r862:58c330ad0b5c
Sun, 04 Oct 2009 10:15:32
[Not Reviewed]
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@@ -116,437 +116,437 @@ |
| 116 | 116 |
int prev, next; |
| 117 | 117 |
int visited; |
| 118 | 118 |
typename Graph::Arc first; |
| 119 | 119 |
bool inverted; |
| 120 | 120 |
}; |
| 121 | 121 |
|
| 122 | 122 |
template <typename Graph> |
| 123 | 123 |
struct NodeDataNode<Graph, false> {
|
| 124 | 124 |
int prev, next; |
| 125 | 125 |
int visited; |
| 126 | 126 |
}; |
| 127 | 127 |
|
| 128 | 128 |
template <typename Graph> |
| 129 | 129 |
struct ChildListNode {
|
| 130 | 130 |
typedef typename Graph::Node Node; |
| 131 | 131 |
Node first; |
| 132 | 132 |
Node prev, next; |
| 133 | 133 |
}; |
| 134 | 134 |
|
| 135 | 135 |
template <typename Graph> |
| 136 | 136 |
struct ArcListNode {
|
| 137 | 137 |
typename Graph::Arc prev, next; |
| 138 | 138 |
}; |
| 139 | 139 |
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template <typename Graph> |
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class PlanarityChecking {
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private: |
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TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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const Graph& _graph; |
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private: |
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typedef typename Graph::template NodeMap<Arc> PredMap; |
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typedef typename Graph::template EdgeMap<bool> TreeMap; |
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typedef typename Graph::template NodeMap<int> OrderMap; |
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typedef std::vector<Node> OrderList; |
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typedef typename Graph::template NodeMap<int> LowMap; |
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typedef typename Graph::template NodeMap<int> AncestorMap; |
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typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
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typedef std::vector<NodeDataNode> NodeData; |
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typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
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typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
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typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
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typedef typename Graph::template NodeMap<bool> EmbedArc; |
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public: |
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PlanarityChecking(const Graph& graph) : _graph(graph) {}
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bool run() {
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typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
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PredMap pred_map(_graph, INVALID); |
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TreeMap tree_map(_graph, false); |
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OrderMap order_map(_graph, -1); |
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OrderList order_list; |
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AncestorMap ancestor_map(_graph, -1); |
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LowMap low_map(_graph, -1); |
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Visitor visitor(_graph, pred_map, tree_map, |
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order_map, order_list, ancestor_map, low_map); |
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DfsVisit<Graph, Visitor> visit(_graph, visitor); |
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visit.run(); |
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ChildLists child_lists(_graph); |
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createChildLists(tree_map, order_map, low_map, child_lists); |
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NodeData node_data(2 * order_list.size()); |
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EmbedArc embed_arc(_graph, false); |
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MergeRoots merge_roots(_graph); |
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for (int i = order_list.size() - 1; i >= 0; --i) {
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Node node = order_list[i]; |
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Node source = node; |
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e); |
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if (order_map[source] < order_map[target] && tree_map[e]) {
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initFace(target, node_data, order_map, order_list); |
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} |
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} |
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e); |
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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embed_arc[target] = true; |
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walkUp(target, source, i, pred_map, low_map, |
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order_map, order_list, node_data, merge_roots); |
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} |
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} |
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for (typename MergeRoots::Value::iterator it = |
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merge_roots[node].begin(); |
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it != merge_roots[node].end(); ++it) {
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int rn = *it; |
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walkDown(rn, i, node_data, order_list, child_lists, |
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ancestor_map, low_map, embed_arc, merge_roots); |
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} |
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merge_roots[node].clear(); |
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for (OutArcIt e(_graph, node); e != INVALID; ++e) {
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Node target = _graph.target(e); |
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if (order_map[source] < order_map[target] && !tree_map[e]) {
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if (embed_arc[target]) {
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return false; |
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} |
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} |
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} |
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} |
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return true; |
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} |
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private: |
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void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
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const LowMap& low_map, ChildLists& child_lists) {
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for (NodeIt n(_graph); n != INVALID; ++n) {
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Node source = n; |
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std::vector<Node> targets; |
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for (OutArcIt e(_graph, n); e != INVALID; ++e) {
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Node target = _graph.target(e); |
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if (order_map[source] < order_map[target] && tree_map[e]) {
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targets.push_back(target); |
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} |
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} |
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if (targets.size() == 0) {
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child_lists[source].first = INVALID; |
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} else if (targets.size() == 1) {
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child_lists[source].first = targets[0]; |
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child_lists[targets[0]].prev = INVALID; |
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child_lists[targets[0]].next = INVALID; |
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} else {
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radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
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for (int i = 1; i < int(targets.size()); ++i) {
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child_lists[targets[i]].prev = targets[i - 1]; |
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child_lists[targets[i - 1]].next = targets[i]; |
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} |
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child_lists[targets.back()].next = INVALID; |
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child_lists[targets.front()].prev = INVALID; |
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child_lists[source].first = targets.front(); |
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} |
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} |
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} |
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void walkUp(const Node& node, Node root, int rorder, |
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const PredMap& pred_map, const LowMap& low_map, |
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const OrderMap& order_map, const OrderList& order_list, |
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NodeData& node_data, MergeRoots& merge_roots) {
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int na, nb; |
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bool da, db; |
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na = nb = order_map[node]; |
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da = true; db = false; |
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while (true) {
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if (node_data[na].visited == rorder) break; |
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if (node_data[nb].visited == rorder) break; |
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node_data[na].visited = rorder; |
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node_data[nb].visited = rorder; |
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int rn = -1; |
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if (na >= int(order_list.size())) {
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rn = na; |
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} else if (nb >= int(order_list.size())) {
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rn = nb; |
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} |
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if (rn == -1) {
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int nn; |
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nn = da ? node_data[na].prev : node_data[na].next; |
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da = node_data[nn].prev != na; |
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na = nn; |
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nn = db ? node_data[nb].prev : node_data[nb].next; |
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db = node_data[nn].prev != nb; |
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nb = nn; |
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} else {
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Node rep = order_list[rn - order_list.size()]; |
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Node parent = _graph.source(pred_map[rep]); |
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if (low_map[rep] < rorder) {
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merge_roots[parent].push_back(rn); |
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} else {
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merge_roots[parent].push_front(rn); |
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} |
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if (parent != root) {
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na = nb = order_map[parent]; |
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da = true; db = false; |
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} else {
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break; |
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} |
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} |
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} |
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} |
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void walkDown(int rn, int rorder, NodeData& node_data, |
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OrderList& order_list, ChildLists& child_lists, |
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AncestorMap& ancestor_map, LowMap& low_map, |
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EmbedArc& embed_arc, MergeRoots& merge_roots) {
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std::vector<std::pair<int, bool> > merge_stack; |
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for (int di = 0; di < 2; ++di) {
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bool rd = di == 0; |
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int pn = rn; |
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int n = rd ? node_data[rn].next : node_data[rn].prev; |
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while (n != rn) {
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Node node = order_list[n]; |
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if (embed_arc[node]) {
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// Merging components on the critical path |
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while (!merge_stack.empty()) {
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// Component root |
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int cn = merge_stack.back().first; |
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bool cd = merge_stack.back().second; |
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merge_stack.pop_back(); |
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// Parent of component |
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int dn = merge_stack.back().first; |
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bool dd = merge_stack.back().second; |
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merge_stack.pop_back(); |
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Node parent = order_list[dn]; |
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// Erasing from merge_roots |
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merge_roots[parent].pop_front(); |
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Node child = order_list[cn - order_list.size()]; |
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// Erasing from child_lists |
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if (child_lists[child].prev != INVALID) {
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child_lists[child_lists[child].prev].next = |
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child_lists[child].next; |
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} else {
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child_lists[parent].first = child_lists[child].next; |
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} |
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if (child_lists[child].next != INVALID) {
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child_lists[child_lists[child].next].prev = |
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child_lists[child].prev; |
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} |
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// Merging external faces |
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{
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int en = cn; |
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cn = cd ? node_data[cn].prev : node_data[cn].next; |
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cd = node_data[cn].next == en; |
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} |
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if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
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if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
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} |
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bool d = pn == node_data[n].prev; |
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if (node_data[n].prev == node_data[n].next && |
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node_data[n].inverted) {
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d = !d; |
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} |
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// Embedding arc into external face |
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if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
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if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
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pn = rn; |
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embed_arc[order_list[n]] = false; |
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} |
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if (!merge_roots[node].empty()) {
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bool d = pn == node_data[n].prev; |
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merge_stack.push_back(std::make_pair(n, d)); |
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int rn = merge_roots[node].front(); |
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int xn = node_data[rn].next; |
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Node xnode = order_list[xn]; |
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int yn = node_data[rn].prev; |
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Node ynode = order_list[yn]; |
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bool rd; |
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if (!external(xnode, rorder, child_lists, |
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ancestor_map, low_map)) {
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rd = true; |
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} else if (!external(ynode, rorder, child_lists, |
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ancestor_map, low_map)) {
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rd = false; |
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} else if (pertinent(xnode, embed_arc, merge_roots)) {
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rd = true; |
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} else {
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rd = false; |
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} |
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merge_stack.push_back(std::make_pair(rn, rd)); |
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pn = rn; |
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n = rd ? xn : yn; |
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} else if (!external(node, rorder, child_lists, |
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ancestor_map, low_map)) {
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int nn = (node_data[n].next != pn ? |
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node_data[n].next : node_data[n].prev); |
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bool nd = n == node_data[nn].prev; |
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if (nd) node_data[nn].prev = pn; |
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else node_data[nn].next = pn; |
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if (n == node_data[pn].prev) node_data[pn].prev = nn; |
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else node_data[pn].next = nn; |
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node_data[nn].inverted = |
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(node_data[nn].prev == node_data[nn].next && nd != rd); |
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n = nn; |
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} |
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else break; |
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} |
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if (!merge_stack.empty() || n == rn) {
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break; |
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} |
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} |
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} |
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void initFace(const Node& node, NodeData& node_data, |
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const OrderMap& order_map, const OrderList& order_list) {
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int n = order_map[node]; |
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int rn = n + order_list.size(); |
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node_data[n].next = node_data[n].prev = rn; |
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node_data[rn].next = node_data[rn].prev = n; |
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node_data[n].visited = order_list.size(); |
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node_data[rn].visited = order_list.size(); |
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} |
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bool external(const Node& node, int rorder, |
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ChildLists& child_lists, AncestorMap& ancestor_map, |
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LowMap& low_map) {
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Node child = child_lists[node].first; |
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if (child != INVALID) {
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if (low_map[child] < rorder) return true; |
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} |
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if (ancestor_map[node] < rorder) return true; |
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return false; |
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} |
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bool pertinent(const Node& node, const EmbedArc& embed_arc, |
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const MergeRoots& merge_roots) {
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return !merge_roots[node].empty() || embed_arc[node]; |
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} |
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}; |
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|
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| 140 | 514 |
} |
| 141 | 515 |
|
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/// \ingroup planar |
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/// |
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/// \brief Planarity checking of an undirected simple graph |
| 145 | 519 |
/// |
| 146 |
/// This class implements the Boyer-Myrvold algorithm for planarity |
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| 147 |
/// checking of an undirected graph. This class is a simplified |
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| 520 |
/// This function implements the Boyer-Myrvold algorithm for |
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/// planarity checking of an undirected graph. It is a simplified |
|
| 148 | 522 |
/// version of the PlanarEmbedding algorithm class because neither |
| 149 | 523 |
/// the embedding nor the kuratowski subdivisons are not computed. |
| 150 |
template <typename Graph> |
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| 151 |
class PlanarityChecking {
|
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| 152 |
private: |
|
| 153 |
|
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| 154 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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| 155 |
|
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| 156 |
const Graph& _graph; |
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|
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private: |
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| 159 |
|
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| 160 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
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| 161 |
|
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typedef typename Graph::template EdgeMap<bool> TreeMap; |
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| 163 |
|
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| 164 |
typedef typename Graph::template NodeMap<int> OrderMap; |
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typedef std::vector<Node> OrderList; |
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| 166 |
|
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| 167 |
typedef typename Graph::template NodeMap<int> LowMap; |
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typedef typename Graph::template NodeMap<int> AncestorMap; |
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|
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| 170 |
typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
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typedef std::vector<NodeDataNode> NodeData; |
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| 172 |
|
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| 173 |
typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
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typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
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| 175 |
|
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| 176 |
typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
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| 177 |
|
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| 178 |
typedef typename Graph::template NodeMap<bool> EmbedArc; |
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|
|
| 180 |
public: |
|
| 181 |
|
|
| 182 |
/// \brief Constructor |
|
| 183 |
/// |
|
| 184 |
/// \note The graph should be simple, i.e. parallel and loop arc |
|
| 185 |
/// free. |
|
| 186 |
PlanarityChecking(const Graph& graph) : _graph(graph) {}
|
|
| 187 |
|
|
| 188 |
/// \brief Runs the algorithm. |
|
| 189 |
/// |
|
| 190 |
/// Runs the algorithm. |
|
| 191 |
/// \return %True when the graph is planar. |
|
| 192 |
bool run() {
|
|
| 193 |
typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
|
| 194 |
|
|
| 195 |
PredMap pred_map(_graph, INVALID); |
|
| 196 |
TreeMap tree_map(_graph, false); |
|
| 197 |
|
|
| 198 |
OrderMap order_map(_graph, -1); |
|
| 199 |
OrderList order_list; |
|
| 200 |
|
|
| 201 |
AncestorMap ancestor_map(_graph, -1); |
|
| 202 |
LowMap low_map(_graph, -1); |
|
| 203 |
|
|
| 204 |
Visitor visitor(_graph, pred_map, tree_map, |
|
| 205 |
order_map, order_list, ancestor_map, low_map); |
|
| 206 |
DfsVisit<Graph, Visitor> visit(_graph, visitor); |
|
| 207 |
visit.run(); |
|
| 208 |
|
|
| 209 |
ChildLists child_lists(_graph); |
|
| 210 |
createChildLists(tree_map, order_map, low_map, child_lists); |
|
| 211 |
|
|
| 212 |
NodeData node_data(2 * order_list.size()); |
|
| 213 |
|
|
| 214 |
EmbedArc embed_arc(_graph, false); |
|
| 215 |
|
|
| 216 |
MergeRoots merge_roots(_graph); |
|
| 217 |
|
|
| 218 |
for (int i = order_list.size() - 1; i >= 0; --i) {
|
|
| 219 |
|
|
| 220 |
Node node = order_list[i]; |
|
| 221 |
|
|
| 222 |
Node source = node; |
|
| 223 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
| 224 |
Node target = _graph.target(e); |
|
| 225 |
|
|
| 226 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
|
| 227 |
initFace(target, node_data, order_map, order_list); |
|
| 228 |
} |
|
| 229 |
} |
|
| 230 |
|
|
| 231 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
| 232 |
Node target = _graph.target(e); |
|
| 233 |
|
|
| 234 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
|
| 235 |
embed_arc[target] = true; |
|
| 236 |
walkUp(target, source, i, pred_map, low_map, |
|
| 237 |
order_map, order_list, node_data, merge_roots); |
|
| 238 |
} |
|
| 239 |
} |
|
| 240 |
|
|
| 241 |
for (typename MergeRoots::Value::iterator it = |
|
| 242 |
merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
|
|
| 243 |
int rn = *it; |
|
| 244 |
walkDown(rn, i, node_data, order_list, child_lists, |
|
| 245 |
ancestor_map, low_map, embed_arc, merge_roots); |
|
| 246 |
} |
|
| 247 |
merge_roots[node].clear(); |
|
| 248 |
|
|
| 249 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
|
| 250 |
Node target = _graph.target(e); |
|
| 251 |
|
|
| 252 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
|
| 253 |
if (embed_arc[target]) {
|
|
| 254 |
return false; |
|
| 255 |
} |
|
| 256 |
} |
|
| 257 |
} |
|
| 258 |
} |
|
| 259 |
|
|
| 260 |
return true; |
|
| 261 |
} |
|
| 262 |
|
|
| 263 |
private: |
|
| 264 |
|
|
| 265 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
|
| 266 |
const LowMap& low_map, ChildLists& child_lists) {
|
|
| 267 |
|
|
| 268 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
| 269 |
Node source = n; |
|
| 270 |
|
|
| 271 |
std::vector<Node> targets; |
|
| 272 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
|
| 273 |
Node target = _graph.target(e); |
|
| 274 |
|
|
| 275 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
|
| 276 |
targets.push_back(target); |
|
| 277 |
} |
|
| 278 |
} |
|
| 279 |
|
|
| 280 |
if (targets.size() == 0) {
|
|
| 281 |
child_lists[source].first = INVALID; |
|
| 282 |
} else if (targets.size() == 1) {
|
|
| 283 |
child_lists[source].first = targets[0]; |
|
| 284 |
child_lists[targets[0]].prev = INVALID; |
|
| 285 |
child_lists[targets[0]].next = INVALID; |
|
| 286 |
} else {
|
|
| 287 |
radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
|
| 288 |
for (int i = 1; i < int(targets.size()); ++i) {
|
|
| 289 |
child_lists[targets[i]].prev = targets[i - 1]; |
|
| 290 |
child_lists[targets[i - 1]].next = targets[i]; |
|
| 291 |
} |
|
| 292 |
child_lists[targets.back()].next = INVALID; |
|
| 293 |
child_lists[targets.front()].prev = INVALID; |
|
| 294 |
child_lists[source].first = targets.front(); |
|
| 295 |
} |
|
| 296 |
} |
|
| 297 |
} |
|
| 298 |
|
|
| 299 |
void walkUp(const Node& node, Node root, int rorder, |
|
| 300 |
const PredMap& pred_map, const LowMap& low_map, |
|
| 301 |
const OrderMap& order_map, const OrderList& order_list, |
|
| 302 |
NodeData& node_data, MergeRoots& merge_roots) {
|
|
| 303 |
|
|
| 304 |
int na, nb; |
|
| 305 |
bool da, db; |
|
| 306 |
|
|
| 307 |
na = nb = order_map[node]; |
|
| 308 |
da = true; db = false; |
|
| 309 |
|
|
| 310 |
while (true) {
|
|
| 311 |
|
|
| 312 |
if (node_data[na].visited == rorder) break; |
|
| 313 |
if (node_data[nb].visited == rorder) break; |
|
| 314 |
|
|
| 315 |
node_data[na].visited = rorder; |
|
| 316 |
node_data[nb].visited = rorder; |
|
| 317 |
|
|
| 318 |
int rn = -1; |
|
| 319 |
|
|
| 320 |
if (na >= int(order_list.size())) {
|
|
| 321 |
rn = na; |
|
| 322 |
} else if (nb >= int(order_list.size())) {
|
|
| 323 |
rn = nb; |
|
| 324 |
} |
|
| 325 |
|
|
| 326 |
if (rn == -1) {
|
|
| 327 |
int nn; |
|
| 328 |
|
|
| 329 |
nn = da ? node_data[na].prev : node_data[na].next; |
|
| 330 |
da = node_data[nn].prev != na; |
|
| 331 |
na = nn; |
|
| 332 |
|
|
| 333 |
nn = db ? node_data[nb].prev : node_data[nb].next; |
|
| 334 |
db = node_data[nn].prev != nb; |
|
| 335 |
nb = nn; |
|
| 336 |
|
|
| 337 |
} else {
|
|
| 338 |
|
|
| 339 |
Node rep = order_list[rn - order_list.size()]; |
|
| 340 |
Node parent = _graph.source(pred_map[rep]); |
|
| 341 |
|
|
| 342 |
if (low_map[rep] < rorder) {
|
|
| 343 |
merge_roots[parent].push_back(rn); |
|
| 344 |
} else {
|
|
| 345 |
merge_roots[parent].push_front(rn); |
|
| 346 |
} |
|
| 347 |
|
|
| 348 |
if (parent != root) {
|
|
| 349 |
na = nb = order_map[parent]; |
|
| 350 |
da = true; db = false; |
|
| 351 |
} else {
|
|
| 352 |
break; |
|
| 353 |
} |
|
| 354 |
} |
|
| 355 |
} |
|
| 356 |
} |
|
| 357 |
|
|
| 358 |
void walkDown(int rn, int rorder, NodeData& node_data, |
|
| 359 |
OrderList& order_list, ChildLists& child_lists, |
|
| 360 |
AncestorMap& ancestor_map, LowMap& low_map, |
|
| 361 |
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
|
| 362 |
|
|
| 363 |
std::vector<std::pair<int, bool> > merge_stack; |
|
| 364 |
|
|
| 365 |
for (int di = 0; di < 2; ++di) {
|
|
| 366 |
bool rd = di == 0; |
|
| 367 |
int pn = rn; |
|
| 368 |
int n = rd ? node_data[rn].next : node_data[rn].prev; |
|
| 369 |
|
|
| 370 |
while (n != rn) {
|
|
| 371 |
|
|
| 372 |
Node node = order_list[n]; |
|
| 373 |
|
|
| 374 |
if (embed_arc[node]) {
|
|
| 375 |
|
|
| 376 |
// Merging components on the critical path |
|
| 377 |
while (!merge_stack.empty()) {
|
|
| 378 |
|
|
| 379 |
// Component root |
|
| 380 |
int cn = merge_stack.back().first; |
|
| 381 |
bool cd = merge_stack.back().second; |
|
| 382 |
merge_stack.pop_back(); |
|
| 383 |
|
|
| 384 |
// Parent of component |
|
| 385 |
int dn = merge_stack.back().first; |
|
| 386 |
bool dd = merge_stack.back().second; |
|
| 387 |
merge_stack.pop_back(); |
|
| 388 |
|
|
| 389 |
Node parent = order_list[dn]; |
|
| 390 |
|
|
| 391 |
// Erasing from merge_roots |
|
| 392 |
merge_roots[parent].pop_front(); |
|
| 393 |
|
|
| 394 |
Node child = order_list[cn - order_list.size()]; |
|
| 395 |
|
|
| 396 |
// Erasing from child_lists |
|
| 397 |
if (child_lists[child].prev != INVALID) {
|
|
| 398 |
child_lists[child_lists[child].prev].next = |
|
| 399 |
child_lists[child].next; |
|
| 400 |
} else {
|
|
| 401 |
child_lists[parent].first = child_lists[child].next; |
|
| 402 |
} |
|
| 403 |
|
|
| 404 |
if (child_lists[child].next != INVALID) {
|
|
| 405 |
child_lists[child_lists[child].next].prev = |
|
| 406 |
child_lists[child].prev; |
|
| 407 |
} |
|
| 408 |
|
|
| 409 |
// Merging external faces |
|
| 410 |
{
|
|
| 411 |
int en = cn; |
|
| 412 |
cn = cd ? node_data[cn].prev : node_data[cn].next; |
|
| 413 |
cd = node_data[cn].next == en; |
|
| 414 |
|
|
| 415 |
} |
|
| 416 |
|
|
| 417 |
if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
|
| 418 |
if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
|
| 419 |
|
|
| 420 |
} |
|
| 421 |
|
|
| 422 |
bool d = pn == node_data[n].prev; |
|
| 423 |
|
|
| 424 |
if (node_data[n].prev == node_data[n].next && |
|
| 425 |
node_data[n].inverted) {
|
|
| 426 |
d = !d; |
|
| 427 |
} |
|
| 428 |
|
|
| 429 |
// Embedding arc into external face |
|
| 430 |
if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
|
| 431 |
if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
|
| 432 |
pn = rn; |
|
| 433 |
|
|
| 434 |
embed_arc[order_list[n]] = false; |
|
| 435 |
} |
|
| 436 |
|
|
| 437 |
if (!merge_roots[node].empty()) {
|
|
| 438 |
|
|
| 439 |
bool d = pn == node_data[n].prev; |
|
| 440 |
|
|
| 441 |
merge_stack.push_back(std::make_pair(n, d)); |
|
| 442 |
|
|
| 443 |
int rn = merge_roots[node].front(); |
|
| 444 |
|
|
| 445 |
int xn = node_data[rn].next; |
|
| 446 |
Node xnode = order_list[xn]; |
|
| 447 |
|
|
| 448 |
int yn = node_data[rn].prev; |
|
| 449 |
Node ynode = order_list[yn]; |
|
| 450 |
|
|
| 451 |
bool rd; |
|
| 452 |
if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
|
|
| 453 |
rd = true; |
|
| 454 |
} else if (!external(ynode, rorder, child_lists, |
|
| 455 |
ancestor_map, low_map)) {
|
|
| 456 |
rd = false; |
|
| 457 |
} else if (pertinent(xnode, embed_arc, merge_roots)) {
|
|
| 458 |
rd = true; |
|
| 459 |
} else {
|
|
| 460 |
rd = false; |
|
| 461 |
} |
|
| 462 |
|
|
| 463 |
merge_stack.push_back(std::make_pair(rn, rd)); |
|
| 464 |
|
|
| 465 |
pn = rn; |
|
| 466 |
n = rd ? xn : yn; |
|
| 467 |
|
|
| 468 |
} else if (!external(node, rorder, child_lists, |
|
| 469 |
ancestor_map, low_map)) {
|
|
| 470 |
int nn = (node_data[n].next != pn ? |
|
| 471 |
node_data[n].next : node_data[n].prev); |
|
| 472 |
|
|
| 473 |
bool nd = n == node_data[nn].prev; |
|
| 474 |
|
|
| 475 |
if (nd) node_data[nn].prev = pn; |
|
| 476 |
else node_data[nn].next = pn; |
|
| 477 |
|
|
| 478 |
if (n == node_data[pn].prev) node_data[pn].prev = nn; |
|
| 479 |
else node_data[pn].next = nn; |
|
| 480 |
|
|
| 481 |
node_data[nn].inverted = |
|
| 482 |
(node_data[nn].prev == node_data[nn].next && nd != rd); |
|
| 483 |
|
|
| 484 |
n = nn; |
|
| 485 |
} |
|
| 486 |
else break; |
|
| 487 |
|
|
| 488 |
} |
|
| 489 |
|
|
| 490 |
if (!merge_stack.empty() || n == rn) {
|
|
| 491 |
break; |
|
| 492 |
} |
|
| 493 |
} |
|
| 494 |
} |
|
| 495 |
|
|
| 496 |
void initFace(const Node& node, NodeData& node_data, |
|
| 497 |
const OrderMap& order_map, const OrderList& order_list) {
|
|
| 498 |
int n = order_map[node]; |
|
| 499 |
int rn = n + order_list.size(); |
|
| 500 |
|
|
| 501 |
node_data[n].next = node_data[n].prev = rn; |
|
| 502 |
node_data[rn].next = node_data[rn].prev = n; |
|
| 503 |
|
|
| 504 |
node_data[n].visited = order_list.size(); |
|
| 505 |
node_data[rn].visited = order_list.size(); |
|
| 506 |
|
|
| 507 |
} |
|
| 508 |
|
|
| 509 |
bool external(const Node& node, int rorder, |
|
| 510 |
ChildLists& child_lists, AncestorMap& ancestor_map, |
|
| 511 |
LowMap& low_map) {
|
|
| 512 |
Node child = child_lists[node].first; |
|
| 513 |
|
|
| 514 |
if (child != INVALID) {
|
|
| 515 |
if (low_map[child] < rorder) return true; |
|
| 516 |
} |
|
| 517 |
|
|
| 518 |
if (ancestor_map[node] < rorder) return true; |
|
| 519 |
|
|
| 520 |
return false; |
|
| 521 |
} |
|
| 522 |
|
|
| 523 |
bool pertinent(const Node& node, const EmbedArc& embed_arc, |
|
| 524 |
const MergeRoots& merge_roots) {
|
|
| 525 |
return !merge_roots[node].empty() || embed_arc[node]; |
|
| 526 |
} |
|
| 527 |
|
|
| 528 |
|
|
| 524 |
template <typename GR> |
|
| 525 |
bool checkPlanarity(const GR& graph) {
|
|
| 526 |
_planarity_bits::PlanarityChecking<GR> pc(graph); |
|
| 527 |
return pc.run(); |
|
| 528 |
} |
|
| 529 | 529 |
|
| 530 | 530 |
/// \ingroup planar |
| 531 | 531 |
/// |
| 532 | 532 |
/// \brief Planar embedding of an undirected simple graph |
| 533 | 533 |
/// |
| 534 | 534 |
/// This class implements the Boyer-Myrvold algorithm for planar |
| 535 | 535 |
/// embedding of an undirected graph. The planar embedding is an |
| 536 | 536 |
/// ordering of the outgoing edges of the nodes, which is a possible |
| 537 | 537 |
/// configuration to draw the graph in the plane. If there is not |
| 538 | 538 |
/// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
| 539 | 539 |
/// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
|
| 540 | 540 |
/// 3 ANode and 3 BNode) subdivision. |
| 541 | 541 |
/// |
| 542 | 542 |
/// The current implementation calculates either an embedding or a |
| 543 | 543 |
/// Kuratowski subdivision. The running time of the algorithm is |
| 544 | 544 |
/// \f$ O(n) \f$. |
| 545 | 545 |
template <typename Graph> |
| 546 | 546 |
class PlanarEmbedding {
|
| 547 | 547 |
private: |
| 548 | 548 |
|
| 549 | 549 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 550 | 550 |
|
| 551 | 551 |
const Graph& _graph; |
| 552 | 552 |
typename Graph::template ArcMap<Arc> _embedding; |
| ... | ... |
@@ -691,49 +691,49 @@ |
| 691 | 691 |
for (int i = 0; i < int(order_list.size()); ++i) {
|
| 692 | 692 |
|
| 693 | 693 |
mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
| 694 | 694 |
child_lists, arc_lists); |
| 695 | 695 |
storeEmbedding(order_list[i], node_data, order_map, pred_map, |
| 696 | 696 |
arc_lists, flip_map); |
| 697 | 697 |
} |
| 698 | 698 |
|
| 699 | 699 |
return true; |
| 700 | 700 |
} |
| 701 | 701 |
|
| 702 | 702 |
/// \brief Gives back the successor of an arc |
| 703 | 703 |
/// |
| 704 | 704 |
/// Gives back the successor of an arc. This function makes |
| 705 | 705 |
/// possible to query the cyclic order of the outgoing arcs from |
| 706 | 706 |
/// a node. |
| 707 | 707 |
Arc next(const Arc& arc) const {
|
| 708 | 708 |
return _embedding[arc]; |
| 709 | 709 |
} |
| 710 | 710 |
|
| 711 | 711 |
/// \brief Gives back the calculated embedding map |
| 712 | 712 |
/// |
| 713 | 713 |
/// The returned map contains the successor of each arc in the |
| 714 | 714 |
/// graph. |
| 715 |
const EmbeddingMap& |
|
| 715 |
const EmbeddingMap& embeddingMap() const {
|
|
| 716 | 716 |
return _embedding; |
| 717 | 717 |
} |
| 718 | 718 |
|
| 719 | 719 |
/// \brief Gives back true if the undirected arc is in the |
| 720 | 720 |
/// kuratowski subdivision |
| 721 | 721 |
/// |
| 722 | 722 |
/// Gives back true if the undirected arc is in the kuratowski |
| 723 | 723 |
/// subdivision |
| 724 | 724 |
/// \note The \c run() had to be called with true value. |
| 725 | 725 |
bool kuratowski(const Edge& edge) {
|
| 726 | 726 |
return _kuratowski[edge]; |
| 727 | 727 |
} |
| 728 | 728 |
|
| 729 | 729 |
private: |
| 730 | 730 |
|
| 731 | 731 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
| 732 | 732 |
const LowMap& low_map, ChildLists& child_lists) {
|
| 733 | 733 |
|
| 734 | 734 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 735 | 735 |
Node source = n; |
| 736 | 736 |
|
| 737 | 737 |
std::vector<Node> targets; |
| 738 | 738 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 739 | 739 |
Node target = _graph.target(e); |
| ... | ... |
@@ -218,42 +218,45 @@ |
| 218 | 218 |
} |
| 219 | 219 |
|
| 220 | 220 |
void checkColoring(const Graph& graph, PC& pc, int num) {
|
| 221 | 221 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 222 | 222 |
check(pc.colorIndex(n) >= 0 && pc.colorIndex(n) < num, |
| 223 | 223 |
"Wrong coloring"); |
| 224 | 224 |
} |
| 225 | 225 |
for (EdgeIt e(graph); e != INVALID; ++e) {
|
| 226 | 226 |
check(pc.colorIndex(graph.u(e)) != pc.colorIndex(graph.v(e)), |
| 227 | 227 |
"Wrong coloring"); |
| 228 | 228 |
} |
| 229 | 229 |
} |
| 230 | 230 |
|
| 231 | 231 |
int main() {
|
| 232 | 232 |
|
| 233 | 233 |
for (int i = 0; i < lgfn; ++i) {
|
| 234 | 234 |
std::istringstream lgfs(lgf[i]); |
| 235 | 235 |
|
| 236 | 236 |
SmartGraph graph; |
| 237 | 237 |
graphReader(graph, lgfs).run(); |
| 238 | 238 |
|
| 239 | 239 |
check(simpleGraph(graph), "Test graphs must be simple"); |
| 240 | 240 |
|
| 241 | 241 |
PE pe(graph); |
| 242 |
|
|
| 242 |
bool planar = pe.run(); |
|
| 243 |
check(checkPlanarity(graph) == planar, "Planarity checking failed"); |
|
| 244 |
|
|
| 245 |
if (planar) {
|
|
| 243 | 246 |
checkEmbedding(graph, pe); |
| 244 | 247 |
|
| 245 | 248 |
PlanarDrawing<Graph> pd(graph); |
| 246 |
pd.run(pe. |
|
| 249 |
pd.run(pe.embeddingMap()); |
|
| 247 | 250 |
checkDrawing(graph, pd); |
| 248 | 251 |
|
| 249 | 252 |
PlanarColoring<Graph> pc(graph); |
| 250 |
pc.runFiveColoring(pe. |
|
| 253 |
pc.runFiveColoring(pe.embeddingMap()); |
|
| 251 | 254 |
checkColoring(graph, pc, 5); |
| 252 | 255 |
|
| 253 | 256 |
} else {
|
| 254 | 257 |
checkKuratowski(graph, pe); |
| 255 | 258 |
} |
| 256 | 259 |
} |
| 257 | 260 |
|
| 258 | 261 |
return 0; |
| 259 | 262 |
} |
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