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chromium / webm / webmlive / 30da35b5e63e20b1436b52538052db391a4f471a / . / third_party / boost / include / boost / graph / planar_detail / boyer_myrvold_impl.hpp
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//=======================================================================
// Copyright (c) Aaron Windsor 2007
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//=======================================================================
#ifndef __BOYER_MYRVOLD_IMPL_HPP__
#define __BOYER_MYRVOLD_IMPL_HPP__
#include <vector>
#include <list>
#include <boost/utility.hpp> //for boost::next
#include <boost/config.hpp> //for std::min macros
#include <boost/shared_ptr.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/graph/planar_detail/face_handles.hpp>
#include <boost/graph/planar_detail/face_iterators.hpp>
#include <boost/graph/planar_detail/bucket_sort.hpp>
namespace boost
{
namespace detail {
enum bm_case_t{BM_NO_CASE_CHOSEN, BM_CASE_A, BM_CASE_B, BM_CASE_C, BM_CASE_D, BM_CASE_E};
}
template<typename LowPointMap, typename DFSParentMap,
typename DFSNumberMap, typename LeastAncestorMap,
typename DFSParentEdgeMap, typename SizeType>
struct planar_dfs_visitor : public dfs_visitor<>
{
planar_dfs_visitor(LowPointMap lpm, DFSParentMap dfs_p,
DFSNumberMap dfs_n, LeastAncestorMap lam,
DFSParentEdgeMap dfs_edge)
: low(lpm),
parent(dfs_p),
df_number(dfs_n),
least_ancestor(lam),
df_edge(dfs_edge),
count(0)
{}
template <typename Vertex, typename Graph>
void start_vertex(const Vertex& u, Graph&)
{
put(parent, u, u);
put(least_ancestor, u, count);
}
template <typename Vertex, typename Graph>
void discover_vertex(const Vertex& u, Graph&)
{
put(low, u, count);
put(df_number, u, count);
++count;
}
template <typename Edge, typename Graph>
void tree_edge(const Edge& e, Graph& g)
{
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
vertex_t s(source(e,g));
vertex_t t(target(e,g));
put(parent, t, s);
put(df_edge, t, e);
put(least_ancestor, t, get(df_number, s));
}
template <typename Edge, typename Graph>
void back_edge(const Edge& e, Graph& g)
{
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
typedef typename graph_traits<Graph>::vertices_size_type v_size_t;
vertex_t s(source(e,g));
vertex_t t(target(e,g));
BOOST_USING_STD_MIN();
if ( t != get(parent, s) ) {
v_size_t s_low_df_number = get(low, s);
v_size_t t_df_number = get(df_number, t);
v_size_t s_least_ancestor_df_number = get(least_ancestor, s);
put(low, s,
min BOOST_PREVENT_MACRO_SUBSTITUTION(s_low_df_number,
t_df_number)
);
put(least_ancestor, s,
min BOOST_PREVENT_MACRO_SUBSTITUTION(s_least_ancestor_df_number,
t_df_number
)
);
}
}
template <typename Vertex, typename Graph>
void finish_vertex(const Vertex& u, Graph&)
{
typedef typename graph_traits<Graph>::vertices_size_type v_size_t;
Vertex u_parent = get(parent, u);
v_size_t u_parent_lowpoint = get(low, u_parent);
v_size_t u_lowpoint = get(low, u);
BOOST_USING_STD_MIN();
if (u_parent != u)
{
put(low, u_parent,
min BOOST_PREVENT_MACRO_SUBSTITUTION(u_lowpoint,
u_parent_lowpoint
)
);
}
}
LowPointMap low;
DFSParentMap parent;
DFSNumberMap df_number;
LeastAncestorMap least_ancestor;
DFSParentEdgeMap df_edge;
SizeType count;
};
template <typename Graph,
typename VertexIndexMap,
typename StoreOldHandlesPolicy = graph::detail::store_old_handles,
typename StoreEmbeddingPolicy = graph::detail::recursive_lazy_list
>
class boyer_myrvold_impl
{
typedef typename graph_traits<Graph>::vertices_size_type v_size_t;
typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
typedef typename graph_traits<Graph>::edge_descriptor edge_t;
typedef typename graph_traits<Graph>::vertex_iterator vertex_iterator_t;
typedef typename graph_traits<Graph>::edge_iterator edge_iterator_t;
typedef typename graph_traits<Graph>::out_edge_iterator
out_edge_iterator_t;
typedef graph::detail::face_handle
<Graph, StoreOldHandlesPolicy, StoreEmbeddingPolicy> face_handle_t;
typedef std::vector<vertex_t> vertex_vector_t;
typedef std::vector<edge_t> edge_vector_t;
typedef std::list<vertex_t> vertex_list_t;
typedef std::list< face_handle_t > face_handle_list_t;
typedef boost::shared_ptr< face_handle_list_t > face_handle_list_ptr_t;
typedef boost::shared_ptr< vertex_list_t > vertex_list_ptr_t;
typedef boost::tuple<vertex_t, bool, bool> merge_stack_frame_t;
typedef std::vector<merge_stack_frame_t> merge_stack_t;
template <typename T>
struct map_vertex_to_
{
typedef iterator_property_map
<typename std::vector<T>::iterator, VertexIndexMap> type;
};
typedef typename map_vertex_to_<v_size_t>::type vertex_to_v_size_map_t;
typedef typename map_vertex_to_<vertex_t>::type vertex_to_vertex_map_t;
typedef typename map_vertex_to_<edge_t>::type vertex_to_edge_map_t;
typedef typename map_vertex_to_<vertex_list_ptr_t>::type
vertex_to_vertex_list_ptr_map_t;
typedef typename map_vertex_to_< edge_vector_t >::type
vertex_to_edge_vector_map_t;
typedef typename map_vertex_to_<bool>::type vertex_to_bool_map_t;
typedef typename map_vertex_to_<face_handle_t>::type
vertex_to_face_handle_map_t;
typedef typename map_vertex_to_<face_handle_list_ptr_t>::type
vertex_to_face_handle_list_ptr_map_t;
typedef typename map_vertex_to_<typename vertex_list_t::iterator>::type
vertex_to_separated_node_map_t;
template <typename BicompSideToTraverse = single_side,
typename VisitorType = lead_visitor,
typename Time = current_iteration>
struct face_vertex_iterator
{
typedef face_iterator<Graph,
vertex_to_face_handle_map_t,
vertex_t,
BicompSideToTraverse,
VisitorType,
Time>
type;
};
template <typename BicompSideToTraverse = single_side,
typename Time = current_iteration>
struct face_edge_iterator
{
typedef face_iterator<Graph,
vertex_to_face_handle_map_t,
edge_t,
BicompSideToTraverse,
lead_visitor,
Time>
type;
};
public:
boyer_myrvold_impl(const Graph& arg_g, VertexIndexMap arg_vm):
g(arg_g),
vm(arg_vm),
low_point_vector(num_vertices(g)),
dfs_parent_vector(num_vertices(g)),
dfs_number_vector(num_vertices(g)),
least_ancestor_vector(num_vertices(g)),
pertinent_roots_vector(num_vertices(g)),
backedge_flag_vector(num_vertices(g), num_vertices(g) + 1),
visited_vector(num_vertices(g), num_vertices(g) + 1),
face_handles_vector(num_vertices(g)),
dfs_child_handles_vector(num_vertices(g)),
separated_dfs_child_list_vector(num_vertices(g)),
separated_node_in_parent_list_vector(num_vertices(g)),
canonical_dfs_child_vector(num_vertices(g)),
flipped_vector(num_vertices(g), false),
backedges_vector(num_vertices(g)),
dfs_parent_edge_vector(num_vertices(g)),
vertices_by_dfs_num(num_vertices(g)),
low_point(low_point_vector.begin(), vm),
dfs_parent(dfs_parent_vector.begin(), vm),
dfs_number(dfs_number_vector.begin(), vm),
least_ancestor(least_ancestor_vector.begin(), vm),
pertinent_roots(pertinent_roots_vector.begin(), vm),
backedge_flag(backedge_flag_vector.begin(), vm),
visited(visited_vector.begin(), vm),
face_handles(face_handles_vector.begin(), vm),
dfs_child_handles(dfs_child_handles_vector.begin(), vm),
separated_dfs_child_list(separated_dfs_child_list_vector.begin(), vm),
separated_node_in_parent_list
(separated_node_in_parent_list_vector.begin(), vm),
canonical_dfs_child(canonical_dfs_child_vector.begin(), vm),
flipped(flipped_vector.begin(), vm),
backedges(backedges_vector.begin(), vm),
dfs_parent_edge(dfs_parent_edge_vector.begin(), vm)
{
planar_dfs_visitor
<vertex_to_v_size_map_t, vertex_to_vertex_map_t,
vertex_to_v_size_map_t, vertex_to_v_size_map_t,
vertex_to_edge_map_t, v_size_t> vis
(low_point, dfs_parent, dfs_number, least_ancestor, dfs_parent_edge);
// Perform a depth-first search to find each vertex's low point, least
// ancestor, and dfs tree information
depth_first_search(g, visitor(vis).vertex_index_map(vm));
// Sort vertices by their lowpoint - need this later in the constructor
vertex_vector_t vertices_by_lowpoint(num_vertices(g));
std::copy( vertices(g).first, vertices(g).second,
vertices_by_lowpoint.begin()
);
bucket_sort(vertices_by_lowpoint.begin(),
vertices_by_lowpoint.end(),
low_point,
num_vertices(g)
);
// Sort vertices by their dfs number - need this to iterate by reverse
// DFS number in the main loop.
std::copy( vertices(g).first, vertices(g).second,
vertices_by_dfs_num.begin()
);
bucket_sort(vertices_by_dfs_num.begin(),
vertices_by_dfs_num.end(),
dfs_number,
num_vertices(g)
);
// Initialize face handles. A face handle is an abstraction that serves
// two uses in our implementation - it allows us to efficiently move
// along the outer face of embedded bicomps in a partially embedded
// graph, and it provides storage for the planar embedding. Face
// handles are implemented by a sequence of edges and are associated
// with a particular vertex - the sequence of edges represents the
// current embedding of edges around that vertex, and the first and
// last edges in the sequence represent the pair of edges on the outer
// face that are adjacent to the associated vertex. This lets us embed
// edges in the graph by just pushing them on the front or back of the
// sequence of edges held by the face handles.
//
// Our algorithm starts with a DFS tree of edges (where every vertex is
// an articulation point and every edge is a singleton bicomp) and
// repeatedly merges bicomps by embedding additional edges. Note that
// any bicomp at any point in the algorithm can be associated with a
// unique edge connecting the vertex of that bicomp with the lowest DFS
// number (which we refer to as the "root" of the bicomp) with its DFS
// child in the bicomp: the existence of two such edges would contradict
// the properties of a DFS tree. We refer to the DFS child of the root
// of a bicomp as the "canonical DFS child" of the bicomp. Note that a
// vertex can be the root of more than one bicomp.
//
// We move around the external faces of a bicomp using a few property
// maps, which we'll initialize presently:
//
// - face_handles: maps a vertex to a face handle that can be used to
// move "up" a bicomp. For a vertex that isn't an articulation point,
// this holds the face handles that can be used to move around that
// vertex's unique bicomp. For a vertex that is an articulation point,
// this holds the face handles associated with the unique bicomp that
// the vertex is NOT the root of. These handles can therefore be used
// to move from any point on the outer face of the tree of bicomps
// around the current outer face towards the root of the DFS tree.
//
// - dfs_child_handles: these are used to hold face handles for
// vertices that are articulation points - dfs_child_handles[v] holds
// the face handles corresponding to vertex u in the bicomp with root
// u and canonical DFS child v.
//
// - canonical_dfs_child: this property map allows one to determine the
// canonical DFS child of a bicomp while traversing the outer face.
// This property map is only valid when applied to one of the two
// vertices adjacent to the root of the bicomp on the outer face. To
// be more precise, if v is the canonical DFS child of a bicomp,
// canonical_dfs_child[dfs_child_handles[v].first_vertex()] == v and
// canonical_dfs_child[dfs_child_handles[v].second_vertex()] == v.
//
// - pertinent_roots: given a vertex v, pertinent_roots[v] contains a
// list of face handles pointing to the top of bicomps that need to
// be visited by the current walkdown traversal (since they lead to
// backedges that need to be embedded). These lists are populated by
// the walkup and consumed by the walkdown.
vertex_iterator_t vi, vi_end;
for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
{
vertex_t v(*vi);
vertex_t parent = dfs_parent[v];
if (parent != v)
{
edge_t parent_edge = dfs_parent_edge[v];
add_to_embedded_edges(parent_edge, StoreOldHandlesPolicy());
face_handles[v] = face_handle_t(v, parent_edge, g);
dfs_child_handles[v] = face_handle_t(parent, parent_edge, g);
}
else
{
face_handles[v] = face_handle_t(v);
dfs_child_handles[v] = face_handle_t(parent);
}
canonical_dfs_child[v] = v;
pertinent_roots[v] = face_handle_list_ptr_t(new face_handle_list_t);
separated_dfs_child_list[v] = vertex_list_ptr_t(new vertex_list_t);
}
// We need to create a list of not-yet-merged depth-first children for
// each vertex that will be updated as bicomps get merged. We sort each
// list by ascending lowpoint, which allows the externally_active
// function to run in constant time, and we keep a pointer to each
// vertex's representation in its parent's list, which allows merging
//in constant time.
for(typename vertex_vector_t::iterator itr =
vertices_by_lowpoint.begin();
itr != vertices_by_lowpoint.end(); ++itr)
{
vertex_t v(*itr);
vertex_t parent(dfs_parent[v]);
if (v != parent)
{
separated_node_in_parent_list[v] =
separated_dfs_child_list[parent]->insert
(separated_dfs_child_list[parent]->end(), v);
}
}
// The merge stack holds path information during a walkdown iteration
merge_stack.reserve(num_vertices(g));
}
bool is_planar()
{
// This is the main algorithm: starting with a DFS tree of embedded
// edges (which, since it's a tree, is planar), iterate through all
// vertices by reverse DFS number, attempting to embed all backedges
// connecting the current vertex to vertices with higher DFS numbers.
//
// The walkup is a procedure that examines all such backedges and sets
// up the required data structures so that they can be searched by the
// walkdown in linear time. The walkdown does the actual work of
// embedding edges and flipping bicomps, and can identify when it has
// come across a kuratowski subgraph.
//
// store_old_face_handles caches face handles from the previous
// iteration - this is used only for the kuratowski subgraph isolation,
// and is therefore dispatched based on the StoreOldHandlesPolicy.
//
// clean_up_embedding does some clean-up and fills in values that have
// to be computed lazily during the actual execution of the algorithm
// (for instance, whether or not a bicomp is flipped in the final
// embedding). It's dispatched on the the StoreEmbeddingPolicy, since
// it's not needed if an embedding isn't desired.
typename vertex_vector_t::reverse_iterator vi, vi_end;
vi_end = vertices_by_dfs_num.rend();
for(vi = vertices_by_dfs_num.rbegin(); vi != vi_end; ++vi)
{
store_old_face_handles(StoreOldHandlesPolicy());
vertex_t v(*vi);
walkup(v);
if (!walkdown(v))
return false;
}
clean_up_embedding(StoreEmbeddingPolicy());
return true;
}
private:
void walkup(vertex_t v)
{
// The point of the walkup is to follow all backedges from v to
// vertices with higher DFS numbers, and update pertinent_roots
// for the bicomp roots on the path from backedge endpoints up
// to v. This will set the stage for the walkdown to efficiently
// traverse the graph of bicomps down from v.
typedef typename face_vertex_iterator<both_sides>::type walkup_iterator_t;
out_edge_iterator_t oi, oi_end;
for(boost::tie(oi,oi_end) = out_edges(v,g); oi != oi_end; ++oi)
{
edge_t e(*oi);
vertex_t e_source(source(e,g));
vertex_t e_target(target(e,g));
if (e_source == e_target)
{
self_loops.push_back(e);
continue;
}
vertex_t w(e_source == v ? e_target : e_source);
//continue if not a back edge or already embedded
if (dfs_number[w] < dfs_number[v] || e == dfs_parent_edge[w])
continue;
backedges[w].push_back(e);
v_size_t timestamp = dfs_number[v];
backedge_flag[w] = timestamp;
walkup_iterator_t walkup_itr(w, face_handles);
walkup_iterator_t walkup_end;
vertex_t lead_vertex = w;
while (true)
{
// Move to the root of the current bicomp or the first visited
// vertex on the bicomp by going up each side in parallel
while(walkup_itr != walkup_end &&
visited[*walkup_itr] != timestamp
)
{
lead_vertex = *walkup_itr;
visited[lead_vertex] = timestamp;
++walkup_itr;
}
// If we've found the root of a bicomp through a path we haven't
// seen before, update pertinent_roots with a handle to the
// current bicomp. Otherwise, we've just seen a path we've been
// up before, so break out of the main while loop.
if (walkup_itr == walkup_end)
{
vertex_t dfs_child = canonical_dfs_child[lead_vertex];
vertex_t parent = dfs_parent[dfs_child];
visited[dfs_child_handles[dfs_child].first_vertex()]
= timestamp;
visited[dfs_child_handles[dfs_child].second_vertex()]
= timestamp;
if (low_point[dfs_child] < dfs_number[v] ||
least_ancestor[dfs_child] < dfs_number[v]
)
{
pertinent_roots[parent]->push_back
(dfs_child_handles[dfs_child]);
}
else
{
pertinent_roots[parent]->push_front
(dfs_child_handles[dfs_child]);
}
if (parent != v && visited[parent] != timestamp)
{
walkup_itr = walkup_iterator_t(parent, face_handles);
lead_vertex = parent;
}
else
break;
}
else
break;
}
}
}
bool walkdown(vertex_t v)
{
// This procedure is where all of the action is - pertinent_roots
// has already been set up by the walkup, so we just need to move
// down bicomps from v until we find vertices that have been
// labeled as backedge endpoints. Once we find such a vertex, we
// embed the corresponding edge and glue together the bicomps on
// the path connecting the two vertices in the edge. This may
// involve flipping bicomps along the way.
vertex_t w; //the other endpoint of the edge we're embedding
while (!pertinent_roots[v]->empty())
{
face_handle_t root_face_handle = pertinent_roots[v]->front();
face_handle_t curr_face_handle = root_face_handle;
pertinent_roots[v]->pop_front();
merge_stack.clear();
while(true)
{
typename face_vertex_iterator<>::type
first_face_itr, second_face_itr, face_end;
vertex_t first_side_vertex
= graph_traits<Graph>::null_vertex();
vertex_t second_side_vertex;
vertex_t first_tail, second_tail;
first_tail = second_tail = curr_face_handle.get_anchor();
first_face_itr = typename face_vertex_iterator<>::type
(curr_face_handle, face_handles, first_side());
second_face_itr = typename face_vertex_iterator<>::type
(curr_face_handle, face_handles, second_side());
for(; first_face_itr != face_end; ++first_face_itr)
{
vertex_t face_vertex(*first_face_itr);
if (pertinent(face_vertex, v) ||
externally_active(face_vertex, v)
)
{
first_side_vertex = face_vertex;
second_side_vertex = face_vertex;
break;
}
first_tail = face_vertex;
}
if (first_side_vertex == graph_traits<Graph>::null_vertex() ||
first_side_vertex == curr_face_handle.get_anchor()
)
break;
for(;second_face_itr != face_end; ++second_face_itr)
{
vertex_t face_vertex(*second_face_itr);
if (pertinent(face_vertex, v) ||
externally_active(face_vertex, v)
)
{
second_side_vertex = face_vertex;
break;
}
second_tail = face_vertex;
}
vertex_t chosen;
bool chose_first_upper_path;
if (internally_active(first_side_vertex, v))
{
chosen = first_side_vertex;
chose_first_upper_path = true;
}
else if (internally_active(second_side_vertex, v))
{
chosen = second_side_vertex;
chose_first_upper_path = false;
}
else if (pertinent(first_side_vertex, v))
{
chosen = first_side_vertex;
chose_first_upper_path = true;
}
else if (pertinent(second_side_vertex, v))
{
chosen = second_side_vertex;
chose_first_upper_path = false;
}
else
{
// If there's a pertinent vertex on the lower face
// between the first_face_itr and the second_face_itr,
// this graph isn't planar.
for(;
*first_face_itr != second_side_vertex;
++first_face_itr
)
{
vertex_t p(*first_face_itr);
if (pertinent(p,v))
{
//Found a Kuratowski subgraph
kuratowski_v = v;
kuratowski_x = first_side_vertex;
kuratowski_y = second_side_vertex;
return false;
}
}
// Otherwise, the fact that we didn't find a pertinent
// vertex on this face is fine - we should set the
// short-circuit edges and break out of this loop to
// start looking at a different pertinent root.
if (first_side_vertex == second_side_vertex)
{
if (first_tail != v)
{
vertex_t first
= face_handles[first_tail].first_vertex();
vertex_t second
= face_handles[first_tail].second_vertex();
boost::tie(first_side_vertex, first_tail)
= make_tuple(first_tail,
first == first_side_vertex ?
second : first
);
}
else if (second_tail != v)
{
vertex_t first
= face_handles[second_tail].first_vertex();
vertex_t second
= face_handles[second_tail].second_vertex();
boost::tie(second_side_vertex, second_tail)
= make_tuple(second_tail,
first == second_side_vertex ?
second : first);
}
else
break;
}
canonical_dfs_child[first_side_vertex]
= canonical_dfs_child[root_face_handle.first_vertex()];
canonical_dfs_child[second_side_vertex]
= canonical_dfs_child[root_face_handle.second_vertex()];
root_face_handle.set_first_vertex(first_side_vertex);
root_face_handle.set_second_vertex(second_side_vertex);
if (face_handles[first_side_vertex].first_vertex() ==
first_tail
)
face_handles[first_side_vertex].set_first_vertex(v);
else
face_handles[first_side_vertex].set_second_vertex(v);
if (face_handles[second_side_vertex].first_vertex() ==
second_tail
)
face_handles[second_side_vertex].set_first_vertex(v);
else
face_handles[second_side_vertex].set_second_vertex(v);
break;
}
// When we unwind the stack, we need to know which direction
// we came down from on the top face handle
bool chose_first_lower_path =
(chose_first_upper_path &&
face_handles[chosen].first_vertex() == first_tail)
||
(!chose_first_upper_path &&
face_handles[chosen].first_vertex() == second_tail);
//If there's a backedge at the chosen vertex, embed it now
if (backedge_flag[chosen] == dfs_number[v])
{
w = chosen;
backedge_flag[chosen] = num_vertices(g) + 1;
add_to_merge_points(chosen, StoreOldHandlesPolicy());
typename edge_vector_t::iterator ei, ei_end;
ei_end = backedges[chosen].end();
for(ei = backedges[chosen].begin(); ei != ei_end; ++ei)
{
edge_t e(*ei);
add_to_embedded_edges(e, StoreOldHandlesPolicy());
if (chose_first_lower_path)
face_handles[chosen].push_first(e, g);
else
face_handles[chosen].push_second(e, g);
}
}
else
{
merge_stack.push_back(make_tuple
(chosen, chose_first_upper_path, chose_first_lower_path)
);
curr_face_handle = *pertinent_roots[chosen]->begin();
continue;
}
//Unwind the merge stack to the root, merging all bicomps
bool bottom_path_follows_first;
bool top_path_follows_first;
bool next_bottom_follows_first = chose_first_upper_path;
face_handle_t top_handle, bottom_handle;
vertex_t merge_point = chosen;
while(!merge_stack.empty())
{
bottom_path_follows_first = next_bottom_follows_first;
boost::tie(merge_point,
next_bottom_follows_first,
top_path_follows_first
) = merge_stack.back();
merge_stack.pop_back();
face_handle_t top_handle(face_handles[merge_point]);
face_handle_t bottom_handle
(*pertinent_roots[merge_point]->begin());
vertex_t bottom_dfs_child = canonical_dfs_child
[pertinent_roots[merge_point]->begin()->first_vertex()];
remove_vertex_from_separated_dfs_child_list(
canonical_dfs_child
[pertinent_roots[merge_point]->begin()->first_vertex()]
);
pertinent_roots[merge_point]->pop_front();
add_to_merge_points(top_handle.get_anchor(),
StoreOldHandlesPolicy()
);
if (top_path_follows_first && bottom_path_follows_first)
{
bottom_handle.flip();
top_handle.glue_first_to_second(bottom_handle);
}
else if (!top_path_follows_first &&
bottom_path_follows_first
)
{
flipped[bottom_dfs_child] = true;
top_handle.glue_second_to_first(bottom_handle);
}
else if (top_path_follows_first &&
!bottom_path_follows_first
)
{
flipped[bottom_dfs_child] = true;
top_handle.glue_first_to_second(bottom_handle);
}
else //!top_path_follows_first && !bottom_path_follows_first
{
bottom_handle.flip();
top_handle.glue_second_to_first(bottom_handle);
}
}
//Finally, embed all edges (v,w) at their upper end points
canonical_dfs_child[w]
= canonical_dfs_child[root_face_handle.first_vertex()];
add_to_merge_points(root_face_handle.get_anchor(),
StoreOldHandlesPolicy()
);
typename edge_vector_t::iterator ei, ei_end;
ei_end = backedges[chosen].end();
for(ei = backedges[chosen].begin(); ei != ei_end; ++ei)
{
if (next_bottom_follows_first)
root_face_handle.push_first(*ei, g);
else
root_face_handle.push_second(*ei, g);
}
backedges[chosen].clear();
curr_face_handle = root_face_handle;
}//while(true)
}//while(!pertinent_roots[v]->empty())
return true;
}
void store_old_face_handles(graph::detail::no_old_handles) {}
void store_old_face_handles(graph::detail::store_old_handles)
{
for(typename std::vector<vertex_t>::iterator mp_itr
= current_merge_points.begin();
mp_itr != current_merge_points.end(); ++mp_itr)
{
face_handles[*mp_itr].store_old_face_handles();
}
current_merge_points.clear();
}
void add_to_merge_points(vertex_t, graph::detail::no_old_handles) {}
void add_to_merge_points(vertex_t v, graph::detail::store_old_handles)
{
current_merge_points.push_back(v);
}
void add_to_embedded_edges(edge_t, graph::detail::no_old_handles) {}
void add_to_embedded_edges(edge_t e, graph::detail::store_old_handles)
{
embedded_edges.push_back(e);
}
void clean_up_embedding(graph::detail::no_embedding) {}
void clean_up_embedding(graph::detail::store_embedding)
{
// If the graph isn't biconnected, we'll still have entries
// in the separated_dfs_child_list for some vertices. Since
// these represent articulation points, we can obtain a
// planar embedding no matter what order we embed them in.
vertex_iterator_t xi, xi_end;
for(boost::tie(xi,xi_end) = vertices(g); xi != xi_end; ++xi)
{
if (!separated_dfs_child_list[*xi]->empty())
{
typename vertex_list_t::iterator yi, yi_end;
yi_end = separated_dfs_child_list[*xi]->end();
for(yi = separated_dfs_child_list[*xi]->begin();
yi != yi_end; ++yi
)
{
dfs_child_handles[*yi].flip();
face_handles[*xi].glue_first_to_second
(dfs_child_handles[*yi]);
}
}
}
// Up until this point, we've flipped bicomps lazily by setting
// flipped[v] to true if the bicomp rooted at v was flipped (the
// lazy aspect of this flip is that all descendents of that vertex
// need to have their orientations reversed as well). Now, we
// traverse the DFS tree by DFS number and perform the actual
// flipping as needed
typedef typename vertex_vector_t::iterator vertex_vector_itr_t;
vertex_vector_itr_t vi_end = vertices_by_dfs_num.end();
for(vertex_vector_itr_t vi = vertices_by_dfs_num.begin();
vi != vi_end; ++vi
)
{
vertex_t v(*vi);
bool v_flipped = flipped[v];
bool p_flipped = flipped[dfs_parent[v]];
if (v_flipped && !p_flipped)
{
face_handles[v].flip();
}
else if (p_flipped && !v_flipped)
{
face_handles[v].flip();
flipped[v] = true;
}
else
{
flipped[v] = false;
}
}
// If there are any self-loops in the graph, they were flagged
// during the walkup, and we should add them to the embedding now.
// Adding a self loop anywhere in the embedding could never
// invalidate the embedding, but they would complicate the traversal
// if they were added during the walkup/walkdown.
typename edge_vector_t::iterator ei, ei_end;
ei_end = self_loops.end();
for(ei = self_loops.begin(); ei != ei_end; ++ei)
{
edge_t e(*ei);
face_handles[source(e,g)].push_second(e,g);
}
}
bool pertinent(vertex_t w, vertex_t v)
{
// w is pertinent with respect to v if there is a backedge (v,w) or if
// w is the root of a bicomp that contains a pertinent vertex.
return backedge_flag[w] == dfs_number[v] || !pertinent_roots[w]->empty();
}
bool externally_active(vertex_t w, vertex_t v)
{
// Let a be any proper depth-first search ancestor of v. w is externally
// active with respect to v if there exists a backedge (a,w) or a
// backedge (a,w_0) for some w_0 in a descendent bicomp of w.
v_size_t dfs_number_of_v = dfs_number[v];
return (least_ancestor[w] < dfs_number_of_v) ||
(!separated_dfs_child_list[w]->empty() &&
low_point[separated_dfs_child_list[w]->front()] < dfs_number_of_v);
}
bool internally_active(vertex_t w, vertex_t v)
{
return pertinent(w,v) && !externally_active(w,v);
}
void remove_vertex_from_separated_dfs_child_list(vertex_t v)
{
typename vertex_list_t::iterator to_delete
= separated_node_in_parent_list[v];
garbage.splice(garbage.end(),
*separated_dfs_child_list[dfs_parent[v]],
to_delete,
boost::next(to_delete)
);
}
// End of the implementation of the basic Boyer-Myrvold Algorithm. The rest
// of the code below implements the isolation of a Kuratowski subgraph in
// the case that the input graph is not planar. This is by far the most
// complicated part of the implementation.
public:
template <typename EdgeToBoolPropertyMap, typename EdgeContainer>
vertex_t kuratowski_walkup(vertex_t v,
EdgeToBoolPropertyMap forbidden_edge,
EdgeToBoolPropertyMap goal_edge,
EdgeToBoolPropertyMap is_embedded,
EdgeContainer& path_edges
)
{
vertex_t current_endpoint;
bool seen_goal_edge = false;
out_edge_iterator_t oi, oi_end;
for(boost::tie(oi,oi_end) = out_edges(v,g); oi != oi_end; ++oi)
forbidden_edge[*oi] = true;
for(boost::tie(oi,oi_end) = out_edges(v,g); oi != oi_end; ++oi)
{
path_edges.clear();
edge_t e(*oi);
current_endpoint = target(*oi,g) == v ?
source(*oi,g) : target(*oi,g);
if (dfs_number[current_endpoint] < dfs_number[v] ||
is_embedded[e] ||
v == current_endpoint //self-loop
)
{
//Not a backedge
continue;
}
path_edges.push_back(e);
if (goal_edge[e])
{
return current_endpoint;
}
typedef typename face_edge_iterator<>::type walkup_itr_t;
walkup_itr_t
walkup_itr(current_endpoint, face_handles, first_side());
walkup_itr_t walkup_end;
seen_goal_edge = false;
while (true)
{
if (walkup_itr != walkup_end && forbidden_edge[*walkup_itr])
break;
while(walkup_itr != walkup_end &&
!goal_edge[*walkup_itr] &&
!forbidden_edge[*walkup_itr]
)
{
edge_t f(*walkup_itr);
forbidden_edge[f] = true;
path_edges.push_back(f);
current_endpoint =
source(f, g) == current_endpoint ?
target(f, g) :
source(f,g);
++walkup_itr;
}
if (walkup_itr != walkup_end && goal_edge[*walkup_itr])
{
path_edges.push_back(*walkup_itr);
seen_goal_edge = true;
break;
}
walkup_itr
= walkup_itr_t(current_endpoint, face_handles, first_side());
}
if (seen_goal_edge)
break;
}
if (seen_goal_edge)
return current_endpoint;
else
return graph_traits<Graph>::null_vertex();
}
template <typename OutputIterator, typename EdgeIndexMap>
void extract_kuratowski_subgraph(OutputIterator o_itr, EdgeIndexMap em)
{
// If the main algorithm has failed to embed one of the back-edges from
// a vertex v, we can use the current state of the algorithm to isolate
// a Kuratowksi subgraph. The isolation process breaks down into five
// cases, A - E. The general configuration of all five cases is shown in
// figure 1. There is a vertex v from which the planar
// v embedding process could not proceed. This means that
// | there exists some bicomp containing three vertices
// ----- x,y, and z as shown such that x and y are externally
// | | active with respect to v (which means that there are
// x y two vertices x_0 and y_0 such that (1) both x_0 and
// | | y_0 are proper depth-first search ancestors of v and
// --z-- (2) there are two disjoint paths, one connecting x
// and x_0 and one connecting y and y_0, both consisting
// fig. 1 entirely of unembedded edges). Furthermore, there
// exists a vertex z_0 such that z is a depth-first
// search ancestor of z_0 and (v,z_0) is an unembedded back-edge from v.
// x,y and z all exist on the same bicomp, which consists entirely of
// embedded edges. The five subcases break down as follows, and are
// handled by the algorithm logically in the order A-E: First, if v is
// not on the same bicomp as x,y, and z, a K_3_3 can be isolated - this
// is case A. So, we'll assume that v is on the same bicomp as x,y, and
// z. If z_0 is on a different bicomp than x,y, and z, a K_3_3 can also
// be isolated - this is a case B - so we'll assume from now on that v
// is on the same bicomp as x, y, and z=z_0. In this case, one can use
// properties of the Boyer-Myrvold algorithm to show the existence of an
// "x-y path" connecting some vertex on the "left side" of the x,y,z
// bicomp with some vertex on the "right side" of the bicomp (where the
// left and right are split by a line drawn through v and z.If either of
// the endpoints of the x-y path is above x or y on the bicomp, a K_3_3
// can be isolated - this is a case C. Otherwise, both endpoints are at
// or below x and y on the bicomp. If there is a vertex alpha on the x-y
// path such that alpha is not x or y and there's a path from alpha to v
// that's disjoint from any of the edges on the bicomp and the x-y path,
// a K_3_3 can be isolated - this is a case D. Otherwise, properties of
// the Boyer-Myrvold algorithm can be used to show that another vertex
// w exists on the lower half of the bicomp such that w is externally
// active with respect to v. w can then be used to isolate a K_5 - this
// is the configuration of case E.
vertex_iterator_t vi, vi_end;
edge_iterator_t ei, ei_end;
out_edge_iterator_t oei, oei_end;
typename std::vector<edge_t>::iterator xi, xi_end;
// Clear the short-circuit edges - these are needed for the planar
// testing/embedding algorithm to run in linear time, but they'll
// complicate the kuratowski subgraph isolation
for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
{
face_handles[*vi].reset_vertex_cache();
dfs_child_handles[*vi].reset_vertex_cache();
}
vertex_t v = kuratowski_v;
vertex_t x = kuratowski_x;
vertex_t y = kuratowski_y;
typedef iterator_property_map
<typename std::vector<bool>::iterator, EdgeIndexMap>
edge_to_bool_map_t;
std::vector<bool> is_in_subgraph_vector(num_edges(g), false);
edge_to_bool_map_t is_in_subgraph(is_in_subgraph_vector.begin(), em);
std::vector<bool> is_embedded_vector(num_edges(g), false);
edge_to_bool_map_t is_embedded(is_embedded_vector.begin(), em);
typename std::vector<edge_t>::iterator embedded_itr, embedded_end;
embedded_end = embedded_edges.end();
for(embedded_itr = embedded_edges.begin();
embedded_itr != embedded_end; ++embedded_itr
)
is_embedded[*embedded_itr] = true;
// upper_face_vertex is true for x,y, and all vertices above x and y in
// the bicomp
std::vector<bool> upper_face_vertex_vector(num_vertices(g), false);
vertex_to_bool_map_t upper_face_vertex
(upper_face_vertex_vector.begin(), vm);
std::vector<bool> lower_face_vertex_vector(num_vertices(g), false);
vertex_to_bool_map_t lower_face_vertex
(lower_face_vertex_vector.begin(), vm);
// These next few variable declarations are all things that we need
// to find.
vertex_t z;
vertex_t bicomp_root;
vertex_t w = graph_traits<Graph>::null_vertex();
face_handle_t w_handle;
face_handle_t v_dfchild_handle;
vertex_t first_x_y_path_endpoint = graph_traits<Graph>::null_vertex();
vertex_t second_x_y_path_endpoint = graph_traits<Graph>::null_vertex();
vertex_t w_ancestor = v;
detail::bm_case_t chosen_case = detail::BM_NO_CASE_CHOSEN;
std::vector<edge_t> x_external_path;
std::vector<edge_t> y_external_path;
std::vector<edge_t> case_d_edges;
std::vector<edge_t> z_v_path;
std::vector<edge_t> w_path;
//first, use a walkup to find a path from V that starts with a
//backedge from V, then goes up until it hits either X or Y
//(but doesn't find X or Y as the root of a bicomp)
typename face_vertex_iterator<>::type
x_upper_itr(x, face_handles, first_side());
typename face_vertex_iterator<>::type
x_lower_itr(x, face_handles, second_side());
typename face_vertex_iterator<>::type face_itr, face_end;
// Don't know which path from x is the upper or lower path -
// we'll find out here
for(face_itr = x_upper_itr; face_itr != face_end; ++face_itr)
{
if (*face_itr == y)
{
std::swap(x_upper_itr, x_lower_itr);
break;
}
}
upper_face_vertex[x] = true;
vertex_t current_vertex = x;
vertex_t previous_vertex;
for(face_itr = x_upper_itr; face_itr != face_end; ++face_itr)
{
previous_vertex = current_vertex;
current_vertex = *face_itr;
upper_face_vertex[current_vertex] = true;
}
v_dfchild_handle
= dfs_child_handles[canonical_dfs_child[previous_vertex]];
for(face_itr = x_lower_itr; *face_itr != y; ++face_itr)
{
vertex_t current_vertex(*face_itr);
lower_face_vertex[current_vertex] = true;
typename face_handle_list_t::iterator roots_itr, roots_end;
if (w == graph_traits<Graph>::null_vertex()) //haven't found a w yet
{
roots_end = pertinent_roots[current_vertex]->end();
for(roots_itr = pertinent_roots[current_vertex]->begin();
roots_itr != roots_end; ++roots_itr
)
{
if (low_point[canonical_dfs_child[roots_itr->first_vertex()]]
< dfs_number[v]
)
{
w = current_vertex;
w_handle = *roots_itr;
break;
}
}
}
}
for(; face_itr != face_end; ++face_itr)
{
vertex_t current_vertex(*face_itr);
upper_face_vertex[current_vertex] = true;
bicomp_root = current_vertex;
}
typedef typename face_edge_iterator<>::type walkup_itr_t;
std::vector<bool> outer_face_edge_vector(num_edges(g), false);
edge_to_bool_map_t outer_face_edge(outer_face_edge_vector.begin(), em);
walkup_itr_t walkup_end;
for(walkup_itr_t walkup_itr(x, face_handles, first_side());
walkup_itr != walkup_end; ++walkup_itr
)
{
outer_face_edge[*walkup_itr] = true;
is_in_subgraph[*walkup_itr] = true;
}
for(walkup_itr_t walkup_itr(x, face_handles, second_side());
walkup_itr != walkup_end; ++walkup_itr
)
{
outer_face_edge[*walkup_itr] = true;
is_in_subgraph[*walkup_itr] = true;
}
std::vector<bool> forbidden_edge_vector(num_edges(g), false);
edge_to_bool_map_t forbidden_edge(forbidden_edge_vector.begin(), em);
std::vector<bool> goal_edge_vector(num_edges(g), false);
edge_to_bool_map_t goal_edge(goal_edge_vector.begin(), em);
//Find external path to x and to y
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
{
edge_t e(*ei);
goal_edge[e]
= !outer_face_edge[e] && (source(e,g) == x || target(e,g) == x);
forbidden_edge[*ei] = outer_face_edge[*ei];
}
vertex_t x_ancestor = v;
vertex_t x_endpoint = graph_traits<Graph>::null_vertex();
while(x_endpoint == graph_traits<Graph>::null_vertex())
{
x_ancestor = dfs_parent[x_ancestor];
x_endpoint = kuratowski_walkup(x_ancestor,
forbidden_edge,
goal_edge,
is_embedded,
x_external_path
);
}
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
{
edge_t e(*ei);
goal_edge[e]
= !outer_face_edge[e] && (source(e,g) == y || target(e,g) == y);
forbidden_edge[*ei] = outer_face_edge[*ei];
}
vertex_t y_ancestor = v;
vertex_t y_endpoint = graph_traits<Graph>::null_vertex();
while(y_endpoint == graph_traits<Graph>::null_vertex())
{
y_ancestor = dfs_parent[y_ancestor];
y_endpoint = kuratowski_walkup(y_ancestor,
forbidden_edge,
goal_edge,
is_embedded,
y_external_path
);
}
vertex_t parent, child;
//If v isn't on the same bicomp as x and y, it's a case A
if (bicomp_root != v)
{
chosen_case = detail::BM_CASE_A;
for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
if (lower_face_vertex[*vi])
for(boost::tie(oei,oei_end) = out_edges(*vi,g); oei != oei_end; ++oei)
if(!outer_face_edge[*oei])
goal_edge[*oei] = true;
for(boost::tie(ei,ei_end) = edges(g); ei != ei_end; ++ei)
forbidden_edge[*ei] = outer_face_edge[*ei];
z = kuratowski_walkup
(v, forbidden_edge, goal_edge, is_embedded, z_v_path);
}
else if (w != graph_traits<Graph>::null_vertex())
{
chosen_case = detail::BM_CASE_B;
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
{
edge_t e(*ei);
goal_edge[e] = false;
forbidden_edge[e] = outer_face_edge[e];
}
goal_edge[w_handle.first_edge()] = true;
goal_edge[w_handle.second_edge()] = true;
z = kuratowski_walkup(v,
forbidden_edge,
goal_edge,
is_embedded,
z_v_path
);
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
{
forbidden_edge[*ei] = outer_face_edge[*ei];
}
typename std::vector<edge_t>::iterator pi, pi_end;
pi_end = z_v_path.end();
for(pi = z_v_path.begin(); pi != pi_end; ++pi)
{
goal_edge[*pi] = true;
}
w_ancestor = v;
vertex_t w_endpoint = graph_traits<Graph>::null_vertex();
while(w_endpoint == graph_traits<Graph>::null_vertex())
{
w_ancestor = dfs_parent[w_ancestor];
w_endpoint = kuratowski_walkup(w_ancestor,
forbidden_edge,
goal_edge,
is_embedded,
w_path
);
}
// We really want both the w walkup and the z walkup to finish on
// exactly the same edge, but for convenience (since we don't have
// control over which side of a bicomp a walkup moves up) we've
// defined the walkup to either end at w_handle.first_edge() or
// w_handle.second_edge(). If both walkups ended at different edges,
// we'll do a little surgery on the w walkup path to make it follow
// the other side of the final bicomp.
if ((w_path.back() == w_handle.first_edge() &&
z_v_path.back() == w_handle.second_edge())
||
(w_path.back() == w_handle.second_edge() &&
z_v_path.back() == w_handle.first_edge())
)
{
walkup_itr_t wi, wi_end;
edge_t final_edge = w_path.back();
vertex_t anchor
= source(final_edge, g) == w_handle.get_anchor() ?
target(final_edge, g) : source(final_edge, g);
if (face_handles[anchor].first_edge() == final_edge)
wi = walkup_itr_t(anchor, face_handles, second_side());
else
wi = walkup_itr_t(anchor, face_handles, first_side());
w_path.pop_back();
for(; wi != wi_end; ++wi)
{
edge_t e(*wi);
if (w_path.back() == e)
w_path.pop_back();
else
w_path.push_back(e);
}
}
}
else
{
//We need to find a valid z, since the x-y path re-defines the lower
//face, and the z we found earlier may now be on the upper face.
chosen_case = detail::BM_CASE_E;
// The z we've used so far is just an externally active vertex on the
// lower face path, but may not be the z we need for a case C, D, or
// E subgraph. the z we need now is any externally active vertex on
// the lower face path with both old_face_handles edges on the outer
// face. Since we know an x-y path exists, such a z must also exist.
//TODO: find this z in the first place.
//find the new z
for(face_itr = x_lower_itr; *face_itr != y; ++face_itr)
{
vertex_t possible_z(*face_itr);
if (pertinent(possible_z,v) &&
outer_face_edge[face_handles[possible_z].old_first_edge()] &&
outer_face_edge[face_handles[possible_z].old_second_edge()]
)
{
z = possible_z;
break;
}
}
//find x-y path, and a w if one exists.
if (externally_active(z,v))
w = z;
typedef typename face_edge_iterator
<single_side, previous_iteration>::type old_face_iterator_t;
old_face_iterator_t
first_old_face_itr(z, face_handles, first_side());
old_face_iterator_t
second_old_face_itr(z, face_handles, second_side());
old_face_iterator_t old_face_itr, old_face_end;
std::vector<old_face_iterator_t> old_face_iterators;
old_face_iterators.push_back(first_old_face_itr);
old_face_iterators.push_back(second_old_face_itr);
std::vector<bool> x_y_path_vertex_vector(num_vertices(g), false);
vertex_to_bool_map_t x_y_path_vertex
(x_y_path_vertex_vector.begin(), vm);
typename std::vector<old_face_iterator_t>::iterator
of_itr, of_itr_end;
of_itr_end = old_face_iterators.end();
for(of_itr = old_face_iterators.begin();
of_itr != of_itr_end; ++of_itr
)
{
old_face_itr = *of_itr;
vertex_t previous_vertex;
bool seen_x_or_y = false;
vertex_t current_vertex = z;
for(; old_face_itr != old_face_end; ++old_face_itr)
{
edge_t e(*old_face_itr);
previous_vertex = current_vertex;
current_vertex = source(e,g) == current_vertex ?
target(e,g) : source(e,g);
if (current_vertex == x || current_vertex == y)
seen_x_or_y = true;
if (w == graph_traits<Graph>::null_vertex() &&
externally_active(current_vertex,v) &&
outer_face_edge[e] &&
outer_face_edge[*boost::next(old_face_itr)] &&
!seen_x_or_y
)
{
w = current_vertex;
}
if (!outer_face_edge[e])
{
if (!upper_face_vertex[current_vertex] &&
!lower_face_vertex[current_vertex]
)
{
x_y_path_vertex[current_vertex] = true;
}
is_in_subgraph[e] = true;
if (upper_face_vertex[source(e,g)] ||
lower_face_vertex[source(e,g)]
)
{
if (first_x_y_path_endpoint ==
graph_traits<Graph>::null_vertex()
)
first_x_y_path_endpoint = source(e,g);
else
second_x_y_path_endpoint = source(e,g);
}
if (upper_face_vertex[target(e,g)] ||
lower_face_vertex[target(e,g)]
)
{
if (first_x_y_path_endpoint ==
graph_traits<Graph>::null_vertex()
)
first_x_y_path_endpoint = target(e,g);
else
second_x_y_path_endpoint = target(e,g);
}
}
else if (previous_vertex == x || previous_vertex == y)
{
chosen_case = detail::BM_CASE_C;
}
}
}
// Look for a case D - one of v's embedded edges will connect to the
// x-y path along an inner face path.
//First, get a list of all of v's embedded child edges
out_edge_iterator_t v_edge_itr, v_edge_end;
for(boost::tie(v_edge_itr,v_edge_end) = out_edges(v,g);
v_edge_itr != v_edge_end; ++v_edge_itr
)
{
edge_t embedded_edge(*v_edge_itr);
if (!is_embedded[embedded_edge] ||
embedded_edge == dfs_parent_edge[v]
)
continue;
case_d_edges.push_back(embedded_edge);
vertex_t current_vertex
= source(embedded_edge,g) == v ?
target(embedded_edge,g) : source(embedded_edge,g);
typename face_edge_iterator<>::type
internal_face_itr, internal_face_end;
if (face_handles[current_vertex].first_vertex() == v)
{
internal_face_itr = typename face_edge_iterator<>::type
(current_vertex, face_handles, second_side());
}
else
{
internal_face_itr = typename face_edge_iterator<>::type
(current_vertex, face_handles, first_side());
}
while(internal_face_itr != internal_face_end &&
!outer_face_edge[*internal_face_itr] &&
!x_y_path_vertex[current_vertex]
)
{
edge_t e(*internal_face_itr);
case_d_edges.push_back(e);
current_vertex =
source(e,g) == current_vertex ? target(e,g) : source(e,g);
++internal_face_itr;
}
if (x_y_path_vertex[current_vertex])
{
chosen_case = detail::BM_CASE_D;
break;
}
else
{
case_d_edges.clear();
}
}
}
if (chosen_case != detail::BM_CASE_B && chosen_case != detail::BM_CASE_A)
{
//Finding z and w.
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
{
edge_t e(*ei);
goal_edge[e] = !outer_face_edge[e] &&
(source(e,g) == z || target(e,g) == z);
forbidden_edge[e] = outer_face_edge[e];
}
kuratowski_walkup(v,
forbidden_edge,
goal_edge,
is_embedded,
z_v_path
);
if (chosen_case == detail::BM_CASE_E)
{
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
{
forbidden_edge[*ei] = outer_face_edge[*ei];
goal_edge[*ei] = !outer_face_edge[*ei] &&
(source(*ei,g) == w || target(*ei,g) == w);
}
for(boost::tie(oei, oei_end) = out_edges(w,g); oei != oei_end; ++oei)
{
if (!outer_face_edge[*oei])
goal_edge[*oei] = true;
}
typename std::vector<edge_t>::iterator pi, pi_end;
pi_end = z_v_path.end();
for(pi = z_v_path.begin(); pi != pi_end; ++pi)
{
goal_edge[*pi] = true;
}
w_ancestor = v;
vertex_t w_endpoint = graph_traits<Graph>::null_vertex();
while(w_endpoint == graph_traits<Graph>::null_vertex())
{
w_ancestor = dfs_parent[w_ancestor];
w_endpoint = kuratowski_walkup(w_ancestor,
forbidden_edge,
goal_edge,
is_embedded,
w_path
);
}
}
}
//We're done isolating the Kuratowski subgraph at this point -
//but there's still some cleaning up to do.
//Update is_in_subgraph with the paths we just found
xi_end = x_external_path.end();
for(xi = x_external_path.begin(); xi != xi_end; ++xi)
is_in_subgraph[*xi] = true;
xi_end = y_external_path.end();
for(xi = y_external_path.begin(); xi != xi_end; ++xi)
is_in_subgraph[*xi] = true;
xi_end = z_v_path.end();
for(xi = z_v_path.begin(); xi != xi_end; ++xi)
is_in_subgraph[*xi] = true;
xi_end = case_d_edges.end();
for(xi = case_d_edges.begin(); xi != xi_end; ++xi)
is_in_subgraph[*xi] = true;
xi_end = w_path.end();
for(xi = w_path.begin(); xi != xi_end; ++xi)
is_in_subgraph[*xi] = true;
child = bicomp_root;
parent = dfs_parent[child];
while(child != parent)
{
is_in_subgraph[dfs_parent_edge[child]] = true;
boost::tie(parent, child) = std::make_pair( dfs_parent[parent], parent );
}
// At this point, we've already isolated the Kuratowski subgraph and
// collected all of the edges that compose it in the is_in_subgraph
// property map. But we want the verification of such a subgraph to be
// a deterministic process, and we can simplify the function
// is_kuratowski_subgraph by cleaning up some edges here.
if (chosen_case == detail::BM_CASE_B)
{
is_in_subgraph[dfs_parent_edge[v]] = false;
}
else if (chosen_case == detail::BM_CASE_C)
{
// In a case C subgraph, at least one of the x-y path endpoints
// (call it alpha) is above either x or y on the outer face. The
// other endpoint may be attached at x or y OR above OR below. In
// any of these three cases, we can form a K_3_3 by removing the
// edge attached to v on the outer face that is NOT on the path to
// alpha.
typename face_vertex_iterator<single_side, follow_visitor>::type
face_itr, face_end;
if (face_handles[v_dfchild_handle.first_vertex()].first_edge() ==
v_dfchild_handle.first_edge()
)
{
face_itr = typename face_vertex_iterator
<single_side, follow_visitor>::type
(v_dfchild_handle.first_vertex(), face_handles, second_side());
}
else
{
face_itr = typename face_vertex_iterator
<single_side, follow_visitor>::type
(v_dfchild_handle.first_vertex(), face_handles, first_side());
}
for(; true; ++face_itr)
{
vertex_t current_vertex(*face_itr);
if (current_vertex == x || current_vertex == y)
{
is_in_subgraph[v_dfchild_handle.first_edge()] = false;
break;
}
else if (current_vertex == first_x_y_path_endpoint ||
current_vertex == second_x_y_path_endpoint)
{
is_in_subgraph[v_dfchild_handle.second_edge()] = false;
break;
}
}
}
else if (chosen_case == detail::BM_CASE_D)
{
// Need to remove both of the edges adjacent to v on the outer face.
// remove the connecting edges from v to bicomp, then
// is_kuratowski_subgraph will shrink vertices of degree 1
// automatically...
is_in_subgraph[v_dfchild_handle.first_edge()] = false;
is_in_subgraph[v_dfchild_handle.second_edge()] = false;
}
else if (chosen_case == detail::BM_CASE_E)
{
// Similarly to case C, if the endpoints of the x-y path are both
// below x and y, we should remove an edge to allow the subgraph to
// contract to a K_3_3.
if ((first_x_y_path_endpoint != x && first_x_y_path_endpoint != y) ||
(second_x_y_path_endpoint != x && second_x_y_path_endpoint != y)
)
{
is_in_subgraph[dfs_parent_edge[v]] = false;
vertex_t deletion_endpoint, other_endpoint;
if (lower_face_vertex[first_x_y_path_endpoint])
{
deletion_endpoint = second_x_y_path_endpoint;
other_endpoint = first_x_y_path_endpoint;
}
else
{
deletion_endpoint = first_x_y_path_endpoint;
other_endpoint = second_x_y_path_endpoint;
}
typename face_edge_iterator<>::type face_itr, face_end;
bool found_other_endpoint = false;
for(face_itr = typename face_edge_iterator<>::type
(deletion_endpoint, face_handles, first_side());
face_itr != face_end; ++face_itr
)
{
edge_t e(*face_itr);
if (source(e,g) == other_endpoint ||
target(e,g) == other_endpoint
)
{
found_other_endpoint = true;
break;
}
}
if (found_other_endpoint)
{
is_in_subgraph[face_handles[deletion_endpoint].first_edge()]
= false;
}
else
{
is_in_subgraph[face_handles[deletion_endpoint].second_edge()]
= false;
}
}
}
for(boost::tie(ei, ei_end) = edges(g); ei != ei_end; ++ei)
if (is_in_subgraph[*ei])
*o_itr = *ei;
}
template<typename EdgePermutation>
void make_edge_permutation(EdgePermutation perm)
{
vertex_iterator_t vi, vi_end;
for(boost::tie(vi,vi_end) = vertices(g); vi != vi_end; ++vi)
{
vertex_t v(*vi);
perm[v].clear();
face_handles[v].get_list(std::back_inserter(perm[v]));
}
}
private:
const Graph& g;
VertexIndexMap vm;
vertex_t kuratowski_v;
vertex_t kuratowski_x;
vertex_t kuratowski_y;
vertex_list_t garbage; // we delete items from linked lists by
// splicing them into garbage
//only need these two for kuratowski subgraph isolation
std::vector<vertex_t> current_merge_points;
std::vector<edge_t> embedded_edges;
//property map storage
std::vector<v_size_t> low_point_vector;
std::vector<vertex_t> dfs_parent_vector;
std::vector<v_size_t> dfs_number_vector;
std::vector<v_size_t> least_ancestor_vector;
std::vector<face_handle_list_ptr_t> pertinent_roots_vector;
std::vector<v_size_t> backedge_flag_vector;
std::vector<v_size_t> visited_vector;
std::vector< face_handle_t > face_handles_vector;
std::vector< face_handle_t > dfs_child_handles_vector;
std::vector< vertex_list_ptr_t > separated_dfs_child_list_vector;
std::vector< typename vertex_list_t::iterator >
separated_node_in_parent_list_vector;
std::vector<vertex_t> canonical_dfs_child_vector;
std::vector<bool> flipped_vector;
std::vector<edge_vector_t> backedges_vector;
edge_vector_t self_loops;
std::vector<edge_t> dfs_parent_edge_vector;
vertex_vector_t vertices_by_dfs_num;
//property maps
vertex_to_v_size_map_t low_point;
vertex_to_vertex_map_t dfs_parent;
vertex_to_v_size_map_t dfs_number;
vertex_to_v_size_map_t least_ancestor;
vertex_to_face_handle_list_ptr_map_t pertinent_roots;
vertex_to_v_size_map_t backedge_flag;
vertex_to_v_size_map_t visited;
vertex_to_face_handle_map_t face_handles;
vertex_to_face_handle_map_t dfs_child_handles;
vertex_to_vertex_list_ptr_map_t separated_dfs_child_list;
vertex_to_separated_node_map_t separated_node_in_parent_list;
vertex_to_vertex_map_t canonical_dfs_child;
vertex_to_bool_map_t flipped;
vertex_to_edge_vector_map_t backedges;
vertex_to_edge_map_t dfs_parent_edge; //only need for kuratowski
merge_stack_t merge_stack;
};
} //namespace boost
#endif //__BOYER_MYRVOLD_IMPL_HPP__