diff --git a/lemon/bfs.h b/lemon/bfs.h
--- a/lemon/bfs.h
+++ b/lemon/bfs.h
@@ -607,11 +607,11 @@
     ///Executes the algorithm until the given target node is reached.
     ///
     ///This method runs the %BFS algorithm from the root node(s)
-    ///in order to compute the shortest path to \c dest.
+    ///in order to compute the shortest path to \c t.
     ///
     ///The algorithm computes
-    ///- the shortest path to \c dest,
-    ///- the distance of \c dest from the root(s).
+    ///- the shortest path to \c t,
+    ///- the distance of \c t from the root(s).
     ///
     ///\pre init() must be called and at least one root node should be
     ///added with addSource() before using this function.
@@ -623,10 +623,10 @@
     ///    b.processNextNode(t, reach);
     ///  }
     ///\endcode
-    void start(Node dest)
+    void start(Node t)
     {
       bool reach = false;
-      while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
+      while ( !emptyQueue() && !reach ) processNextNode(t, reach);
     }
 
     ///Executes the algorithm until a condition is met.
@@ -664,7 +664,7 @@
       return rnode;
     }
 
-    ///Runs the algorithm from the given node.
+    ///Runs the algorithm from the given source node.
 
     ///This method runs the %BFS algorithm from node \c s
     ///in order to compute the shortest path to each node.
@@ -688,10 +688,10 @@
     ///Finds the shortest path between \c s and \c t.
 
     ///This method runs the %BFS algorithm from node \c s
-    ///in order to compute the shortest path to \c t.
+    ///in order to compute the shortest path to node \c t
+    ///(it stops searching when \c t is processed).
     ///
-    ///\return The length of the shortest <tt>s</tt>--<tt>t</tt> path,
-    ///if \c t is reachable form \c s, \c 0 otherwise.
+    ///\return \c true if \c t is reachable form \c s.
     ///
     ///\note Apart from the return value, <tt>b.run(s,t)</tt> is just a
     ///shortcut of the following code.
@@ -700,11 +700,11 @@
     ///  b.addSource(s);
     ///  b.start(t);
     ///\endcode
-    int run(Node s,Node t) {
+    bool run(Node s,Node t) {
       init();
       addSource(s);
       start(t);
-      return reached(t) ? _curr_dist : 0;
+      return reached(t);
     }
 
     ///Runs the algorithm to visit all nodes in the digraph.
@@ -1621,11 +1621,11 @@
     /// Executes the algorithm until the given target node is reached.
     ///
     /// This method runs the %BFS algorithm from the root node(s)
-    /// in order to compute the shortest path to \c dest.
+    /// in order to compute the shortest path to \c t.
     ///
     /// The algorithm computes
-    /// - the shortest path to \c dest,
-    /// - the distance of \c dest from the root(s).
+    /// - the shortest path to \c t,
+    /// - the distance of \c t from the root(s).
     ///
     /// \pre init() must be called and at least one root node should be
     /// added with addSource() before using this function.
@@ -1637,9 +1637,9 @@
     ///     b.processNextNode(t, reach);
     ///   }
     /// \endcode
-    void start(Node dest) {
+    void start(Node t) {
       bool reach = false;
-      while ( !emptyQueue() && !reach ) processNextNode(dest, reach);
+      while ( !emptyQueue() && !reach ) processNextNode(t, reach);
     }
 
     /// \brief Executes the algorithm until a condition is met.
@@ -1677,7 +1677,7 @@
       return rnode;
     }
 
-    /// \brief Runs the algorithm from the given node.
+    /// \brief Runs the algorithm from the given source node.
     ///
     /// This method runs the %BFS algorithm from node \c s
     /// in order to compute the shortest path to each node.
@@ -1698,6 +1698,28 @@
       start();
     }
 
+    /// \brief Finds the shortest path between \c s and \c t.
+    ///
+    /// This method runs the %BFS algorithm from node \c s
+    /// in order to compute the shortest path to node \c t
+    /// (it stops searching when \c t is processed).
+    ///
+    /// \return \c true if \c t is reachable form \c s.
+    ///
+    /// \note Apart from the return value, <tt>b.run(s,t)</tt> is just a
+    /// shortcut of the following code.
+    ///\code
+    ///   b.init();
+    ///   b.addSource(s);
+    ///   b.start(t);
+    ///\endcode
+    bool run(Node s,Node t) {
+      init();
+      addSource(s);
+      start(t);
+      return reached(t);
+    }
+
     /// \brief Runs the algorithm to visit all nodes in the digraph.
     ///
     /// This method runs the %BFS algorithm in order to
diff --git a/lemon/dfs.h b/lemon/dfs.h
--- a/lemon/dfs.h
+++ b/lemon/dfs.h
@@ -558,17 +558,17 @@
     ///Executes the algorithm until the given target node is reached.
     ///
     ///This method runs the %DFS algorithm from the root node
-    ///in order to compute the DFS path to \c dest.
+    ///in order to compute the DFS path to \c t.
     ///
     ///The algorithm computes
-    ///- the %DFS path to \c dest,
-    ///- the distance of \c dest from the root in the %DFS tree.
+    ///- the %DFS path to \c t,
+    ///- the distance of \c t from the root in the %DFS tree.
     ///
     ///\pre init() must be called and a root node should be
     ///added with addSource() before using this function.
-    void start(Node dest)
+    void start(Node t)
     {
-      while ( !emptyQueue() && G->target(_stack[_stack_head])!=dest )
+      while ( !emptyQueue() && G->target(_stack[_stack_head])!=t )
         processNextArc();
     }
 
@@ -598,7 +598,7 @@
       return emptyQueue() ? INVALID : _stack[_stack_head];
     }
 
-    ///Runs the algorithm from the given node.
+    ///Runs the algorithm from the given source node.
 
     ///This method runs the %DFS algorithm from node \c s
     ///in order to compute the DFS path to each node.
@@ -622,10 +622,10 @@
     ///Finds the %DFS path between \c s and \c t.
 
     ///This method runs the %DFS algorithm from node \c s
-    ///in order to compute the DFS path to \c t.
+    ///in order to compute the DFS path to node \c t
+    ///(it stops searching when \c t is processed)
     ///
-    ///\return The length of the <tt>s</tt>--<tt>t</tt> DFS path,
-    ///if \c t is reachable form \c s, \c 0 otherwise.
+    ///\return \c true if \c t is reachable form \c s.
     ///
     ///\note Apart from the return value, <tt>d.run(s,t)</tt> is
     ///just a shortcut of the following code.
@@ -634,11 +634,11 @@
     ///  d.addSource(s);
     ///  d.start(t);
     ///\endcode
-    int run(Node s,Node t) {
+    bool run(Node s,Node t) {
       init();
       addSource(s);
       start(t);
-      return reached(t)?_stack_head+1:0;
+      return reached(t);
     }
 
     ///Runs the algorithm to visit all nodes in the digraph.
@@ -1526,16 +1526,16 @@
     /// Executes the algorithm until the given target node is reached.
     ///
     /// This method runs the %DFS algorithm from the root node
-    /// in order to compute the DFS path to \c dest.
+    /// in order to compute the DFS path to \c t.
     ///
     /// The algorithm computes
-    /// - the %DFS path to \c dest,
-    /// - the distance of \c dest from the root in the %DFS tree.
+    /// - the %DFS path to \c t,
+    /// - the distance of \c t from the root in the %DFS tree.
     ///
     /// \pre init() must be called and a root node should be added
     /// with addSource() before using this function.
-    void start(Node dest) {
-      while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != dest )
+    void start(Node t) {
+      while ( !emptyQueue() && _digraph->target(_stack[_stack_head]) != t )
         processNextArc();
     }
 
@@ -1564,7 +1564,7 @@
       return emptyQueue() ? INVALID : _stack[_stack_head];
     }
 
-    /// \brief Runs the algorithm from the given node.
+    /// \brief Runs the algorithm from the given source node.
     ///
     /// This method runs the %DFS algorithm from node \c s.
     /// in order to compute the DFS path to each node.
@@ -1588,10 +1588,10 @@
     /// \brief Finds the %DFS path between \c s and \c t.
 
     /// This method runs the %DFS algorithm from node \c s
-    /// in order to compute the DFS path to \c t.
+    /// in order to compute the DFS path to node \c t
+    /// (it stops searching when \c t is processed).
     ///
-    /// \return The length of the <tt>s</tt>--<tt>t</tt> DFS path,
-    /// if \c t is reachable form \c s, \c 0 otherwise.
+    /// \return \c true if \c t is reachable form \c s.
     ///
     /// \note Apart from the return value, <tt>d.run(s,t)</tt> is
     /// just a shortcut of the following code.
@@ -1600,11 +1600,11 @@
     ///   d.addSource(s);
     ///   d.start(t);
     ///\endcode
-    int run(Node s,Node t) {
+    bool run(Node s,Node t) {
       init();
       addSource(s);
       start(t);
-      return reached(t)?_stack_head+1:0;
+      return reached(t);
     }
 
     /// \brief Runs the algorithm to visit all nodes in the digraph.
diff --git a/lemon/dijkstra.h b/lemon/dijkstra.h
--- a/lemon/dijkstra.h
+++ b/lemon/dijkstra.h
@@ -728,23 +728,26 @@
       while ( !emptyQueue() ) processNextNode();
     }
 
-    ///Executes the algorithm until the given target node is reached.
+    ///Executes the algorithm until the given target node is processed.
 
-    ///Executes the algorithm until the given target node is reached.
+    ///Executes the algorithm until the given target node is processed.
     ///
     ///This method runs the %Dijkstra algorithm from the root node(s)
-    ///in order to compute the shortest path to \c dest.
+    ///in order to compute the shortest path to \c t.
     ///
     ///The algorithm computes
-    ///- the shortest path to \c dest,
-    ///- the distance of \c dest from the root(s).
+    ///- the shortest path to \c t,
+    ///- the distance of \c t from the root(s).
     ///
     ///\pre init() must be called and at least one root node should be
     ///added with addSource() before using this function.
-    void start(Node dest)
+    void start(Node t)
     {
-      while ( !_heap->empty() && _heap->top()!=dest ) processNextNode();
-      if ( !_heap->empty() ) finalizeNodeData(_heap->top(),_heap->prio());
+      while ( !_heap->empty() && _heap->top()!=t ) processNextNode();
+      if ( !_heap->empty() ) {
+        finalizeNodeData(_heap->top(),_heap->prio());
+        _heap->pop();
+      }
     }
 
     ///Executes the algorithm until a condition is met.
@@ -772,7 +775,7 @@
       return _heap->top();
     }
 
-    ///Runs the algorithm from the given node.
+    ///Runs the algorithm from the given source node.
 
     ///This method runs the %Dijkstra algorithm from node \c s
     ///in order to compute the shortest path to each node.
@@ -796,10 +799,10 @@
     ///Finds the shortest path between \c s and \c t.
 
     ///This method runs the %Dijkstra algorithm from node \c s
-    ///in order to compute the shortest path to \c t.
+    ///in order to compute the shortest path to node \c t
+    ///(it stops searching when \c t is processed).
     ///
-    ///\return The length of the shortest <tt>s</tt>--<tt>t</tt> path,
-    ///if \c t is reachable form \c s, \c 0 otherwise.
+    ///\return \c true if \c t is reachable form \c s.
     ///
     ///\note Apart from the return value, <tt>d.run(s,t)</tt> is just a
     ///shortcut of the following code.
@@ -808,11 +811,11 @@
     ///  d.addSource(s);
     ///  d.start(t);
     ///\endcode
-    Value run(Node s,Node t) {
+    bool run(Node s,Node t) {
       init();
       addSource(s);
       start(t);
-      return (*_pred)[t]==INVALID?OperationTraits::zero():(*_dist)[t];
+      return (*_heap_cross_ref)[t] == Heap::POST_HEAP;
     }
 
     ///@}
@@ -908,7 +911,7 @@
 
     ///Returns \c true if \c v is processed, i.e. the shortest
     ///path to \c v has already found.
-    ///\pre Either \ref run() or \ref start()
+    ///\pre Either \ref run() or \ref init()
     ///must be called before using this function.
     bool processed(Node v) const { return (*_heap_cross_ref)[v] ==
                                           Heap::POST_HEAP; }
@@ -917,8 +920,12 @@
 
     ///Returns the current distance of a node from the root(s).
     ///It may be decreased in the following processes.
-    ///\pre \c v should be reached but not processed.
-    Value currentDist(Node v) const { return (*_heap)[v]; }
+    ///\pre Either \ref run() or \ref init()
+    ///must be called before using this function and
+    ///node \c v must be reached but not necessarily processed.
+    Value currentDist(Node v) const {
+      return processed(v) ? (*_dist)[v] : (*_heap)[v];
+    }
 
     ///@}
   };
diff --git a/test/bfs_test.cc b/test/bfs_test.cc
--- a/test/bfs_test.cc
+++ b/test/bfs_test.cc
@@ -54,27 +54,52 @@
 {
   typedef concepts::Digraph Digraph;
   typedef Bfs<Digraph> BType;
+  typedef Digraph::Node Node;
+  typedef Digraph::Arc Arc;
 
   Digraph G;
-  Digraph::Node n;
-  Digraph::Arc e;
+  Node s, t;
+  Arc e;
   int l;
   bool b;
   BType::DistMap d(G);
   BType::PredMap p(G);
+  Path<Digraph> pp;
 
-  BType bfs_test(G);
+  {
+    BType bfs_test(G);
 
-  bfs_test.run(n);
+    bfs_test.run(s);
+    bfs_test.run(s,t);
+    bfs_test.run();
 
-  l  = bfs_test.dist(n);
-  e  = bfs_test.predArc(n);
-  n  = bfs_test.predNode(n);
-  d  = bfs_test.distMap();
-  p  = bfs_test.predMap();
-  b  = bfs_test.reached(n);
+    l  = bfs_test.dist(t);
+    e  = bfs_test.predArc(t);
+    s  = bfs_test.predNode(t);
+    b  = bfs_test.reached(t);
+    d  = bfs_test.distMap();
+    p  = bfs_test.predMap();
+    pp = bfs_test.path(t);
+  }
+  {
+    BType
+      ::SetPredMap<concepts::ReadWriteMap<Node,Arc> >
+      ::SetDistMap<concepts::ReadWriteMap<Node,int> >
+      ::SetReachedMap<concepts::ReadWriteMap<Node,bool> >
+      ::SetProcessedMap<concepts::WriteMap<Node,bool> >
+      ::SetStandardProcessedMap
+      ::Create bfs_test(G);
 
-  Path<Digraph> pp = bfs_test.path(n);
+    bfs_test.run(s);
+    bfs_test.run(s,t);
+    bfs_test.run();
+
+    l  = bfs_test.dist(t);
+    e  = bfs_test.predArc(t);
+    s  = bfs_test.predNode(t);
+    b  = bfs_test.reached(t);
+    pp = bfs_test.path(t);
+  }
 }
 
 void checkBfsFunctionCompile()
diff --git a/test/dfs_test.cc b/test/dfs_test.cc
--- a/test/dfs_test.cc
+++ b/test/dfs_test.cc
@@ -56,27 +56,52 @@
 {
   typedef concepts::Digraph Digraph;
   typedef Dfs<Digraph> DType;
+  typedef Digraph::Node Node;
+  typedef Digraph::Arc Arc;
 
   Digraph G;
-  Digraph::Node n;
-  Digraph::Arc e;
+  Node s, t;
+  Arc e;
   int l;
   bool b;
   DType::DistMap d(G);
   DType::PredMap p(G);
+  Path<Digraph> pp;
 
-  DType dfs_test(G);
+  {
+    DType dfs_test(G);
 
-  dfs_test.run(n);
+    dfs_test.run(s);
+    dfs_test.run(s,t);
+    dfs_test.run();
 
-  l  = dfs_test.dist(n);
-  e  = dfs_test.predArc(n);
-  n  = dfs_test.predNode(n);
-  d  = dfs_test.distMap();
-  p  = dfs_test.predMap();
-  b  = dfs_test.reached(n);
+    l  = dfs_test.dist(t);
+    e  = dfs_test.predArc(t);
+    s  = dfs_test.predNode(t);
+    b  = dfs_test.reached(t);
+    d  = dfs_test.distMap();
+    p  = dfs_test.predMap();
+    pp = dfs_test.path(t);
+  }
+  {
+    DType
+      ::SetPredMap<concepts::ReadWriteMap<Node,Arc> >
+      ::SetDistMap<concepts::ReadWriteMap<Node,int> >
+      ::SetReachedMap<concepts::ReadWriteMap<Node,bool> >
+      ::SetProcessedMap<concepts::WriteMap<Node,bool> >
+      ::SetStandardProcessedMap
+      ::Create dfs_test(G);
 
-  Path<Digraph> pp = dfs_test.path(n);
+    dfs_test.run(s);
+    dfs_test.run(s,t);
+    dfs_test.run();
+
+    l  = dfs_test.dist(t);
+    e  = dfs_test.predArc(t);
+    s  = dfs_test.predNode(t);
+    b  = dfs_test.reached(t);
+    pp = dfs_test.path(t);
+  }
 }
 
 void checkDfsFunctionCompile()
diff --git a/test/dijkstra_test.cc b/test/dijkstra_test.cc
--- a/test/dijkstra_test.cc
+++ b/test/dijkstra_test.cc
@@ -22,6 +22,7 @@
 #include <lemon/lgf_reader.h>
 #include <lemon/dijkstra.h>
 #include <lemon/path.h>
+#include <lemon/bin_heap.h>
 
 #include "graph_test.h"
 #include "test_tools.h"
@@ -55,28 +56,54 @@
   typedef concepts::Digraph Digraph;
   typedef concepts::ReadMap<Digraph::Arc,VType> LengthMap;
   typedef Dijkstra<Digraph, LengthMap> DType;
+  typedef Digraph::Node Node;
+  typedef Digraph::Arc Arc;
 
   Digraph G;
-  Digraph::Node n;
-  Digraph::Arc e;
+  Node s, t;
+  Arc e;
   VType l;
   bool b;
   DType::DistMap d(G);
   DType::PredMap p(G);
   LengthMap length;
+  Path<Digraph> pp;
 
-  DType dijkstra_test(G,length);
+  {
+    DType dijkstra_test(G,length);
 
-  dijkstra_test.run(n);
+    dijkstra_test.run(s);
+    dijkstra_test.run(s,t);
 
-  l  = dijkstra_test.dist(n);
-  e  = dijkstra_test.predArc(n);
-  n  = dijkstra_test.predNode(n);
-  d  = dijkstra_test.distMap();
-  p  = dijkstra_test.predMap();
-  b  = dijkstra_test.reached(n);
+    l  = dijkstra_test.dist(t);
+    e  = dijkstra_test.predArc(t);
+    s  = dijkstra_test.predNode(t);
+    b  = dijkstra_test.reached(t);
+    d  = dijkstra_test.distMap();
+    p  = dijkstra_test.predMap();
+    pp = dijkstra_test.path(t);
+  }
+  {
+    DType
+      ::SetPredMap<concepts::ReadWriteMap<Node,Arc> >
+      ::SetDistMap<concepts::ReadWriteMap<Node,VType> >
+      ::SetProcessedMap<concepts::WriteMap<Node,bool> >
+      ::SetStandardProcessedMap
+      ::SetOperationTraits<DijkstraWidestPathOperationTraits<VType> >
+      ::SetHeap<BinHeap<VType, concepts::ReadWriteMap<Node,int> > >
+      ::SetStandardHeap<BinHeap<VType, concepts::ReadWriteMap<Node,int> > >
+      ::Create dijkstra_test(G,length);
 
-  Path<Digraph> pp = dijkstra_test.path(n);
+    dijkstra_test.run(s);
+    dijkstra_test.run(s,t);
+
+    l  = dijkstra_test.dist(t);
+    e  = dijkstra_test.predArc(t);
+    s  = dijkstra_test.predNode(t);
+    b  = dijkstra_test.reached(t);
+    pp = dijkstra_test.path(t);
+  }
+
 }
 
 void checkDijkstraFunctionCompile()