n-th arc in O(n) time.
     /// \pre \c n is in the <tt>[0..length() - 1]</tt> range.
     const Arc& nth(int n) const {
@@ -517 +517 @@
     }
 
-    /// \brief Initializes arc iterator to point to the nth arc.
+    /// \brief Initializes arc iterator to point to the n-th arc.
     ArcIt nthIt(int n) const {
       Node *node = first;
@@ -736 +736 @@
   ///
   /// In a sense, the path can be treated as a list of arcs. The
-  /// lemon path type stores just this list. As a consequence it
+  /// LEMON path type stores just this list. As a consequence it
   /// cannot enumerate the nodes in the path and the source node of
   /// a zero length path is undefined.
@@ -832 +832 @@
     };
 
-    /// \brief The nth arc.
+    /// \brief The n-th arc.
     ///
     /// \pre \c n is in the <tt>[0..length() - 1]</tt> range.
@@ -839 +839 @@
     }
 
-    /// \brief The arc iterator pointing to the nth arc.
+    /// \brief The arc iterator pointing to the n-th arc.
     ArcIt nthIt(int n) const {
       return ArcIt(*this, n);
@@ -1043 +1043 @@
   ///
   /// In a sense, the path can be treated as a list of arcs. The
-  /// lemon path type stores only this list. As a consequence, it
+  /// LEMON path type stores only this list. As a consequence, it
   /// cannot enumerate the nodes in the path and the zero length paths
   /// cannot have a source node.

test/CMakeLists.txt

@@ -37 +37 @@
   maps_test
   matching_test
+  max_cardinality_search_test
+  max_clique_test
   min_cost_arborescence_test
   min_cost_flow_test
   min_mean_cycle_test
+  nagamochi_ibaraki_test
   path_test
   planarity_test

test/Makefile.am

@@ -35 +35 @@
         test/maps_test \
         test/matching_test \
+        test/max_cardinality_search_test \
+        test/max_clique_test \
         test/min_cost_arborescence_test \
         test/min_cost_flow_test \
         test/min_mean_cycle_test \
+        test/nagamochi_ibaraki_test \
         test/path_test \
         test/planarity_test \
@@ -79 +82 @@
 test_graph_test_SOURCES = test/graph_test.cc
 test_graph_utils_test_SOURCES = test/graph_utils_test.cc
+test_hao_orlin_test_SOURCES = test/hao_orlin_test.cc
 test_heap_test_SOURCES = test/heap_test.cc
 test_kruskal_test_SOURCES = test/kruskal_test.cc
-test_hao_orlin_test_SOURCES = test/hao_orlin_test.cc
 test_lgf_test_SOURCES = test/lgf_test.cc
 test_lp_test_SOURCES = test/lp_test.cc
@@ -87 +90 @@
 test_mip_test_SOURCES = test/mip_test.cc
 test_matching_test_SOURCES = test/matching_test.cc
+test_max_cardinality_search_test_SOURCES = test/max_cardinality_search_test.cc
+test_max_clique_test_SOURCES = test/max_clique_test.cc
 test_min_cost_arborescence_test_SOURCES = test/min_cost_arborescence_test.cc
 test_min_cost_flow_test_SOURCES = test/min_cost_flow_test.cc
 test_min_mean_cycle_test_SOURCES = test/min_mean_cycle_test.cc
+test_nagamochi_ibaraki_test_SOURCES = test/nagamochi_ibaraki_test.cc
 test_path_test_SOURCES = test/path_test.cc
 test_planarity_test_SOURCES = test/planarity_test.cc

test/graph_copy_test.cc

@@ -19 +19 @@
 #include <lemon/smart_graph.h>
 #include <lemon/list_graph.h>
+#include <lemon/static_graph.h>
 #include <lemon/lgf_reader.h>
 #include <lemon/error.h>
@@ -27 +28 @@
 using namespace lemon;
 
+template <typename GR>
 void digraph_copy_test() {
   const int nn = 10;
@@ -52 +54 @@
     }
   }
-
+  
   // Test digraph copy
-  ListDigraph to;
-  ListDigraph::NodeMap<int> tnm(to);
-  ListDigraph::ArcMap<int> tam(to);
-  ListDigraph::Node tn;
-  ListDigraph::Arc ta;
-
-  SmartDigraph::NodeMap<ListDigraph::Node> nr(from);
-  SmartDigraph::ArcMap<ListDigraph::Arc> er(from);
-
-  ListDigraph::NodeMap<SmartDigraph::Node> ncr(to);
-  ListDigraph::ArcMap<SmartDigraph::Arc> ecr(to);
+  GR to;
+  typename GR::template NodeMap<int> tnm(to);
+  typename GR::template ArcMap<int> tam(to);
+  typename GR::Node tn;
+  typename GR::Arc ta;
+
+  SmartDigraph::NodeMap<typename GR::Node> nr(from);
+  SmartDigraph::ArcMap<typename GR::Arc> er(from);
+
+  typename GR::template NodeMap<SmartDigraph::Node> ncr(to);
+  typename GR::template ArcMap<SmartDigraph::Arc> ecr(to);
 
   digraphCopy(from, to).
@@ -87 +89 @@
   }
 
-  for (ListDigraph::NodeIt it(to); it != INVALID; ++it) {
+  for (typename GR::NodeIt it(to); it != INVALID; ++it) {
     check(nr[ncr[it]] == it, "Wrong copy.");
   }
 
-  for (ListDigraph::ArcIt it(to); it != INVALID; ++it) {
+  for (typename GR::ArcIt it(to); it != INVALID; ++it) {
     check(er[ecr[it]] == it, "Wrong copy.");
   }
@@ -104 +106 @@
 }
 
+template <typename GR>
 void graph_copy_test() {
   const int nn = 10;
@@ -136 +139 @@
 
   // Test graph copy
-  ListGraph to;
-  ListGraph::NodeMap<int> tnm(to);
-  ListGraph::ArcMap<int> tam(to);
-  ListGraph::EdgeMap<int> tem(to);
-  ListGraph::Node tn;
-  ListGraph::Arc ta;
-  ListGraph::Edge te;
-
-  SmartGraph::NodeMap<ListGraph::Node> nr(from);
-  SmartGraph::ArcMap<ListGraph::Arc> ar(from);
-  SmartGraph::EdgeMap<ListGraph::Edge> er(from);
-
-  ListGraph::NodeMap<SmartGraph::Node> ncr(to);
-  ListGraph::ArcMap<SmartGraph::Arc> acr(to);
-  ListGraph::EdgeMap<SmartGraph::Edge> ecr(to);
+  GR to;
+  typename GR::template NodeMap<int> tnm(to);
+  typename GR::template ArcMap<int> tam(to);
+  typename GR::template EdgeMap<int> tem(to);
+  typename GR::Node tn;
+  typename GR::Arc ta;
+  typename GR::Edge te;
+
+  SmartGraph::NodeMap<typename GR::Node> nr(from);
+  SmartGraph::ArcMap<typename GR::Arc> ar(from);
+  SmartGraph::EdgeMap<typename GR::Edge> er(from);
+
+  typename GR::template NodeMap<SmartGraph::Node> ncr(to);
+  typename GR::template ArcMap<SmartGraph::Arc> acr(to);
+  typename GR::template EdgeMap<SmartGraph::Edge> ecr(to);
 
   graphCopy(from, to).
@@ -185 +188 @@
   }
 
-  for (ListGraph::NodeIt it(to); it != INVALID; ++it) {
+  for (typename GR::NodeIt it(to); it != INVALID; ++it) {
     check(nr[ncr[it]] == it, "Wrong copy.");
   }
 
-  for (ListGraph::ArcIt it(to); it != INVALID; ++it) {
+  for (typename GR::ArcIt it(to); it != INVALID; ++it) {
     check(ar[acr[it]] == it, "Wrong copy.");
   }
-  for (ListGraph::EdgeIt it(to); it != INVALID; ++it) {
+  for (typename GR::EdgeIt it(to); it != INVALID; ++it) {
     check(er[ecr[it]] == it, "Wrong copy.");
   }
@@ -209 +212 @@
 
 int main() {
-  digraph_copy_test();
-  graph_copy_test();
+  digraph_copy_test<SmartDigraph>();
+  digraph_copy_test<ListDigraph>();
+  digraph_copy_test<StaticDigraph>();
+  graph_copy_test<SmartGraph>();
+  graph_copy_test<ListGraph>();
 
   return 0;