Fix the O(n^3) performance issue in is_connected utility function

include/boost/graph/graph_utility.hpp

@@ -23,6 +23,8 @@
 #include <boost/graph/properties.hpp>
 #include <boost/pending/container_traits.hpp>
 #include <boost/graph/depth_first_search.hpp>
+// only for backward-compatibility error message
+#include <boost/graph/is_connected.hpp>
 // iota moved to detail/algorithm.hpp
 #include <boost/detail/algorithm.hpp>
 
@@ -339,26 +341,7 @@ inline bool is_reachable(
     return get(color, y) != color_traits< ColorValue >::white();
 }
 
-// Is the undirected graph connected?
-// Is the directed graph strongly connected?
-template < typename VertexListGraph, typename VertexColorMap >
-inline bool is_connected(const VertexListGraph& g, VertexColorMap color)
-{
-    typedef typename property_traits< VertexColorMap >::value_type ColorValue;
-    typedef color_traits< ColorValue > Color;
-    typename graph_traits< VertexListGraph >::vertex_iterator ui, ui_end, vi,
-        vi_end, ci, ci_end;
-    for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui)
-        for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
-            if (*ui != *vi)
-            {
-                for (boost::tie(ci, ci_end) = vertices(g); ci != ci_end; ++ci)
-                    put(color, *ci, Color::white());
-                if (!is_reachable(*ui, *vi, g, color))
-                    return false;
-            }
-    return true;
-}
+// is_connected is moved to `is_connected.hpp`
 
 template < typename Graph >
 bool is_self_loop(

include/boost/graph/is_connected.hpp

@@ -0,0 +1,241 @@
+#ifndef BOOST_GRAPH_IS_CONNECTED_HPP
+#define BOOST_GRAPH_IS_CONNECTED_HPP
+
+#include <boost/graph/graph_traits.hpp>
+#include <boost/graph/strong_components.hpp>
+#include <boost/graph/depth_first_search.hpp>
+#include <boost/graph/neighbor_bfs.hpp>
+#include <boost/graph/create_condensation_graph.hpp>
+#include <boost/graph/adjacency_list.hpp>
+
+namespace boost
+{
+
+struct connected_kind {
+    enum weak_t { weak };
+    enum unilateral_t { unilateral };
+    enum strong_t { strong };
+    enum unspecified_t { unspecified };
+};
+
+// used for static assert below
+BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(has_value_type_ic, value_type, false)
+
+template < typename Graph, typename ConnectedKind = connected_kind::unspecified_t >
+inline bool is_connected(const Graph& g, ConnectedKind kind = connected_kind::unspecified)
+{
+    // Issue error message if these functions are called with a ColorMap.
+    // This is to gracefully handle possible old usages of is_connected.
+    // todo: consider checking for ColorValueConcept as well
+    BOOST_STATIC_ASSERT_MSG(
+        (mpl::not_< has_value_type_ic< ConnectedKind > >::value),
+        "ColorMap argument to is_connected is deprecated. Omit the second "
+        "argument for undirected graphs or specify connected_kind::strong "
+        "to preserve the old behavior.");
+
+    typedef typename graph_traits< Graph >::directed_category Cat;
+    BOOST_STATIC_ASSERT_MSG(
+        (mpl::not_< mpl::and_ <
+                is_same < ConnectedKind, connected_kind::unspecified_t >,
+                is_directed_graph< Graph > > >::value),
+        "connected_kind must be specified for directed graphs");
+
+    return is_connected_dispatch(g, Cat(), kind);
+}
+
+// Undirected graph
+template < typename IncidenceGraph, typename ConnectedKind >
+inline bool is_connected_dispatch(const IncidenceGraph& g, undirected_tag,
+                                  ConnectedKind)
+{
+    // ignore the connection kind for undirected graph
+    return is_connected_undirected(g);
+}
+
+template < typename IncidenceGraph >
+inline bool is_connected_undirected(const IncidenceGraph& g)
+{
+    BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< IncidenceGraph >));
+
+    return is_connected_undirected(g,
+        make_two_bit_color_map(num_vertices(g), get(boost::vertex_index, g)));
+}
+
+// color should start out white for every vertex
+template < typename IncidenceGraph, typename VertexColorMap >
+inline bool is_connected_undirected(const IncidenceGraph& g,
+    VertexColorMap colormap)
+{
+    typedef typename property_traits< VertexColorMap >::value_type ColorValue;
+    typedef color_traits< ColorValue > Color;
+
+    default_dfs_visitor vis;
+    depth_first_visit(g, detail::get_default_starting_vertex(g), vis, colormap);
+
+    // If an undirected graph is connected, then each vertex is reachable in a
+    // single DFS visit. If any vertex was unreachable, grpah is not connected.
+    typename graph_traits< IncidenceGraph >::vertex_iterator ui, ui_end;
+    for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui)
+        if (get(colormap, *ui) == Color::white())
+            return false;
+    return true;
+}
+
+// Directed graph, strongly connected
+template < typename IncidenceGraph >
+inline bool is_connected_dispatch(const IncidenceGraph& g, directed_tag,
+                                  connected_kind::strong_t)
+{
+    return is_strongly_connected(g);
+}
+
+template < typename Graph >
+inline bool is_strongly_connected(const Graph& g)
+{
+    // A directed graph is stronly connected if and only if all its vertices
+    // are in a sinlge stronly connected component
+
+    BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< Graph >));
+    BOOST_STATIC_ASSERT((is_directed_graph< Graph >::value));
+
+    // Run the Tarjan's SCC algorithm
+    std::vector< size_t > comp_map(num_vertices(g));
+    size_t num_scc = strong_components(
+        g, make_iterator_property_map(comp_map.begin(), get(vertex_index, g)));
+
+    return num_scc == 1;
+}
+
+// Directed graph, weakly connected
+template < typename IncidenceGraph >
+inline bool is_connected_dispatch(const IncidenceGraph& g, directed_tag,
+                                  connected_kind::weak_t)
+{
+    return is_weakly_connected(g);
+}
+
+template < typename BidirectionalGraph >
+inline bool is_weakly_connected(const BidirectionalGraph& g)
+{
+    BOOST_CONCEPT_ASSERT((BidirectionalGraphConcept< BidirectionalGraph >));
+
+    // For now do an undirected BFS walk
+    return is_weakly_connected(g,
+        make_two_bit_color_map(num_vertices(g), get(boost::vertex_index, g)));
+}
+
+template < typename BidirectionalGraph , typename VertexColorMap >
+inline bool is_weakly_connected(const BidirectionalGraph& g, VertexColorMap colormap)
+{
+    // A directed graph is weakly connected if and only if all its vertices
+    // can be reached in a single undirected BFS (or DFS) visit.
+    typedef typename property_traits< VertexColorMap >::value_type ColorValue;
+    typedef color_traits< ColorValue > Color;
+
+    // todo: consider reimplementing this as DFS (is_connected above) over an
+    // as_undirected adaptor.
+
+    neighbor_breadth_first_visit(
+        g,
+        detail::get_default_starting_vertex(g),
+        color_map(colormap)
+    );
+
+    typename graph_traits< BidirectionalGraph >::vertex_iterator ui, ui_end;
+    for (boost::tie(ui, ui_end) = vertices(g); ui != ui_end; ++ui)
+        if (get(colormap, *ui) == Color::white())
+            return false;
+    return true;
+}
+
+// Directed graph, unilaterally connected
+template < typename IncidenceGraph >
+inline bool is_connected_dispatch(const IncidenceGraph& g, directed_tag,
+                                  connected_kind::unilateral_t)
+{
+    return is_unilaterally_connected(g);
+}
+
+namespace detail {
+
+    template < typename Graph >
+    struct unique_topological_order_visitor : public default_dfs_visitor
+    {
+        typedef typename graph_traits< Graph >::vertex_descriptor vertex_t;
+        vertex_t last_vertex;
+        bool& result;
+
+        unique_topological_order_visitor(bool& result)
+            : last_vertex(graph_traits< Graph >::null_vertex()), result(result)
+        {
+            result = true;
+        }
+
+        // Check that each finished vertex has an arrow to the last finished one
+        template < typename Vertex, typename G >
+        void finish_vertex(const Vertex& u, const G& g)
+        {
+            // todo: consider using TerminatorFunc or an exception to exit
+            // the DFS early (performance optimization)
+            if (result == false)
+                return;
+
+            if (last_vertex != graph_traits< Graph >::null_vertex())
+            {
+                if (!edge(u, last_vertex, g).second)
+                {
+                    result = false;
+                }
+            }
+            last_vertex = u;
+        }
+
+    };
+
+}
+
+// Checks if the graph is in unique topological order, i.e. linear
+template < typename Graph >
+bool has_unique_topological_order(const Graph& g)
+{
+    bool result;
+    detail::unique_topological_order_visitor<Graph> vis(result);
+    depth_first_search(g, visitor(vis));
+    return result;
+}
+
+
+template < typename Graph >
+inline bool is_unilaterally_connected(const Graph& g)
+{
+    // A directed graph is unilaterally connected if and only if its
+    // condensation graph is in unique topological order.
+    // Warning: condensation might be slow and consume 2x memory for the graph.
+
+    BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< Graph >));
+    // See comment about renumber_vertex_indices above
+    // BOOST_CONCEPT_ASSERT((VertexIndexGraphConcept< Graph >));
+    BOOST_STATIC_ASSERT((is_directed_graph< Graph >::value));
+
+    // Run the Tarjan's SCC algorithm
+    std::vector< size_t > comp_number(num_vertices(g));
+    size_t num_scc = strong_components(
+        g, make_iterator_property_map(comp_number.begin(), get(vertex_index, g)));
+    if (num_scc == 1) // strongly connected case
+        return true;
+
+    // Build the condensation graph
+    adjacency_list<> c;
+    std::vector< std::vector< typename graph_traits< Graph >::vertices_size_type > > components;
+    build_component_lists(g, num_scc, comp_number, components);
+    create_condensation_graph(g, components, comp_number, c);
+    // Check if the condensation is linear
+    return has_unique_topological_order(c);
+}
+
+
+} // namespace boost
+
+#endif /* BOOST_GRAPH_IS_CONNECTED_HPP */
+
+

include/boost/pending/detail/disjoint_sets.hpp

@@ -7,12 +7,14 @@
 #define BOOST_DETAIL_DISJOINT_SETS_HPP
 
 #include <cassert>
+#include <boost/property_map/property_map.hpp>
 
 namespace boost
 {
 
 namespace detail
 {
+    using boost::get;
 
     template < class ParentPA, class Vertex >
     Vertex find_representative_with_path_halving(ParentPA p, Vertex v)

test/Jamfile.v2

@@ -159,6 +159,7 @@ alias graph_test_regular :
     [ run delete_edge.cpp ]
     [ run johnson-test.cpp ]
     [ run lvalue_pmap.cpp ]
+    [ run is_connected.cpp ]
     ;
 
 alias graph_test_with_filesystem : :