deba@797: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@797: *
deba@797: * This file is a part of LEMON, a generic C++ optimization library.
deba@797: *
deba@797: * Copyright (C) 2003-2009
deba@797: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@797: * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@797: *
deba@797: * Permission to use, modify and distribute this software is granted
deba@797: * provided that this copyright notice appears in all copies. For
deba@797: * precise terms see the accompanying LICENSE file.
deba@797: *
deba@797: * This software is provided "AS IS" with no warranty of any kind,
deba@797: * express or implied, and with no claim as to its suitability for any
deba@797: * purpose.
deba@797: *
deba@797: */
deba@797:
deba@797: #ifndef LEMON_PLANARITY_H
deba@797: #define LEMON_PLANARITY_H
deba@797:
deba@797: /// \ingroup planar
deba@797: /// \file
deba@797: /// \brief Planarity checking, embedding, drawing and coloring
deba@797:
deba@797: #include <vector>
deba@797: #include <list>
deba@797:
deba@797: #include <lemon/dfs.h>
deba@797: #include <lemon/bfs.h>
deba@797: #include <lemon/radix_sort.h>
deba@797: #include <lemon/maps.h>
deba@797: #include <lemon/path.h>
deba@797: #include <lemon/bucket_heap.h>
deba@797: #include <lemon/adaptors.h>
deba@797: #include <lemon/edge_set.h>
deba@797: #include <lemon/color.h>
deba@797: #include <lemon/dim2.h>
deba@797:
deba@797: namespace lemon {
deba@797:
deba@797: namespace _planarity_bits {
deba@797:
deba@797: template <typename Graph>
deba@797: struct PlanarityVisitor : DfsVisitor<Graph> {
deba@797:
deba@797: TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@797:
deba@797: typedef typename Graph::template NodeMap<Arc> PredMap;
deba@797:
deba@797: typedef typename Graph::template EdgeMap<bool> TreeMap;
deba@797:
deba@797: typedef typename Graph::template NodeMap<int> OrderMap;
deba@797: typedef std::vector<Node> OrderList;
deba@797:
deba@797: typedef typename Graph::template NodeMap<int> LowMap;
deba@797: typedef typename Graph::template NodeMap<int> AncestorMap;
deba@797:
deba@797: PlanarityVisitor(const Graph& graph,
deba@797: PredMap& pred_map, TreeMap& tree_map,
deba@797: OrderMap& order_map, OrderList& order_list,
deba@797: AncestorMap& ancestor_map, LowMap& low_map)
deba@797: : _graph(graph), _pred_map(pred_map), _tree_map(tree_map),
deba@797: _order_map(order_map), _order_list(order_list),
deba@797: _ancestor_map(ancestor_map), _low_map(low_map) {}
deba@797:
deba@797: void reach(const Node& node) {
deba@797: _order_map[node] = _order_list.size();
deba@797: _low_map[node] = _order_list.size();
deba@797: _ancestor_map[node] = _order_list.size();
deba@797: _order_list.push_back(node);
deba@797: }
deba@797:
deba@797: void discover(const Arc& arc) {
deba@797: Node source = _graph.source(arc);
deba@797: Node target = _graph.target(arc);
deba@797:
deba@797: _tree_map[arc] = true;
deba@797: _pred_map[target] = arc;
deba@797: }
deba@797:
deba@797: void examine(const Arc& arc) {
deba@797: Node source = _graph.source(arc);
deba@797: Node target = _graph.target(arc);
deba@797:
deba@797: if (_order_map[target] < _order_map[source] && !_tree_map[arc]) {
deba@797: if (_low_map[source] > _order_map[target]) {
deba@797: _low_map[source] = _order_map[target];
deba@797: }
deba@797: if (_ancestor_map[source] > _order_map[target]) {
deba@797: _ancestor_map[source] = _order_map[target];
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: void backtrack(const Arc& arc) {
deba@797: Node source = _graph.source(arc);
deba@797: Node target = _graph.target(arc);
deba@797:
deba@797: if (_low_map[source] > _low_map[target]) {
deba@797: _low_map[source] = _low_map[target];
deba@797: }
deba@797: }
deba@797:
deba@797: const Graph& _graph;
deba@797: PredMap& _pred_map;
deba@797: TreeMap& _tree_map;
deba@797: OrderMap& _order_map;
deba@797: OrderList& _order_list;
deba@797: AncestorMap& _ancestor_map;
deba@797: LowMap& _low_map;
deba@797: };
deba@797:
deba@797: template <typename Graph, bool embedding = true>
deba@797: struct NodeDataNode {
deba@797: int prev, next;
deba@797: int visited;
deba@797: typename Graph::Arc first;
deba@797: bool inverted;
deba@797: };
deba@797:
deba@797: template <typename Graph>
deba@797: struct NodeDataNode<Graph, false> {
deba@797: int prev, next;
deba@797: int visited;
deba@797: };
deba@797:
deba@797: template <typename Graph>
deba@797: struct ChildListNode {
deba@797: typedef typename Graph::Node Node;
deba@797: Node first;
deba@797: Node prev, next;
deba@797: };
deba@797:
deba@797: template <typename Graph>
deba@797: struct ArcListNode {
deba@797: typename Graph::Arc prev, next;
deba@797: };
deba@797:
deba@798: template <typename Graph>
deba@798: class PlanarityChecking {
deba@798: private:
deba@798:
deba@798: TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@798:
deba@798: const Graph& _graph;
deba@798:
deba@798: private:
deba@798:
deba@798: typedef typename Graph::template NodeMap<Arc> PredMap;
deba@798:
deba@798: typedef typename Graph::template EdgeMap<bool> TreeMap;
deba@798:
deba@798: typedef typename Graph::template NodeMap<int> OrderMap;
deba@798: typedef std::vector<Node> OrderList;
deba@798:
deba@798: typedef typename Graph::template NodeMap<int> LowMap;
deba@798: typedef typename Graph::template NodeMap<int> AncestorMap;
deba@798:
deba@798: typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
deba@798: typedef std::vector<NodeDataNode> NodeData;
deba@798:
deba@798: typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
deba@798: typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
deba@798:
deba@798: typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
deba@798:
deba@798: typedef typename Graph::template NodeMap<bool> EmbedArc;
deba@798:
deba@798: public:
deba@798:
deba@798: PlanarityChecking(const Graph& graph) : _graph(graph) {}
deba@798:
deba@798: bool run() {
deba@798: typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
deba@798:
deba@798: PredMap pred_map(_graph, INVALID);
deba@798: TreeMap tree_map(_graph, false);
deba@798:
deba@798: OrderMap order_map(_graph, -1);
deba@798: OrderList order_list;
deba@798:
deba@798: AncestorMap ancestor_map(_graph, -1);
deba@798: LowMap low_map(_graph, -1);
deba@798:
deba@798: Visitor visitor(_graph, pred_map, tree_map,
deba@798: order_map, order_list, ancestor_map, low_map);
deba@798: DfsVisit<Graph, Visitor> visit(_graph, visitor);
deba@798: visit.run();
deba@798:
deba@798: ChildLists child_lists(_graph);
deba@798: createChildLists(tree_map, order_map, low_map, child_lists);
deba@798:
deba@798: NodeData node_data(2 * order_list.size());
deba@798:
deba@798: EmbedArc embed_arc(_graph, false);
deba@798:
deba@798: MergeRoots merge_roots(_graph);
deba@798:
deba@798: for (int i = order_list.size() - 1; i >= 0; --i) {
deba@798:
deba@798: Node node = order_list[i];
deba@798:
deba@798: Node source = node;
deba@798: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@798: Node target = _graph.target(e);
deba@798:
deba@798: if (order_map[source] < order_map[target] && tree_map[e]) {
deba@798: initFace(target, node_data, order_map, order_list);
deba@798: }
deba@798: }
deba@798:
deba@798: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@798: Node target = _graph.target(e);
deba@798:
deba@798: if (order_map[source] < order_map[target] && !tree_map[e]) {
deba@798: embed_arc[target] = true;
deba@798: walkUp(target, source, i, pred_map, low_map,
deba@798: order_map, order_list, node_data, merge_roots);
deba@798: }
deba@798: }
deba@798:
deba@798: for (typename MergeRoots::Value::iterator it =
deba@798: merge_roots[node].begin();
deba@798: it != merge_roots[node].end(); ++it) {
deba@798: int rn = *it;
deba@798: walkDown(rn, i, node_data, order_list, child_lists,
deba@798: ancestor_map, low_map, embed_arc, merge_roots);
deba@798: }
deba@798: merge_roots[node].clear();
deba@798:
deba@798: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@798: Node target = _graph.target(e);
deba@798:
deba@798: if (order_map[source] < order_map[target] && !tree_map[e]) {
deba@798: if (embed_arc[target]) {
deba@798: return false;
deba@798: }
deba@798: }
deba@798: }
deba@798: }
deba@798:
deba@798: return true;
deba@798: }
deba@798:
deba@798: private:
deba@798:
deba@798: void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
deba@798: const LowMap& low_map, ChildLists& child_lists) {
deba@798:
deba@798: for (NodeIt n(_graph); n != INVALID; ++n) {
deba@798: Node source = n;
deba@798:
deba@798: std::vector<Node> targets;
deba@798: for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@798: Node target = _graph.target(e);
deba@798:
deba@798: if (order_map[source] < order_map[target] && tree_map[e]) {
deba@798: targets.push_back(target);
deba@798: }
deba@798: }
deba@798:
deba@798: if (targets.size() == 0) {
deba@798: child_lists[source].first = INVALID;
deba@798: } else if (targets.size() == 1) {
deba@798: child_lists[source].first = targets[0];
deba@798: child_lists[targets[0]].prev = INVALID;
deba@798: child_lists[targets[0]].next = INVALID;
deba@798: } else {
deba@798: radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
deba@798: for (int i = 1; i < int(targets.size()); ++i) {
deba@798: child_lists[targets[i]].prev = targets[i - 1];
deba@798: child_lists[targets[i - 1]].next = targets[i];
deba@798: }
deba@798: child_lists[targets.back()].next = INVALID;
deba@798: child_lists[targets.front()].prev = INVALID;
deba@798: child_lists[source].first = targets.front();
deba@798: }
deba@798: }
deba@798: }
deba@798:
deba@798: void walkUp(const Node& node, Node root, int rorder,
deba@798: const PredMap& pred_map, const LowMap& low_map,
deba@798: const OrderMap& order_map, const OrderList& order_list,
deba@798: NodeData& node_data, MergeRoots& merge_roots) {
deba@798:
deba@798: int na, nb;
deba@798: bool da, db;
deba@798:
deba@798: na = nb = order_map[node];
deba@798: da = true; db = false;
deba@798:
deba@798: while (true) {
deba@798:
deba@798: if (node_data[na].visited == rorder) break;
deba@798: if (node_data[nb].visited == rorder) break;
deba@798:
deba@798: node_data[na].visited = rorder;
deba@798: node_data[nb].visited = rorder;
deba@798:
deba@798: int rn = -1;
deba@798:
deba@798: if (na >= int(order_list.size())) {
deba@798: rn = na;
deba@798: } else if (nb >= int(order_list.size())) {
deba@798: rn = nb;
deba@798: }
deba@798:
deba@798: if (rn == -1) {
deba@798: int nn;
deba@798:
deba@798: nn = da ? node_data[na].prev : node_data[na].next;
deba@798: da = node_data[nn].prev != na;
deba@798: na = nn;
deba@798:
deba@798: nn = db ? node_data[nb].prev : node_data[nb].next;
deba@798: db = node_data[nn].prev != nb;
deba@798: nb = nn;
deba@798:
deba@798: } else {
deba@798:
deba@798: Node rep = order_list[rn - order_list.size()];
deba@798: Node parent = _graph.source(pred_map[rep]);
deba@798:
deba@798: if (low_map[rep] < rorder) {
deba@798: merge_roots[parent].push_back(rn);
deba@798: } else {
deba@798: merge_roots[parent].push_front(rn);
deba@798: }
deba@798:
deba@798: if (parent != root) {
deba@798: na = nb = order_map[parent];
deba@798: da = true; db = false;
deba@798: } else {
deba@798: break;
deba@798: }
deba@798: }
deba@798: }
deba@798: }
deba@798:
deba@798: void walkDown(int rn, int rorder, NodeData& node_data,
deba@798: OrderList& order_list, ChildLists& child_lists,
deba@798: AncestorMap& ancestor_map, LowMap& low_map,
deba@798: EmbedArc& embed_arc, MergeRoots& merge_roots) {
deba@798:
deba@798: std::vector<std::pair<int, bool> > merge_stack;
deba@798:
deba@798: for (int di = 0; di < 2; ++di) {
deba@798: bool rd = di == 0;
deba@798: int pn = rn;
deba@798: int n = rd ? node_data[rn].next : node_data[rn].prev;
deba@798:
deba@798: while (n != rn) {
deba@798:
deba@798: Node node = order_list[n];
deba@798:
deba@798: if (embed_arc[node]) {
deba@798:
deba@798: // Merging components on the critical path
deba@798: while (!merge_stack.empty()) {
deba@798:
deba@798: // Component root
deba@798: int cn = merge_stack.back().first;
deba@798: bool cd = merge_stack.back().second;
deba@798: merge_stack.pop_back();
deba@798:
deba@798: // Parent of component
deba@798: int dn = merge_stack.back().first;
deba@798: bool dd = merge_stack.back().second;
deba@798: merge_stack.pop_back();
deba@798:
deba@798: Node parent = order_list[dn];
deba@798:
deba@798: // Erasing from merge_roots
deba@798: merge_roots[parent].pop_front();
deba@798:
deba@798: Node child = order_list[cn - order_list.size()];
deba@798:
deba@798: // Erasing from child_lists
deba@798: if (child_lists[child].prev != INVALID) {
deba@798: child_lists[child_lists[child].prev].next =
deba@798: child_lists[child].next;
deba@798: } else {
deba@798: child_lists[parent].first = child_lists[child].next;
deba@798: }
deba@798:
deba@798: if (child_lists[child].next != INVALID) {
deba@798: child_lists[child_lists[child].next].prev =
deba@798: child_lists[child].prev;
deba@798: }
deba@798:
deba@798: // Merging external faces
deba@798: {
deba@798: int en = cn;
deba@798: cn = cd ? node_data[cn].prev : node_data[cn].next;
deba@798: cd = node_data[cn].next == en;
deba@798:
deba@798: }
deba@798:
deba@798: if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
deba@798: if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
deba@798:
deba@798: }
deba@798:
deba@798: bool d = pn == node_data[n].prev;
deba@798:
deba@798: if (node_data[n].prev == node_data[n].next &&
deba@798: node_data[n].inverted) {
deba@798: d = !d;
deba@798: }
deba@798:
deba@798: // Embedding arc into external face
deba@798: if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
deba@798: if (d) node_data[n].prev = rn; else node_data[n].next = rn;
deba@798: pn = rn;
deba@798:
deba@798: embed_arc[order_list[n]] = false;
deba@798: }
deba@798:
deba@798: if (!merge_roots[node].empty()) {
deba@798:
deba@798: bool d = pn == node_data[n].prev;
deba@798:
deba@798: merge_stack.push_back(std::make_pair(n, d));
deba@798:
deba@798: int rn = merge_roots[node].front();
deba@798:
deba@798: int xn = node_data[rn].next;
deba@798: Node xnode = order_list[xn];
deba@798:
deba@798: int yn = node_data[rn].prev;
deba@798: Node ynode = order_list[yn];
deba@798:
deba@798: bool rd;
deba@798: if (!external(xnode, rorder, child_lists,
deba@798: ancestor_map, low_map)) {
deba@798: rd = true;
deba@798: } else if (!external(ynode, rorder, child_lists,
deba@798: ancestor_map, low_map)) {
deba@798: rd = false;
deba@798: } else if (pertinent(xnode, embed_arc, merge_roots)) {
deba@798: rd = true;
deba@798: } else {
deba@798: rd = false;
deba@798: }
deba@798:
deba@798: merge_stack.push_back(std::make_pair(rn, rd));
deba@798:
deba@798: pn = rn;
deba@798: n = rd ? xn : yn;
deba@798:
deba@798: } else if (!external(node, rorder, child_lists,
deba@798: ancestor_map, low_map)) {
deba@798: int nn = (node_data[n].next != pn ?
deba@798: node_data[n].next : node_data[n].prev);
deba@798:
deba@798: bool nd = n == node_data[nn].prev;
deba@798:
deba@798: if (nd) node_data[nn].prev = pn;
deba@798: else node_data[nn].next = pn;
deba@798:
deba@798: if (n == node_data[pn].prev) node_data[pn].prev = nn;
deba@798: else node_data[pn].next = nn;
deba@798:
deba@798: node_data[nn].inverted =
deba@798: (node_data[nn].prev == node_data[nn].next && nd != rd);
deba@798:
deba@798: n = nn;
deba@798: }
deba@798: else break;
deba@798:
deba@798: }
deba@798:
deba@798: if (!merge_stack.empty() || n == rn) {
deba@798: break;
deba@798: }
deba@798: }
deba@798: }
deba@798:
deba@798: void initFace(const Node& node, NodeData& node_data,
deba@798: const OrderMap& order_map, const OrderList& order_list) {
deba@798: int n = order_map[node];
deba@798: int rn = n + order_list.size();
deba@798:
deba@798: node_data[n].next = node_data[n].prev = rn;
deba@798: node_data[rn].next = node_data[rn].prev = n;
deba@798:
deba@798: node_data[n].visited = order_list.size();
deba@798: node_data[rn].visited = order_list.size();
deba@798:
deba@798: }
deba@798:
deba@798: bool external(const Node& node, int rorder,
deba@798: ChildLists& child_lists, AncestorMap& ancestor_map,
deba@798: LowMap& low_map) {
deba@798: Node child = child_lists[node].first;
deba@798:
deba@798: if (child != INVALID) {
deba@798: if (low_map[child] < rorder) return true;
deba@798: }
deba@798:
deba@798: if (ancestor_map[node] < rorder) return true;
deba@798:
deba@798: return false;
deba@798: }
deba@798:
deba@798: bool pertinent(const Node& node, const EmbedArc& embed_arc,
deba@798: const MergeRoots& merge_roots) {
deba@798: return !merge_roots[node].empty() || embed_arc[node];
deba@798: }
deba@798:
deba@798: };
deba@798:
deba@797: }
deba@797:
deba@797: /// \ingroup planar
deba@797: ///
deba@797: /// \brief Planarity checking of an undirected simple graph
deba@797: ///
deba@798: /// This function implements the Boyer-Myrvold algorithm for
kpeter@828: /// planarity checking of an undirected simple graph. It is a simplified
deba@797: /// version of the PlanarEmbedding algorithm class because neither
kpeter@828: /// the embedding nor the Kuratowski subdivisons are computed.
deba@798: template <typename GR>
deba@798: bool checkPlanarity(const GR& graph) {
deba@798: _planarity_bits::PlanarityChecking<GR> pc(graph);
deba@798: return pc.run();
deba@798: }
deba@797:
deba@797: /// \ingroup planar
deba@797: ///
deba@797: /// \brief Planar embedding of an undirected simple graph
deba@797: ///
deba@797: /// This class implements the Boyer-Myrvold algorithm for planar
kpeter@828: /// embedding of an undirected simple graph. The planar embedding is an
deba@797: /// ordering of the outgoing edges of the nodes, which is a possible
deba@797: /// configuration to draw the graph in the plane. If there is not
kpeter@828: /// such ordering then the graph contains a K<sub>5</sub> (full graph
kpeter@828: /// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on
kpeter@828: /// 3 Red and 3 Blue nodes) subdivision.
deba@797: ///
deba@797: /// The current implementation calculates either an embedding or a
kpeter@828: /// Kuratowski subdivision. The running time of the algorithm is O(n).
kpeter@828: ///
kpeter@828: /// \see PlanarDrawing, checkPlanarity()
deba@797: template <typename Graph>
deba@797: class PlanarEmbedding {
deba@797: private:
deba@797:
deba@797: TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@797:
deba@797: const Graph& _graph;
deba@797: typename Graph::template ArcMap<Arc> _embedding;
deba@797:
deba@797: typename Graph::template EdgeMap<bool> _kuratowski;
deba@797:
deba@797: private:
deba@797:
deba@797: typedef typename Graph::template NodeMap<Arc> PredMap;
deba@797:
deba@797: typedef typename Graph::template EdgeMap<bool> TreeMap;
deba@797:
deba@797: typedef typename Graph::template NodeMap<int> OrderMap;
deba@797: typedef std::vector<Node> OrderList;
deba@797:
deba@797: typedef typename Graph::template NodeMap<int> LowMap;
deba@797: typedef typename Graph::template NodeMap<int> AncestorMap;
deba@797:
deba@797: typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode;
deba@797: typedef std::vector<NodeDataNode> NodeData;
deba@797:
deba@797: typedef _planarity_bits::ChildListNode<Graph> ChildListNode;
deba@797: typedef typename Graph::template NodeMap<ChildListNode> ChildLists;
deba@797:
deba@797: typedef typename Graph::template NodeMap<std::list<int> > MergeRoots;
deba@797:
deba@797: typedef typename Graph::template NodeMap<Arc> EmbedArc;
deba@797:
deba@797: typedef _planarity_bits::ArcListNode<Graph> ArcListNode;
deba@797: typedef typename Graph::template ArcMap<ArcListNode> ArcLists;
deba@797:
deba@797: typedef typename Graph::template NodeMap<bool> FlipMap;
deba@797:
deba@797: typedef typename Graph::template NodeMap<int> TypeMap;
deba@797:
deba@797: enum IsolatorNodeType {
deba@797: HIGHX = 6, LOWX = 7,
deba@797: HIGHY = 8, LOWY = 9,
deba@797: ROOT = 10, PERTINENT = 11,
deba@797: INTERNAL = 12
deba@797: };
deba@797:
deba@797: public:
deba@797:
kpeter@828: /// \brief The map type for storing the embedding
kpeter@828: ///
kpeter@828: /// The map type for storing the embedding.
kpeter@828: /// \see embeddingMap()
deba@797: typedef typename Graph::template ArcMap<Arc> EmbeddingMap;
deba@797:
deba@797: /// \brief Constructor
deba@797: ///
kpeter@828: /// Constructor.
kpeter@828: /// \pre The graph must be simple, i.e. it should not
kpeter@828: /// contain parallel or loop arcs.
deba@797: PlanarEmbedding(const Graph& graph)
deba@797: : _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
deba@797:
kpeter@828: /// \brief Run the algorithm.
deba@797: ///
kpeter@828: /// This function runs the algorithm.
kpeter@828: /// \param kuratowski If this parameter is set to \c false, then the
deba@797: /// algorithm does not compute a Kuratowski subdivision.
kpeter@828: /// \return \c true if the graph is planar.
deba@797: bool run(bool kuratowski = true) {
deba@797: typedef _planarity_bits::PlanarityVisitor<Graph> Visitor;
deba@797:
deba@797: PredMap pred_map(_graph, INVALID);
deba@797: TreeMap tree_map(_graph, false);
deba@797:
deba@797: OrderMap order_map(_graph, -1);
deba@797: OrderList order_list;
deba@797:
deba@797: AncestorMap ancestor_map(_graph, -1);
deba@797: LowMap low_map(_graph, -1);
deba@797:
deba@797: Visitor visitor(_graph, pred_map, tree_map,
deba@797: order_map, order_list, ancestor_map, low_map);
deba@797: DfsVisit<Graph, Visitor> visit(_graph, visitor);
deba@797: visit.run();
deba@797:
deba@797: ChildLists child_lists(_graph);
deba@797: createChildLists(tree_map, order_map, low_map, child_lists);
deba@797:
deba@797: NodeData node_data(2 * order_list.size());
deba@797:
deba@797: EmbedArc embed_arc(_graph, INVALID);
deba@797:
deba@797: MergeRoots merge_roots(_graph);
deba@797:
deba@797: ArcLists arc_lists(_graph);
deba@797:
deba@797: FlipMap flip_map(_graph, false);
deba@797:
deba@797: for (int i = order_list.size() - 1; i >= 0; --i) {
deba@797:
deba@797: Node node = order_list[i];
deba@797:
deba@797: node_data[i].first = INVALID;
deba@797:
deba@797: Node source = node;
deba@797: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@797: Node target = _graph.target(e);
deba@797:
deba@797: if (order_map[source] < order_map[target] && tree_map[e]) {
deba@797: initFace(target, arc_lists, node_data,
deba@797: pred_map, order_map, order_list);
deba@797: }
deba@797: }
deba@797:
deba@797: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@797: Node target = _graph.target(e);
deba@797:
deba@797: if (order_map[source] < order_map[target] && !tree_map[e]) {
deba@797: embed_arc[target] = e;
deba@797: walkUp(target, source, i, pred_map, low_map,
deba@797: order_map, order_list, node_data, merge_roots);
deba@797: }
deba@797: }
deba@797:
deba@797: for (typename MergeRoots::Value::iterator it =
deba@797: merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
deba@797: int rn = *it;
deba@797: walkDown(rn, i, node_data, arc_lists, flip_map, order_list,
deba@797: child_lists, ancestor_map, low_map, embed_arc, merge_roots);
deba@797: }
deba@797: merge_roots[node].clear();
deba@797:
deba@797: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@797: Node target = _graph.target(e);
deba@797:
deba@797: if (order_map[source] < order_map[target] && !tree_map[e]) {
deba@797: if (embed_arc[target] != INVALID) {
deba@797: if (kuratowski) {
deba@797: isolateKuratowski(e, node_data, arc_lists, flip_map,
deba@797: order_map, order_list, pred_map, child_lists,
deba@797: ancestor_map, low_map,
deba@797: embed_arc, merge_roots);
deba@797: }
deba@797: return false;
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: for (int i = 0; i < int(order_list.size()); ++i) {
deba@797:
deba@797: mergeRemainingFaces(order_list[i], node_data, order_list, order_map,
deba@797: child_lists, arc_lists);
deba@797: storeEmbedding(order_list[i], node_data, order_map, pred_map,
deba@797: arc_lists, flip_map);
deba@797: }
deba@797:
deba@797: return true;
deba@797: }
deba@797:
kpeter@828: /// \brief Give back the successor of an arc
deba@797: ///
kpeter@828: /// This function gives back the successor of an arc. It makes
deba@797: /// possible to query the cyclic order of the outgoing arcs from
deba@797: /// a node.
deba@797: Arc next(const Arc& arc) const {
deba@797: return _embedding[arc];
deba@797: }
deba@797:
kpeter@828: /// \brief Give back the calculated embedding map
deba@797: ///
kpeter@828: /// This function gives back the calculated embedding map, which
kpeter@828: /// contains the successor of each arc in the cyclic order of the
kpeter@828: /// outgoing arcs of its source node.
deba@798: const EmbeddingMap& embeddingMap() const {
deba@797: return _embedding;
deba@797: }
deba@797:
kpeter@828: /// \brief Give back \c true if the given edge is in the Kuratowski
kpeter@828: /// subdivision
deba@797: ///
kpeter@828: /// This function gives back \c true if the given edge is in the found
kpeter@828: /// Kuratowski subdivision.
kpeter@828: /// \pre The \c run() function must be called with \c true parameter
kpeter@828: /// before using this function.
kpeter@828: bool kuratowski(const Edge& edge) const {
deba@797: return _kuratowski[edge];
deba@797: }
deba@797:
deba@797: private:
deba@797:
deba@797: void createChildLists(const TreeMap& tree_map, const OrderMap& order_map,
deba@797: const LowMap& low_map, ChildLists& child_lists) {
deba@797:
deba@797: for (NodeIt n(_graph); n != INVALID; ++n) {
deba@797: Node source = n;
deba@797:
deba@797: std::vector<Node> targets;
deba@797: for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@797: Node target = _graph.target(e);
deba@797:
deba@797: if (order_map[source] < order_map[target] && tree_map[e]) {
deba@797: targets.push_back(target);
deba@797: }
deba@797: }
deba@797:
deba@797: if (targets.size() == 0) {
deba@797: child_lists[source].first = INVALID;
deba@797: } else if (targets.size() == 1) {
deba@797: child_lists[source].first = targets[0];
deba@797: child_lists[targets[0]].prev = INVALID;
deba@797: child_lists[targets[0]].next = INVALID;
deba@797: } else {
deba@797: radixSort(targets.begin(), targets.end(), mapToFunctor(low_map));
deba@797: for (int i = 1; i < int(targets.size()); ++i) {
deba@797: child_lists[targets[i]].prev = targets[i - 1];
deba@797: child_lists[targets[i - 1]].next = targets[i];
deba@797: }
deba@797: child_lists[targets.back()].next = INVALID;
deba@797: child_lists[targets.front()].prev = INVALID;
deba@797: child_lists[source].first = targets.front();
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: void walkUp(const Node& node, Node root, int rorder,
deba@797: const PredMap& pred_map, const LowMap& low_map,
deba@797: const OrderMap& order_map, const OrderList& order_list,
deba@797: NodeData& node_data, MergeRoots& merge_roots) {
deba@797:
deba@797: int na, nb;
deba@797: bool da, db;
deba@797:
deba@797: na = nb = order_map[node];
deba@797: da = true; db = false;
deba@797:
deba@797: while (true) {
deba@797:
deba@797: if (node_data[na].visited == rorder) break;
deba@797: if (node_data[nb].visited == rorder) break;
deba@797:
deba@797: node_data[na].visited = rorder;
deba@797: node_data[nb].visited = rorder;
deba@797:
deba@797: int rn = -1;
deba@797:
deba@797: if (na >= int(order_list.size())) {
deba@797: rn = na;
deba@797: } else if (nb >= int(order_list.size())) {
deba@797: rn = nb;
deba@797: }
deba@797:
deba@797: if (rn == -1) {
deba@797: int nn;
deba@797:
deba@797: nn = da ? node_data[na].prev : node_data[na].next;
deba@797: da = node_data[nn].prev != na;
deba@797: na = nn;
deba@797:
deba@797: nn = db ? node_data[nb].prev : node_data[nb].next;
deba@797: db = node_data[nn].prev != nb;
deba@797: nb = nn;
deba@797:
deba@797: } else {
deba@797:
deba@797: Node rep = order_list[rn - order_list.size()];
deba@797: Node parent = _graph.source(pred_map[rep]);
deba@797:
deba@797: if (low_map[rep] < rorder) {
deba@797: merge_roots[parent].push_back(rn);
deba@797: } else {
deba@797: merge_roots[parent].push_front(rn);
deba@797: }
deba@797:
deba@797: if (parent != root) {
deba@797: na = nb = order_map[parent];
deba@797: da = true; db = false;
deba@797: } else {
deba@797: break;
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: void walkDown(int rn, int rorder, NodeData& node_data,
deba@797: ArcLists& arc_lists, FlipMap& flip_map,
deba@797: OrderList& order_list, ChildLists& child_lists,
deba@797: AncestorMap& ancestor_map, LowMap& low_map,
deba@797: EmbedArc& embed_arc, MergeRoots& merge_roots) {
deba@797:
deba@797: std::vector<std::pair<int, bool> > merge_stack;
deba@797:
deba@797: for (int di = 0; di < 2; ++di) {
deba@797: bool rd = di == 0;
deba@797: int pn = rn;
deba@797: int n = rd ? node_data[rn].next : node_data[rn].prev;
deba@797:
deba@797: while (n != rn) {
deba@797:
deba@797: Node node = order_list[n];
deba@797:
deba@797: if (embed_arc[node] != INVALID) {
deba@797:
deba@797: // Merging components on the critical path
deba@797: while (!merge_stack.empty()) {
deba@797:
deba@797: // Component root
deba@797: int cn = merge_stack.back().first;
deba@797: bool cd = merge_stack.back().second;
deba@797: merge_stack.pop_back();
deba@797:
deba@797: // Parent of component
deba@797: int dn = merge_stack.back().first;
deba@797: bool dd = merge_stack.back().second;
deba@797: merge_stack.pop_back();
deba@797:
deba@797: Node parent = order_list[dn];
deba@797:
deba@797: // Erasing from merge_roots
deba@797: merge_roots[parent].pop_front();
deba@797:
deba@797: Node child = order_list[cn - order_list.size()];
deba@797:
deba@797: // Erasing from child_lists
deba@797: if (child_lists[child].prev != INVALID) {
deba@797: child_lists[child_lists[child].prev].next =
deba@797: child_lists[child].next;
deba@797: } else {
deba@797: child_lists[parent].first = child_lists[child].next;
deba@797: }
deba@797:
deba@797: if (child_lists[child].next != INVALID) {
deba@797: child_lists[child_lists[child].next].prev =
deba@797: child_lists[child].prev;
deba@797: }
deba@797:
deba@797: // Merging arcs + flipping
deba@797: Arc de = node_data[dn].first;
deba@797: Arc ce = node_data[cn].first;
deba@797:
deba@797: flip_map[order_list[cn - order_list.size()]] = cd != dd;
deba@797: if (cd != dd) {
deba@797: std::swap(arc_lists[ce].prev, arc_lists[ce].next);
deba@797: ce = arc_lists[ce].prev;
deba@797: std::swap(arc_lists[ce].prev, arc_lists[ce].next);
deba@797: }
deba@797:
deba@797: {
deba@797: Arc dne = arc_lists[de].next;
deba@797: Arc cne = arc_lists[ce].next;
deba@797:
deba@797: arc_lists[de].next = cne;
deba@797: arc_lists[ce].next = dne;
deba@797:
deba@797: arc_lists[dne].prev = ce;
deba@797: arc_lists[cne].prev = de;
deba@797: }
deba@797:
deba@797: if (dd) {
deba@797: node_data[dn].first = ce;
deba@797: }
deba@797:
deba@797: // Merging external faces
deba@797: {
deba@797: int en = cn;
deba@797: cn = cd ? node_data[cn].prev : node_data[cn].next;
deba@797: cd = node_data[cn].next == en;
deba@797:
deba@797: if (node_data[cn].prev == node_data[cn].next &&
deba@797: node_data[cn].inverted) {
deba@797: cd = !cd;
deba@797: }
deba@797: }
deba@797:
deba@797: if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn;
deba@797: if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn;
deba@797:
deba@797: }
deba@797:
deba@797: bool d = pn == node_data[n].prev;
deba@797:
deba@797: if (node_data[n].prev == node_data[n].next &&
deba@797: node_data[n].inverted) {
deba@797: d = !d;
deba@797: }
deba@797:
deba@797: // Add new arc
deba@797: {
deba@797: Arc arc = embed_arc[node];
deba@797: Arc re = node_data[rn].first;
deba@797:
deba@797: arc_lists[arc_lists[re].next].prev = arc;
deba@797: arc_lists[arc].next = arc_lists[re].next;
deba@797: arc_lists[arc].prev = re;
deba@797: arc_lists[re].next = arc;
deba@797:
deba@797: if (!rd) {
deba@797: node_data[rn].first = arc;
deba@797: }
deba@797:
deba@797: Arc rev = _graph.oppositeArc(arc);
deba@797: Arc e = node_data[n].first;
deba@797:
deba@797: arc_lists[arc_lists[e].next].prev = rev;
deba@797: arc_lists[rev].next = arc_lists[e].next;
deba@797: arc_lists[rev].prev = e;
deba@797: arc_lists[e].next = rev;
deba@797:
deba@797: if (d) {
deba@797: node_data[n].first = rev;
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: // Embedding arc into external face
deba@797: if (rd) node_data[rn].next = n; else node_data[rn].prev = n;
deba@797: if (d) node_data[n].prev = rn; else node_data[n].next = rn;
deba@797: pn = rn;
deba@797:
deba@797: embed_arc[order_list[n]] = INVALID;
deba@797: }
deba@797:
deba@797: if (!merge_roots[node].empty()) {
deba@797:
deba@797: bool d = pn == node_data[n].prev;
deba@797: if (node_data[n].prev == node_data[n].next &&
deba@797: node_data[n].inverted) {
deba@797: d = !d;
deba@797: }
deba@797:
deba@797: merge_stack.push_back(std::make_pair(n, d));
deba@797:
deba@797: int rn = merge_roots[node].front();
deba@797:
deba@797: int xn = node_data[rn].next;
deba@797: Node xnode = order_list[xn];
deba@797:
deba@797: int yn = node_data[rn].prev;
deba@797: Node ynode = order_list[yn];
deba@797:
deba@797: bool rd;
deba@797: if (!external(xnode, rorder, child_lists, ancestor_map, low_map)) {
deba@797: rd = true;
deba@797: } else if (!external(ynode, rorder, child_lists,
deba@797: ancestor_map, low_map)) {
deba@797: rd = false;
deba@797: } else if (pertinent(xnode, embed_arc, merge_roots)) {
deba@797: rd = true;
deba@797: } else {
deba@797: rd = false;
deba@797: }
deba@797:
deba@797: merge_stack.push_back(std::make_pair(rn, rd));
deba@797:
deba@797: pn = rn;
deba@797: n = rd ? xn : yn;
deba@797:
deba@797: } else if (!external(node, rorder, child_lists,
deba@797: ancestor_map, low_map)) {
deba@797: int nn = (node_data[n].next != pn ?
deba@797: node_data[n].next : node_data[n].prev);
deba@797:
deba@797: bool nd = n == node_data[nn].prev;
deba@797:
deba@797: if (nd) node_data[nn].prev = pn;
deba@797: else node_data[nn].next = pn;
deba@797:
deba@797: if (n == node_data[pn].prev) node_data[pn].prev = nn;
deba@797: else node_data[pn].next = nn;
deba@797:
deba@797: node_data[nn].inverted =
deba@797: (node_data[nn].prev == node_data[nn].next && nd != rd);
deba@797:
deba@797: n = nn;
deba@797: }
deba@797: else break;
deba@797:
deba@797: }
deba@797:
deba@797: if (!merge_stack.empty() || n == rn) {
deba@797: break;
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: void initFace(const Node& node, ArcLists& arc_lists,
deba@797: NodeData& node_data, const PredMap& pred_map,
deba@797: const OrderMap& order_map, const OrderList& order_list) {
deba@797: int n = order_map[node];
deba@797: int rn = n + order_list.size();
deba@797:
deba@797: node_data[n].next = node_data[n].prev = rn;
deba@797: node_data[rn].next = node_data[rn].prev = n;
deba@797:
deba@797: node_data[n].visited = order_list.size();
deba@797: node_data[rn].visited = order_list.size();
deba@797:
deba@797: node_data[n].inverted = false;
deba@797: node_data[rn].inverted = false;
deba@797:
deba@797: Arc arc = pred_map[node];
deba@797: Arc rev = _graph.oppositeArc(arc);
deba@797:
deba@797: node_data[rn].first = arc;
deba@797: node_data[n].first = rev;
deba@797:
deba@797: arc_lists[arc].prev = arc;
deba@797: arc_lists[arc].next = arc;
deba@797:
deba@797: arc_lists[rev].prev = rev;
deba@797: arc_lists[rev].next = rev;
deba@797:
deba@797: }
deba@797:
deba@797: void mergeRemainingFaces(const Node& node, NodeData& node_data,
deba@797: OrderList& order_list, OrderMap& order_map,
deba@797: ChildLists& child_lists, ArcLists& arc_lists) {
deba@797: while (child_lists[node].first != INVALID) {
deba@797: int dd = order_map[node];
deba@797: Node child = child_lists[node].first;
deba@797: int cd = order_map[child] + order_list.size();
deba@797: child_lists[node].first = child_lists[child].next;
deba@797:
deba@797: Arc de = node_data[dd].first;
deba@797: Arc ce = node_data[cd].first;
deba@797:
deba@797: if (de != INVALID) {
deba@797: Arc dne = arc_lists[de].next;
deba@797: Arc cne = arc_lists[ce].next;
deba@797:
deba@797: arc_lists[de].next = cne;
deba@797: arc_lists[ce].next = dne;
deba@797:
deba@797: arc_lists[dne].prev = ce;
deba@797: arc_lists[cne].prev = de;
deba@797: }
deba@797:
deba@797: node_data[dd].first = ce;
deba@797:
deba@797: }
deba@797: }
deba@797:
deba@797: void storeEmbedding(const Node& node, NodeData& node_data,
deba@797: OrderMap& order_map, PredMap& pred_map,
deba@797: ArcLists& arc_lists, FlipMap& flip_map) {
deba@797:
deba@797: if (node_data[order_map[node]].first == INVALID) return;
deba@797:
deba@797: if (pred_map[node] != INVALID) {
deba@797: Node source = _graph.source(pred_map[node]);
deba@797: flip_map[node] = flip_map[node] != flip_map[source];
deba@797: }
deba@797:
deba@797: Arc first = node_data[order_map[node]].first;
deba@797: Arc prev = first;
deba@797:
deba@797: Arc arc = flip_map[node] ?
deba@797: arc_lists[prev].prev : arc_lists[prev].next;
deba@797:
deba@797: _embedding[prev] = arc;
deba@797:
deba@797: while (arc != first) {
deba@797: Arc next = arc_lists[arc].prev == prev ?
deba@797: arc_lists[arc].next : arc_lists[arc].prev;
deba@797: prev = arc; arc = next;
deba@797: _embedding[prev] = arc;
deba@797: }
deba@797: }
deba@797:
deba@797:
deba@797: bool external(const Node& node, int rorder,
deba@797: ChildLists& child_lists, AncestorMap& ancestor_map,
deba@797: LowMap& low_map) {
deba@797: Node child = child_lists[node].first;
deba@797:
deba@797: if (child != INVALID) {
deba@797: if (low_map[child] < rorder) return true;
deba@797: }
deba@797:
deba@797: if (ancestor_map[node] < rorder) return true;
deba@797:
deba@797: return false;
deba@797: }
deba@797:
deba@797: bool pertinent(const Node& node, const EmbedArc& embed_arc,
deba@797: const MergeRoots& merge_roots) {
deba@797: return !merge_roots[node].empty() || embed_arc[node] != INVALID;
deba@797: }
deba@797:
deba@797: int lowPoint(const Node& node, OrderMap& order_map, ChildLists& child_lists,
deba@797: AncestorMap& ancestor_map, LowMap& low_map) {
deba@797: int low_point;
deba@797:
deba@797: Node child = child_lists[node].first;
deba@797:
deba@797: if (child != INVALID) {
deba@797: low_point = low_map[child];
deba@797: } else {
deba@797: low_point = order_map[node];
deba@797: }
deba@797:
deba@797: if (low_point > ancestor_map[node]) {
deba@797: low_point = ancestor_map[node];
deba@797: }
deba@797:
deba@797: return low_point;
deba@797: }
deba@797:
deba@797: int findComponentRoot(Node root, Node node, ChildLists& child_lists,
deba@797: OrderMap& order_map, OrderList& order_list) {
deba@797:
deba@797: int order = order_map[root];
deba@797: int norder = order_map[node];
deba@797:
deba@797: Node child = child_lists[root].first;
deba@797: while (child != INVALID) {
deba@797: int corder = order_map[child];
deba@797: if (corder > order && corder < norder) {
deba@797: order = corder;
deba@797: }
deba@797: child = child_lists[child].next;
deba@797: }
deba@797: return order + order_list.size();
deba@797: }
deba@797:
deba@797: Node findPertinent(Node node, OrderMap& order_map, NodeData& node_data,
deba@797: EmbedArc& embed_arc, MergeRoots& merge_roots) {
deba@797: Node wnode =_graph.target(node_data[order_map[node]].first);
deba@797: while (!pertinent(wnode, embed_arc, merge_roots)) {
deba@797: wnode = _graph.target(node_data[order_map[wnode]].first);
deba@797: }
deba@797: return wnode;
deba@797: }
deba@797:
deba@797:
deba@797: Node findExternal(Node node, int rorder, OrderMap& order_map,
deba@797: ChildLists& child_lists, AncestorMap& ancestor_map,
deba@797: LowMap& low_map, NodeData& node_data) {
deba@797: Node wnode =_graph.target(node_data[order_map[node]].first);
deba@797: while (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
deba@797: wnode = _graph.target(node_data[order_map[wnode]].first);
deba@797: }
deba@797: return wnode;
deba@797: }
deba@797:
deba@797: void markCommonPath(Node node, int rorder, Node& wnode, Node& znode,
deba@797: OrderList& order_list, OrderMap& order_map,
deba@797: NodeData& node_data, ArcLists& arc_lists,
deba@797: EmbedArc& embed_arc, MergeRoots& merge_roots,
deba@797: ChildLists& child_lists, AncestorMap& ancestor_map,
deba@797: LowMap& low_map) {
deba@797:
deba@797: Node cnode = node;
deba@797: Node pred = INVALID;
deba@797:
deba@797: while (true) {
deba@797:
deba@797: bool pert = pertinent(cnode, embed_arc, merge_roots);
deba@797: bool ext = external(cnode, rorder, child_lists, ancestor_map, low_map);
deba@797:
deba@797: if (pert && ext) {
deba@797: if (!merge_roots[cnode].empty()) {
deba@797: int cn = merge_roots[cnode].back();
deba@797:
deba@797: if (low_map[order_list[cn - order_list.size()]] < rorder) {
deba@797: Arc arc = node_data[cn].first;
deba@797: _kuratowski.set(arc, true);
deba@797:
deba@797: pred = cnode;
deba@797: cnode = _graph.target(arc);
deba@797:
deba@797: continue;
deba@797: }
deba@797: }
deba@797: wnode = znode = cnode;
deba@797: return;
deba@797:
deba@797: } else if (pert) {
deba@797: wnode = cnode;
deba@797:
deba@797: while (!external(cnode, rorder, child_lists, ancestor_map, low_map)) {
deba@797: Arc arc = node_data[order_map[cnode]].first;
deba@797:
deba@797: if (_graph.target(arc) == pred) {
deba@797: arc = arc_lists[arc].next;
deba@797: }
deba@797: _kuratowski.set(arc, true);
deba@797:
deba@797: Node next = _graph.target(arc);
deba@797: pred = cnode; cnode = next;
deba@797: }
deba@797:
deba@797: znode = cnode;
deba@797: return;
deba@797:
deba@797: } else if (ext) {
deba@797: znode = cnode;
deba@797:
deba@797: while (!pertinent(cnode, embed_arc, merge_roots)) {
deba@797: Arc arc = node_data[order_map[cnode]].first;
deba@797:
deba@797: if (_graph.target(arc) == pred) {
deba@797: arc = arc_lists[arc].next;
deba@797: }
deba@797: _kuratowski.set(arc, true);
deba@797:
deba@797: Node next = _graph.target(arc);
deba@797: pred = cnode; cnode = next;
deba@797: }
deba@797:
deba@797: wnode = cnode;
deba@797: return;
deba@797:
deba@797: } else {
deba@797: Arc arc = node_data[order_map[cnode]].first;
deba@797:
deba@797: if (_graph.target(arc) == pred) {
deba@797: arc = arc_lists[arc].next;
deba@797: }
deba@797: _kuratowski.set(arc, true);
deba@797:
deba@797: Node next = _graph.target(arc);
deba@797: pred = cnode; cnode = next;
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: void orientComponent(Node root, int rn, OrderMap& order_map,
deba@797: PredMap& pred_map, NodeData& node_data,
deba@797: ArcLists& arc_lists, FlipMap& flip_map,
deba@797: TypeMap& type_map) {
deba@797: node_data[order_map[root]].first = node_data[rn].first;
deba@797: type_map[root] = 1;
deba@797:
deba@797: std::vector<Node> st, qu;
deba@797:
deba@797: st.push_back(root);
deba@797: while (!st.empty()) {
deba@797: Node node = st.back();
deba@797: st.pop_back();
deba@797: qu.push_back(node);
deba@797:
deba@797: Arc arc = node_data[order_map[node]].first;
deba@797:
deba@797: if (type_map[_graph.target(arc)] == 0) {
deba@797: st.push_back(_graph.target(arc));
deba@797: type_map[_graph.target(arc)] = 1;
deba@797: }
deba@797:
deba@797: Arc last = arc, pred = arc;
deba@797: arc = arc_lists[arc].next;
deba@797: while (arc != last) {
deba@797:
deba@797: if (type_map[_graph.target(arc)] == 0) {
deba@797: st.push_back(_graph.target(arc));
deba@797: type_map[_graph.target(arc)] = 1;
deba@797: }
deba@797:
deba@797: Arc next = arc_lists[arc].next != pred ?
deba@797: arc_lists[arc].next : arc_lists[arc].prev;
deba@797: pred = arc; arc = next;
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: type_map[root] = 2;
deba@797: flip_map[root] = false;
deba@797:
deba@797: for (int i = 1; i < int(qu.size()); ++i) {
deba@797:
deba@797: Node node = qu[i];
deba@797:
deba@797: while (type_map[node] != 2) {
deba@797: st.push_back(node);
deba@797: type_map[node] = 2;
deba@797: node = _graph.source(pred_map[node]);
deba@797: }
deba@797:
deba@797: bool flip = flip_map[node];
deba@797:
deba@797: while (!st.empty()) {
deba@797: node = st.back();
deba@797: st.pop_back();
deba@797:
deba@797: flip_map[node] = flip != flip_map[node];
deba@797: flip = flip_map[node];
deba@797:
deba@797: if (flip) {
deba@797: Arc arc = node_data[order_map[node]].first;
deba@797: std::swap(arc_lists[arc].prev, arc_lists[arc].next);
deba@797: arc = arc_lists[arc].prev;
deba@797: std::swap(arc_lists[arc].prev, arc_lists[arc].next);
deba@797: node_data[order_map[node]].first = arc;
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: for (int i = 0; i < int(qu.size()); ++i) {
deba@797:
deba@797: Arc arc = node_data[order_map[qu[i]]].first;
deba@797: Arc last = arc, pred = arc;
deba@797:
deba@797: arc = arc_lists[arc].next;
deba@797: while (arc != last) {
deba@797:
deba@797: if (arc_lists[arc].next == pred) {
deba@797: std::swap(arc_lists[arc].next, arc_lists[arc].prev);
deba@797: }
deba@797: pred = arc; arc = arc_lists[arc].next;
deba@797: }
deba@797:
deba@797: }
deba@797: }
deba@797:
deba@797: void setFaceFlags(Node root, Node wnode, Node ynode, Node xnode,
deba@797: OrderMap& order_map, NodeData& node_data,
deba@797: TypeMap& type_map) {
deba@797: Node node = _graph.target(node_data[order_map[root]].first);
deba@797:
deba@797: while (node != ynode) {
deba@797: type_map[node] = HIGHY;
deba@797: node = _graph.target(node_data[order_map[node]].first);
deba@797: }
deba@797:
deba@797: while (node != wnode) {
deba@797: type_map[node] = LOWY;
deba@797: node = _graph.target(node_data[order_map[node]].first);
deba@797: }
deba@797:
deba@797: node = _graph.target(node_data[order_map[wnode]].first);
deba@797:
deba@797: while (node != xnode) {
deba@797: type_map[node] = LOWX;
deba@797: node = _graph.target(node_data[order_map[node]].first);
deba@797: }
deba@797: type_map[node] = LOWX;
deba@797:
deba@797: node = _graph.target(node_data[order_map[xnode]].first);
deba@797: while (node != root) {
deba@797: type_map[node] = HIGHX;
deba@797: node = _graph.target(node_data[order_map[node]].first);
deba@797: }
deba@797:
deba@797: type_map[wnode] = PERTINENT;
deba@797: type_map[root] = ROOT;
deba@797: }
deba@797:
deba@797: void findInternalPath(std::vector<Arc>& ipath,
deba@797: Node wnode, Node root, TypeMap& type_map,
deba@797: OrderMap& order_map, NodeData& node_data,
deba@797: ArcLists& arc_lists) {
deba@797: std::vector<Arc> st;
deba@797:
deba@797: Node node = wnode;
deba@797:
deba@797: while (node != root) {
deba@797: Arc arc = arc_lists[node_data[order_map[node]].first].next;
deba@797: st.push_back(arc);
deba@797: node = _graph.target(arc);
deba@797: }
deba@797:
deba@797: while (true) {
deba@797: Arc arc = st.back();
deba@797: if (type_map[_graph.target(arc)] == LOWX ||
deba@797: type_map[_graph.target(arc)] == HIGHX) {
deba@797: break;
deba@797: }
deba@797: if (type_map[_graph.target(arc)] == 2) {
deba@797: type_map[_graph.target(arc)] = 3;
deba@797:
deba@797: arc = arc_lists[_graph.oppositeArc(arc)].next;
deba@797: st.push_back(arc);
deba@797: } else {
deba@797: st.pop_back();
deba@797: arc = arc_lists[arc].next;
deba@797:
deba@797: while (_graph.oppositeArc(arc) == st.back()) {
deba@797: arc = st.back();
deba@797: st.pop_back();
deba@797: arc = arc_lists[arc].next;
deba@797: }
deba@797: st.push_back(arc);
deba@797: }
deba@797: }
deba@797:
deba@797: for (int i = 0; i < int(st.size()); ++i) {
deba@797: if (type_map[_graph.target(st[i])] != LOWY &&
deba@797: type_map[_graph.target(st[i])] != HIGHY) {
deba@797: for (; i < int(st.size()); ++i) {
deba@797: ipath.push_back(st[i]);
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: void setInternalFlags(std::vector<Arc>& ipath, TypeMap& type_map) {
deba@797: for (int i = 1; i < int(ipath.size()); ++i) {
deba@797: type_map[_graph.source(ipath[i])] = INTERNAL;
deba@797: }
deba@797: }
deba@797:
deba@797: void findPilePath(std::vector<Arc>& ppath,
deba@797: Node root, TypeMap& type_map, OrderMap& order_map,
deba@797: NodeData& node_data, ArcLists& arc_lists) {
deba@797: std::vector<Arc> st;
deba@797:
deba@797: st.push_back(_graph.oppositeArc(node_data[order_map[root]].first));
deba@797: st.push_back(node_data[order_map[root]].first);
deba@797:
deba@797: while (st.size() > 1) {
deba@797: Arc arc = st.back();
deba@797: if (type_map[_graph.target(arc)] == INTERNAL) {
deba@797: break;
deba@797: }
deba@797: if (type_map[_graph.target(arc)] == 3) {
deba@797: type_map[_graph.target(arc)] = 4;
deba@797:
deba@797: arc = arc_lists[_graph.oppositeArc(arc)].next;
deba@797: st.push_back(arc);
deba@797: } else {
deba@797: st.pop_back();
deba@797: arc = arc_lists[arc].next;
deba@797:
deba@797: while (!st.empty() && _graph.oppositeArc(arc) == st.back()) {
deba@797: arc = st.back();
deba@797: st.pop_back();
deba@797: arc = arc_lists[arc].next;
deba@797: }
deba@797: st.push_back(arc);
deba@797: }
deba@797: }
deba@797:
deba@797: for (int i = 1; i < int(st.size()); ++i) {
deba@797: ppath.push_back(st[i]);
deba@797: }
deba@797: }
deba@797:
deba@797:
deba@797: int markExternalPath(Node node, OrderMap& order_map,
deba@797: ChildLists& child_lists, PredMap& pred_map,
deba@797: AncestorMap& ancestor_map, LowMap& low_map) {
deba@797: int lp = lowPoint(node, order_map, child_lists,
deba@797: ancestor_map, low_map);
deba@797:
deba@797: if (ancestor_map[node] != lp) {
deba@797: node = child_lists[node].first;
deba@797: _kuratowski[pred_map[node]] = true;
deba@797:
deba@797: while (ancestor_map[node] != lp) {
deba@797: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@797: Node tnode = _graph.target(e);
deba@797: if (order_map[tnode] > order_map[node] && low_map[tnode] == lp) {
deba@797: node = tnode;
deba@797: _kuratowski[e] = true;
deba@797: break;
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: for (OutArcIt e(_graph, node); e != INVALID; ++e) {
deba@797: if (order_map[_graph.target(e)] == lp) {
deba@797: _kuratowski[e] = true;
deba@797: break;
deba@797: }
deba@797: }
deba@797:
deba@797: return lp;
deba@797: }
deba@797:
deba@797: void markPertinentPath(Node node, OrderMap& order_map,
deba@797: NodeData& node_data, ArcLists& arc_lists,
deba@797: EmbedArc& embed_arc, MergeRoots& merge_roots) {
deba@797: while (embed_arc[node] == INVALID) {
deba@797: int n = merge_roots[node].front();
deba@797: Arc arc = node_data[n].first;
deba@797:
deba@797: _kuratowski.set(arc, true);
deba@797:
deba@797: Node pred = node;
deba@797: node = _graph.target(arc);
deba@797: while (!pertinent(node, embed_arc, merge_roots)) {
deba@797: arc = node_data[order_map[node]].first;
deba@797: if (_graph.target(arc) == pred) {
deba@797: arc = arc_lists[arc].next;
deba@797: }
deba@797: _kuratowski.set(arc, true);
deba@797: pred = node;
deba@797: node = _graph.target(arc);
deba@797: }
deba@797: }
deba@797: _kuratowski.set(embed_arc[node], true);
deba@797: }
deba@797:
deba@797: void markPredPath(Node node, Node snode, PredMap& pred_map) {
deba@797: while (node != snode) {
deba@797: _kuratowski.set(pred_map[node], true);
deba@797: node = _graph.source(pred_map[node]);
deba@797: }
deba@797: }
deba@797:
deba@797: void markFacePath(Node ynode, Node xnode,
deba@797: OrderMap& order_map, NodeData& node_data) {
deba@797: Arc arc = node_data[order_map[ynode]].first;
deba@797: Node node = _graph.target(arc);
deba@797: _kuratowski.set(arc, true);
deba@797:
deba@797: while (node != xnode) {
deba@797: arc = node_data[order_map[node]].first;
deba@797: _kuratowski.set(arc, true);
deba@797: node = _graph.target(arc);
deba@797: }
deba@797: }
deba@797:
deba@797: void markInternalPath(std::vector<Arc>& path) {
deba@797: for (int i = 0; i < int(path.size()); ++i) {
deba@797: _kuratowski.set(path[i], true);
deba@797: }
deba@797: }
deba@797:
deba@797: void markPilePath(std::vector<Arc>& path) {
deba@797: for (int i = 0; i < int(path.size()); ++i) {
deba@797: _kuratowski.set(path[i], true);
deba@797: }
deba@797: }
deba@797:
deba@797: void isolateKuratowski(Arc arc, NodeData& node_data,
deba@797: ArcLists& arc_lists, FlipMap& flip_map,
deba@797: OrderMap& order_map, OrderList& order_list,
deba@797: PredMap& pred_map, ChildLists& child_lists,
deba@797: AncestorMap& ancestor_map, LowMap& low_map,
deba@797: EmbedArc& embed_arc, MergeRoots& merge_roots) {
deba@797:
deba@797: Node root = _graph.source(arc);
deba@797: Node enode = _graph.target(arc);
deba@797:
deba@797: int rorder = order_map[root];
deba@797:
deba@797: TypeMap type_map(_graph, 0);
deba@797:
deba@797: int rn = findComponentRoot(root, enode, child_lists,
deba@797: order_map, order_list);
deba@797:
deba@797: Node xnode = order_list[node_data[rn].next];
deba@797: Node ynode = order_list[node_data[rn].prev];
deba@797:
deba@797: // Minor-A
deba@797: {
deba@797: while (!merge_roots[xnode].empty() || !merge_roots[ynode].empty()) {
deba@797:
deba@797: if (!merge_roots[xnode].empty()) {
deba@797: root = xnode;
deba@797: rn = merge_roots[xnode].front();
deba@797: } else {
deba@797: root = ynode;
deba@797: rn = merge_roots[ynode].front();
deba@797: }
deba@797:
deba@797: xnode = order_list[node_data[rn].next];
deba@797: ynode = order_list[node_data[rn].prev];
deba@797: }
deba@797:
deba@797: if (root != _graph.source(arc)) {
deba@797: orientComponent(root, rn, order_map, pred_map,
deba@797: node_data, arc_lists, flip_map, type_map);
deba@797: markFacePath(root, root, order_map, node_data);
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
deba@797: Node lwnode = findPertinent(ynode, order_map, node_data,
deba@797: embed_arc, merge_roots);
deba@797:
deba@797: markPertinentPath(lwnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797:
deba@797: return;
deba@797: }
deba@797: }
deba@797:
deba@797: orientComponent(root, rn, order_map, pred_map,
deba@797: node_data, arc_lists, flip_map, type_map);
deba@797:
deba@797: Node wnode = findPertinent(ynode, order_map, node_data,
deba@797: embed_arc, merge_roots);
deba@797: setFaceFlags(root, wnode, ynode, xnode, order_map, node_data, type_map);
deba@797:
deba@797:
deba@797: //Minor-B
deba@797: if (!merge_roots[wnode].empty()) {
deba@797: int cn = merge_roots[wnode].back();
deba@797: Node rep = order_list[cn - order_list.size()];
deba@797: if (low_map[rep] < rorder) {
deba@797: markFacePath(root, root, order_map, node_data);
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797:
deba@797: Node lwnode, lznode;
deba@797: markCommonPath(wnode, rorder, lwnode, lznode, order_list,
deba@797: order_map, node_data, arc_lists, embed_arc,
deba@797: merge_roots, child_lists, ancestor_map, low_map);
deba@797:
deba@797: markPertinentPath(lwnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797: int zlp = markExternalPath(lznode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797:
deba@797: int minlp = xlp < ylp ? xlp : ylp;
deba@797: if (zlp < minlp) minlp = zlp;
deba@797:
deba@797: int maxlp = xlp > ylp ? xlp : ylp;
deba@797: if (zlp > maxlp) maxlp = zlp;
deba@797:
deba@797: markPredPath(order_list[maxlp], order_list[minlp], pred_map);
deba@797:
deba@797: return;
deba@797: }
deba@797: }
deba@797:
deba@797: Node pxnode, pynode;
deba@797: std::vector<Arc> ipath;
deba@797: findInternalPath(ipath, wnode, root, type_map, order_map,
deba@797: node_data, arc_lists);
deba@797: setInternalFlags(ipath, type_map);
deba@797: pynode = _graph.source(ipath.front());
deba@797: pxnode = _graph.target(ipath.back());
deba@797:
deba@797: wnode = findPertinent(pynode, order_map, node_data,
deba@797: embed_arc, merge_roots);
deba@797:
deba@797: // Minor-C
deba@797: {
deba@797: if (type_map[_graph.source(ipath.front())] == HIGHY) {
deba@797: if (type_map[_graph.target(ipath.back())] == HIGHX) {
deba@797: markFacePath(xnode, pxnode, order_map, node_data);
deba@797: }
deba@797: markFacePath(root, xnode, order_map, node_data);
deba@797: markPertinentPath(wnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797: markInternalPath(ipath);
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: if (type_map[_graph.target(ipath.back())] == HIGHX) {
deba@797: markFacePath(ynode, root, order_map, node_data);
deba@797: markPertinentPath(wnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797: markInternalPath(ipath);
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
deba@797: return;
deba@797: }
deba@797: }
deba@797:
deba@797: std::vector<Arc> ppath;
deba@797: findPilePath(ppath, root, type_map, order_map, node_data, arc_lists);
deba@797:
deba@797: // Minor-D
deba@797: if (!ppath.empty()) {
deba@797: markFacePath(ynode, xnode, order_map, node_data);
deba@797: markPertinentPath(wnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797: markPilePath(ppath);
deba@797: markInternalPath(ipath);
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: // Minor-E*
deba@797: {
deba@797:
deba@797: if (!external(wnode, rorder, child_lists, ancestor_map, low_map)) {
deba@797: Node znode = findExternal(pynode, rorder, order_map,
deba@797: child_lists, ancestor_map,
deba@797: low_map, node_data);
deba@797:
deba@797: if (type_map[znode] == LOWY) {
deba@797: markFacePath(root, xnode, order_map, node_data);
deba@797: markPertinentPath(wnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797: markInternalPath(ipath);
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int zlp = markExternalPath(znode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: markPredPath(root, order_list[xlp < zlp ? xlp : zlp], pred_map);
deba@797: } else {
deba@797: markFacePath(ynode, root, order_map, node_data);
deba@797: markPertinentPath(wnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797: markInternalPath(ipath);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int zlp = markExternalPath(znode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: markPredPath(root, order_list[ylp < zlp ? ylp : zlp], pred_map);
deba@797: }
deba@797: return;
deba@797: }
deba@797:
deba@797: int xlp = markExternalPath(xnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int ylp = markExternalPath(ynode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797: int wlp = markExternalPath(wnode, order_map, child_lists,
deba@797: pred_map, ancestor_map, low_map);
deba@797:
deba@797: if (wlp > xlp && wlp > ylp) {
deba@797: markFacePath(root, root, order_map, node_data);
deba@797: markPredPath(root, order_list[xlp < ylp ? xlp : ylp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: markInternalPath(ipath);
deba@797: markPertinentPath(wnode, order_map, node_data, arc_lists,
deba@797: embed_arc, merge_roots);
deba@797:
deba@797: if (xlp > ylp && xlp > wlp) {
deba@797: markFacePath(root, pynode, order_map, node_data);
deba@797: markFacePath(wnode, xnode, order_map, node_data);
deba@797: markPredPath(root, order_list[ylp < wlp ? ylp : wlp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: if (ylp > xlp && ylp > wlp) {
deba@797: markFacePath(pxnode, root, order_map, node_data);
deba@797: markFacePath(ynode, wnode, order_map, node_data);
deba@797: markPredPath(root, order_list[xlp < wlp ? xlp : wlp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: if (pynode != ynode) {
deba@797: markFacePath(pxnode, wnode, order_map, node_data);
deba@797:
deba@797: int minlp = xlp < ylp ? xlp : ylp;
deba@797: if (wlp < minlp) minlp = wlp;
deba@797:
deba@797: int maxlp = xlp > ylp ? xlp : ylp;
deba@797: if (wlp > maxlp) maxlp = wlp;
deba@797:
deba@797: markPredPath(order_list[maxlp], order_list[minlp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: if (pxnode != xnode) {
deba@797: markFacePath(wnode, pynode, order_map, node_data);
deba@797:
deba@797: int minlp = xlp < ylp ? xlp : ylp;
deba@797: if (wlp < minlp) minlp = wlp;
deba@797:
deba@797: int maxlp = xlp > ylp ? xlp : ylp;
deba@797: if (wlp > maxlp) maxlp = wlp;
deba@797:
deba@797: markPredPath(order_list[maxlp], order_list[minlp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: markFacePath(root, root, order_map, node_data);
deba@797: int minlp = xlp < ylp ? xlp : ylp;
deba@797: if (wlp < minlp) minlp = wlp;
deba@797: markPredPath(root, order_list[minlp], pred_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: };
deba@797:
deba@797: namespace _planarity_bits {
deba@797:
deba@797: template <typename Graph, typename EmbeddingMap>
deba@797: void makeConnected(Graph& graph, EmbeddingMap& embedding) {
deba@797: DfsVisitor<Graph> null_visitor;
deba@797: DfsVisit<Graph, DfsVisitor<Graph> > dfs(graph, null_visitor);
deba@797: dfs.init();
deba@797:
deba@797: typename Graph::Node u = INVALID;
deba@797: for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
deba@797: if (!dfs.reached(n)) {
deba@797: dfs.addSource(n);
deba@797: dfs.start();
deba@797: if (u == INVALID) {
deba@797: u = n;
deba@797: } else {
deba@797: typename Graph::Node v = n;
deba@797:
deba@797: typename Graph::Arc ue = typename Graph::OutArcIt(graph, u);
deba@797: typename Graph::Arc ve = typename Graph::OutArcIt(graph, v);
deba@797:
deba@797: typename Graph::Arc e = graph.direct(graph.addEdge(u, v), true);
deba@797:
deba@797: if (ue != INVALID) {
deba@797: embedding[e] = embedding[ue];
deba@797: embedding[ue] = e;
deba@797: } else {
deba@797: embedding[e] = e;
deba@797: }
deba@797:
deba@797: if (ve != INVALID) {
deba@797: embedding[graph.oppositeArc(e)] = embedding[ve];
deba@797: embedding[ve] = graph.oppositeArc(e);
deba@797: } else {
deba@797: embedding[graph.oppositeArc(e)] = graph.oppositeArc(e);
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: template <typename Graph, typename EmbeddingMap>
deba@797: void makeBiNodeConnected(Graph& graph, EmbeddingMap& embedding) {
deba@797: typename Graph::template ArcMap<bool> processed(graph);
deba@797:
deba@797: std::vector<typename Graph::Arc> arcs;
deba@797: for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
deba@797: arcs.push_back(e);
deba@797: }
deba@797:
deba@797: IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
deba@797:
deba@797: for (int i = 0; i < int(arcs.size()); ++i) {
deba@797: typename Graph::Arc pp = arcs[i];
deba@797: if (processed[pp]) continue;
deba@797:
deba@797: typename Graph::Arc e = embedding[graph.oppositeArc(pp)];
deba@797: processed[e] = true;
deba@797: visited.set(graph.source(e), true);
deba@797:
deba@797: typename Graph::Arc p = e, l = e;
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797:
deba@797: while (e != l) {
deba@797: processed[e] = true;
deba@797:
deba@797: if (visited[graph.source(e)]) {
deba@797:
deba@797: typename Graph::Arc n =
deba@797: graph.direct(graph.addEdge(graph.source(p),
deba@797: graph.target(e)), true);
deba@797: embedding[n] = p;
deba@797: embedding[graph.oppositeArc(pp)] = n;
deba@797:
deba@797: embedding[graph.oppositeArc(n)] =
deba@797: embedding[graph.oppositeArc(e)];
deba@797: embedding[graph.oppositeArc(e)] =
deba@797: graph.oppositeArc(n);
deba@797:
deba@797: p = n;
deba@797: e = embedding[graph.oppositeArc(n)];
deba@797: } else {
deba@797: visited.set(graph.source(e), true);
deba@797: pp = p;
deba@797: p = e;
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: }
deba@797: }
deba@797: visited.setAll(false);
deba@797: }
deba@797: }
deba@797:
deba@797:
deba@797: template <typename Graph, typename EmbeddingMap>
deba@797: void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) {
deba@797:
deba@797: typename Graph::template NodeMap<int> degree(graph);
deba@797:
deba@797: for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
deba@797: degree[n] = countIncEdges(graph, n);
deba@797: }
deba@797:
deba@797: typename Graph::template ArcMap<bool> processed(graph);
deba@797: IterableBoolMap<Graph, typename Graph::Node> visited(graph, false);
deba@797:
deba@797: std::vector<typename Graph::Arc> arcs;
deba@797: for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
deba@797: arcs.push_back(e);
deba@797: }
deba@797:
deba@797: for (int i = 0; i < int(arcs.size()); ++i) {
deba@797: typename Graph::Arc e = arcs[i];
deba@797:
deba@797: if (processed[e]) continue;
deba@797: processed[e] = true;
deba@797:
deba@797: typename Graph::Arc mine = e;
deba@797: int mind = degree[graph.source(e)];
deba@797:
deba@797: int face_size = 1;
deba@797:
deba@797: typename Graph::Arc l = e;
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: while (l != e) {
deba@797: processed[e] = true;
deba@797:
deba@797: ++face_size;
deba@797:
deba@797: if (degree[graph.source(e)] < mind) {
deba@797: mine = e;
deba@797: mind = degree[graph.source(e)];
deba@797: }
deba@797:
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: }
deba@797:
deba@797: if (face_size < 4) {
deba@797: continue;
deba@797: }
deba@797:
deba@797: typename Graph::Node s = graph.source(mine);
deba@797: for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) {
deba@797: visited.set(graph.target(e), true);
deba@797: }
deba@797:
deba@797: typename Graph::Arc oppe = INVALID;
deba@797:
deba@797: e = embedding[graph.oppositeArc(mine)];
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: while (graph.target(e) != s) {
deba@797: if (visited[graph.source(e)]) {
deba@797: oppe = e;
deba@797: break;
deba@797: }
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: }
deba@797: visited.setAll(false);
deba@797:
deba@797: if (oppe == INVALID) {
deba@797:
deba@797: e = embedding[graph.oppositeArc(mine)];
deba@797: typename Graph::Arc pn = mine, p = e;
deba@797:
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: while (graph.target(e) != s) {
deba@797: typename Graph::Arc n =
deba@797: graph.direct(graph.addEdge(s, graph.source(e)), true);
deba@797:
deba@797: embedding[n] = pn;
deba@797: embedding[graph.oppositeArc(n)] = e;
deba@797: embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
deba@797:
deba@797: pn = n;
deba@797:
deba@797: p = e;
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797: }
deba@797:
deba@797: embedding[graph.oppositeArc(e)] = pn;
deba@797:
deba@797: } else {
deba@797:
deba@797: mine = embedding[graph.oppositeArc(mine)];
deba@797: s = graph.source(mine);
deba@797: oppe = embedding[graph.oppositeArc(oppe)];
deba@797: typename Graph::Node t = graph.source(oppe);
deba@797:
deba@797: typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true);
deba@797: embedding[ce] = mine;
deba@797: embedding[graph.oppositeArc(ce)] = oppe;
deba@797:
deba@797: typename Graph::Arc pn = ce, p = oppe;
deba@797: e = embedding[graph.oppositeArc(oppe)];
deba@797: while (graph.target(e) != s) {
deba@797: typename Graph::Arc n =
deba@797: graph.direct(graph.addEdge(s, graph.source(e)), true);
deba@797:
deba@797: embedding[n] = pn;
deba@797: embedding[graph.oppositeArc(n)] = e;
deba@797: embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
deba@797:
deba@797: pn = n;
deba@797:
deba@797: p = e;
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797:
deba@797: }
deba@797: embedding[graph.oppositeArc(e)] = pn;
deba@797:
deba@797: pn = graph.oppositeArc(ce), p = mine;
deba@797: e = embedding[graph.oppositeArc(mine)];
deba@797: while (graph.target(e) != t) {
deba@797: typename Graph::Arc n =
deba@797: graph.direct(graph.addEdge(t, graph.source(e)), true);
deba@797:
deba@797: embedding[n] = pn;
deba@797: embedding[graph.oppositeArc(n)] = e;
deba@797: embedding[graph.oppositeArc(p)] = graph.oppositeArc(n);
deba@797:
deba@797: pn = n;
deba@797:
deba@797: p = e;
deba@797: e = embedding[graph.oppositeArc(e)];
deba@797:
deba@797: }
deba@797: embedding[graph.oppositeArc(e)] = pn;
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: /// \ingroup planar
deba@797: ///
deba@797: /// \brief Schnyder's planar drawing algorithm
deba@797: ///
deba@797: /// The planar drawing algorithm calculates positions for the nodes
kpeter@828: /// in the plane. These coordinates satisfy that if the edges are
kpeter@828: /// represented with straight lines, then they will not intersect
deba@797: /// each other.
deba@797: ///
kpeter@828: /// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid,
kpeter@828: /// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square.
deba@797: /// The time complexity of the algorithm is O(n).
kpeter@828: ///
kpeter@828: /// \see PlanarEmbedding
deba@797: template <typename Graph>
deba@797: class PlanarDrawing {
deba@797: public:
deba@797:
deba@797: TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@797:
kpeter@828: /// \brief The point type for storing coordinates
deba@797: typedef dim2::Point<int> Point;
kpeter@828: /// \brief The map type for storing the coordinates of the nodes
deba@797: typedef typename Graph::template NodeMap<Point> PointMap;
deba@797:
deba@797:
deba@797: /// \brief Constructor
deba@797: ///
deba@797: /// Constructor
kpeter@828: /// \pre The graph must be simple, i.e. it should not
kpeter@828: /// contain parallel or loop arcs.
deba@797: PlanarDrawing(const Graph& graph)
deba@797: : _graph(graph), _point_map(graph) {}
deba@797:
deba@797: private:
deba@797:
deba@797: template <typename AuxGraph, typename AuxEmbeddingMap>
deba@797: void drawing(const AuxGraph& graph,
deba@797: const AuxEmbeddingMap& next,
deba@797: PointMap& point_map) {
deba@797: TEMPLATE_GRAPH_TYPEDEFS(AuxGraph);
deba@797:
deba@797: typename AuxGraph::template ArcMap<Arc> prev(graph);
deba@797:
deba@797: for (NodeIt n(graph); n != INVALID; ++n) {
deba@797: Arc e = OutArcIt(graph, n);
deba@797:
deba@797: Arc p = e, l = e;
deba@797:
deba@797: e = next[e];
deba@797: while (e != l) {
deba@797: prev[e] = p;
deba@797: p = e;
deba@797: e = next[e];
deba@797: }
deba@797: prev[e] = p;
deba@797: }
deba@797:
deba@797: Node anode, bnode, cnode;
deba@797:
deba@797: {
deba@797: Arc e = ArcIt(graph);
deba@797: anode = graph.source(e);
deba@797: bnode = graph.target(e);
deba@797: cnode = graph.target(next[graph.oppositeArc(e)]);
deba@797: }
deba@797:
deba@797: IterableBoolMap<AuxGraph, Node> proper(graph, false);
deba@797: typename AuxGraph::template NodeMap<int> conn(graph, -1);
deba@797:
deba@797: conn[anode] = conn[bnode] = -2;
deba@797: {
deba@797: for (OutArcIt e(graph, anode); e != INVALID; ++e) {
deba@797: Node m = graph.target(e);
deba@797: if (conn[m] == -1) {
deba@797: conn[m] = 1;
deba@797: }
deba@797: }
deba@797: conn[cnode] = 2;
deba@797:
deba@797: for (OutArcIt e(graph, bnode); e != INVALID; ++e) {
deba@797: Node m = graph.target(e);
deba@797: if (conn[m] == -1) {
deba@797: conn[m] = 1;
deba@797: } else if (conn[m] != -2) {
deba@797: conn[m] += 1;
deba@797: Arc pe = graph.oppositeArc(e);
deba@797: if (conn[graph.target(next[pe])] == -2) {
deba@797: conn[m] -= 1;
deba@797: }
deba@797: if (conn[graph.target(prev[pe])] == -2) {
deba@797: conn[m] -= 1;
deba@797: }
deba@797:
deba@797: proper.set(m, conn[m] == 1);
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797:
deba@797: typename AuxGraph::template ArcMap<int> angle(graph, -1);
deba@797:
deba@797: while (proper.trueNum() != 0) {
deba@797: Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper);
deba@797: proper.set(n, false);
deba@797: conn[n] = -2;
deba@797:
deba@797: for (OutArcIt e(graph, n); e != INVALID; ++e) {
deba@797: Node m = graph.target(e);
deba@797: if (conn[m] == -1) {
deba@797: conn[m] = 1;
deba@797: } else if (conn[m] != -2) {
deba@797: conn[m] += 1;
deba@797: Arc pe = graph.oppositeArc(e);
deba@797: if (conn[graph.target(next[pe])] == -2) {
deba@797: conn[m] -= 1;
deba@797: }
deba@797: if (conn[graph.target(prev[pe])] == -2) {
deba@797: conn[m] -= 1;
deba@797: }
deba@797:
deba@797: proper.set(m, conn[m] == 1);
deba@797: }
deba@797: }
deba@797:
deba@797: {
deba@797: Arc e = OutArcIt(graph, n);
deba@797: Arc p = e, l = e;
deba@797:
deba@797: e = next[e];
deba@797: while (e != l) {
deba@797:
deba@797: if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
deba@797: Arc f = e;
deba@797: angle[f] = 0;
deba@797: f = next[graph.oppositeArc(f)];
deba@797: angle[f] = 1;
deba@797: f = next[graph.oppositeArc(f)];
deba@797: angle[f] = 2;
deba@797: }
deba@797:
deba@797: p = e;
deba@797: e = next[e];
deba@797: }
deba@797:
deba@797: if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
deba@797: Arc f = e;
deba@797: angle[f] = 0;
deba@797: f = next[graph.oppositeArc(f)];
deba@797: angle[f] = 1;
deba@797: f = next[graph.oppositeArc(f)];
deba@797: angle[f] = 2;
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<Node> apred(graph, INVALID);
deba@797: typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID);
deba@797: typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID);
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> apredid(graph, -1);
deba@797: typename AuxGraph::template NodeMap<int> bpredid(graph, -1);
deba@797: typename AuxGraph::template NodeMap<int> cpredid(graph, -1);
deba@797:
deba@797: for (ArcIt e(graph); e != INVALID; ++e) {
deba@797: if (angle[e] == angle[next[e]]) {
deba@797: switch (angle[e]) {
deba@797: case 2:
deba@797: apred[graph.target(e)] = graph.source(e);
deba@797: apredid[graph.target(e)] = graph.id(graph.source(e));
deba@797: break;
deba@797: case 1:
deba@797: bpred[graph.target(e)] = graph.source(e);
deba@797: bpredid[graph.target(e)] = graph.id(graph.source(e));
deba@797: break;
deba@797: case 0:
deba@797: cpred[graph.target(e)] = graph.source(e);
deba@797: cpredid[graph.target(e)] = graph.id(graph.source(e));
deba@797: break;
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: cpred[anode] = INVALID;
deba@797: cpred[bnode] = INVALID;
deba@797:
deba@797: std::vector<Node> aorder, border, corder;
deba@797:
deba@797: {
deba@797: typename AuxGraph::template NodeMap<bool> processed(graph, false);
deba@797: std::vector<Node> st;
deba@797: for (NodeIt n(graph); n != INVALID; ++n) {
deba@797: if (!processed[n] && n != bnode && n != cnode) {
deba@797: st.push_back(n);
deba@797: processed[n] = true;
deba@797: Node m = apred[n];
deba@797: while (m != INVALID && !processed[m]) {
deba@797: st.push_back(m);
deba@797: processed[m] = true;
deba@797: m = apred[m];
deba@797: }
deba@797: while (!st.empty()) {
deba@797: aorder.push_back(st.back());
deba@797: st.pop_back();
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: {
deba@797: typename AuxGraph::template NodeMap<bool> processed(graph, false);
deba@797: std::vector<Node> st;
deba@797: for (NodeIt n(graph); n != INVALID; ++n) {
deba@797: if (!processed[n] && n != cnode && n != anode) {
deba@797: st.push_back(n);
deba@797: processed[n] = true;
deba@797: Node m = bpred[n];
deba@797: while (m != INVALID && !processed[m]) {
deba@797: st.push_back(m);
deba@797: processed[m] = true;
deba@797: m = bpred[m];
deba@797: }
deba@797: while (!st.empty()) {
deba@797: border.push_back(st.back());
deba@797: st.pop_back();
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: {
deba@797: typename AuxGraph::template NodeMap<bool> processed(graph, false);
deba@797: std::vector<Node> st;
deba@797: for (NodeIt n(graph); n != INVALID; ++n) {
deba@797: if (!processed[n] && n != anode && n != bnode) {
deba@797: st.push_back(n);
deba@797: processed[n] = true;
deba@797: Node m = cpred[n];
deba@797: while (m != INVALID && !processed[m]) {
deba@797: st.push_back(m);
deba@797: processed[m] = true;
deba@797: m = cpred[m];
deba@797: }
deba@797: while (!st.empty()) {
deba@797: corder.push_back(st.back());
deba@797: st.pop_back();
deba@797: }
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> atree(graph, 0);
deba@797: for (int i = aorder.size() - 1; i >= 0; --i) {
deba@797: Node n = aorder[i];
deba@797: atree[n] = 1;
deba@797: for (OutArcIt e(graph, n); e != INVALID; ++e) {
deba@797: if (apred[graph.target(e)] == n) {
deba@797: atree[n] += atree[graph.target(e)];
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> btree(graph, 0);
deba@797: for (int i = border.size() - 1; i >= 0; --i) {
deba@797: Node n = border[i];
deba@797: btree[n] = 1;
deba@797: for (OutArcIt e(graph, n); e != INVALID; ++e) {
deba@797: if (bpred[graph.target(e)] == n) {
deba@797: btree[n] += btree[graph.target(e)];
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> apath(graph, 0);
deba@797: apath[bnode] = apath[cnode] = 1;
deba@797: typename AuxGraph::template NodeMap<int> apath_btree(graph, 0);
deba@797: apath_btree[bnode] = btree[bnode];
deba@797: for (int i = 1; i < int(aorder.size()); ++i) {
deba@797: Node n = aorder[i];
deba@797: apath[n] = apath[apred[n]] + 1;
deba@797: apath_btree[n] = btree[n] + apath_btree[apred[n]];
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0);
deba@797: bpath_atree[anode] = atree[anode];
deba@797: for (int i = 1; i < int(border.size()); ++i) {
deba@797: Node n = border[i];
deba@797: bpath_atree[n] = atree[n] + bpath_atree[bpred[n]];
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> cpath(graph, 0);
deba@797: cpath[anode] = cpath[bnode] = 1;
deba@797: typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0);
deba@797: cpath_atree[anode] = atree[anode];
deba@797: typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0);
deba@797: cpath_btree[bnode] = btree[bnode];
deba@797: for (int i = 1; i < int(corder.size()); ++i) {
deba@797: Node n = corder[i];
deba@797: cpath[n] = cpath[cpred[n]] + 1;
deba@797: cpath_atree[n] = atree[n] + cpath_atree[cpred[n]];
deba@797: cpath_btree[n] = btree[n] + cpath_btree[cpred[n]];
deba@797: }
deba@797:
deba@797: typename AuxGraph::template NodeMap<int> third(graph);
deba@797: for (NodeIt n(graph); n != INVALID; ++n) {
deba@797: point_map[n].x =
deba@797: bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1;
deba@797: point_map[n].y =
deba@797: cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1;
deba@797: }
deba@797:
deba@797: }
deba@797:
deba@797: public:
deba@797:
kpeter@828: /// \brief Calculate the node positions
deba@797: ///
kpeter@828: /// This function calculates the node positions on the plane.
kpeter@828: /// \return \c true if the graph is planar.
deba@797: bool run() {
deba@797: PlanarEmbedding<Graph> pe(_graph);
deba@797: if (!pe.run()) return false;
deba@797:
deba@797: run(pe);
deba@797: return true;
deba@797: }
deba@797:
kpeter@828: /// \brief Calculate the node positions according to a
deba@797: /// combinatorical embedding
deba@797: ///
kpeter@828: /// This function calculates the node positions on the plane.
kpeter@828: /// The given \c embedding map should contain a valid combinatorical
kpeter@828: /// embedding, i.e. a valid cyclic order of the arcs.
kpeter@828: /// It can be computed using PlanarEmbedding.
deba@797: template <typename EmbeddingMap>
deba@797: void run(const EmbeddingMap& embedding) {
deba@797: typedef SmartEdgeSet<Graph> AuxGraph;
deba@797:
deba@797: if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
deba@797: drawing(_graph, embedding, _point_map);
deba@797: return;
deba@797: }
deba@797:
deba@797: AuxGraph aux_graph(_graph);
deba@797: typename AuxGraph::template ArcMap<typename AuxGraph::Arc>
deba@797: aux_embedding(aux_graph);
deba@797:
deba@797: {
deba@797:
deba@797: typename Graph::template EdgeMap<typename AuxGraph::Edge>
deba@797: ref(_graph);
deba@797:
deba@797: for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@797: ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e));
deba@797: }
deba@797:
deba@797: for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@797: Arc ee = embedding[_graph.direct(e, true)];
deba@797: aux_embedding[aux_graph.direct(ref[e], true)] =
deba@797: aux_graph.direct(ref[ee], _graph.direction(ee));
deba@797: ee = embedding[_graph.direct(e, false)];
deba@797: aux_embedding[aux_graph.direct(ref[e], false)] =
deba@797: aux_graph.direct(ref[ee], _graph.direction(ee));
deba@797: }
deba@797: }
deba@797: _planarity_bits::makeConnected(aux_graph, aux_embedding);
deba@797: _planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding);
deba@797: _planarity_bits::makeMaxPlanar(aux_graph, aux_embedding);
deba@797: drawing(aux_graph, aux_embedding, _point_map);
deba@797: }
deba@797:
deba@797: /// \brief The coordinate of the given node
deba@797: ///
kpeter@828: /// This function returns the coordinate of the given node.
deba@797: Point operator[](const Node& node) const {
deba@797: return _point_map[node];
deba@797: }
deba@797:
kpeter@828: /// \brief Return the grid embedding in a node map
deba@797: ///
kpeter@828: /// This function returns the grid embedding in a node map of
kpeter@828: /// \c dim2::Point<int> coordinates.
deba@797: const PointMap& coords() const {
deba@797: return _point_map;
deba@797: }
deba@797:
deba@797: private:
deba@797:
deba@797: const Graph& _graph;
deba@797: PointMap _point_map;
deba@797:
deba@797: };
deba@797:
deba@797: namespace _planarity_bits {
deba@797:
deba@797: template <typename ColorMap>
deba@797: class KempeFilter {
deba@797: public:
deba@797: typedef typename ColorMap::Key Key;
deba@797: typedef bool Value;
deba@797:
deba@797: KempeFilter(const ColorMap& color_map,
deba@797: const typename ColorMap::Value& first,
deba@797: const typename ColorMap::Value& second)
deba@797: : _color_map(color_map), _first(first), _second(second) {}
deba@797:
deba@797: Value operator[](const Key& key) const {
deba@797: return _color_map[key] == _first || _color_map[key] == _second;
deba@797: }
deba@797:
deba@797: private:
deba@797: const ColorMap& _color_map;
deba@797: typename ColorMap::Value _first, _second;
deba@797: };
deba@797: }
deba@797:
deba@797: /// \ingroup planar
deba@797: ///
deba@797: /// \brief Coloring planar graphs
deba@797: ///
deba@797: /// The graph coloring problem is the coloring of the graph nodes
kpeter@828: /// so that there are no adjacent nodes with the same color. The
kpeter@828: /// planar graphs can always be colored with four colors, which is
kpeter@828: /// proved by Appel and Haken. Their proofs provide a quadratic
deba@797: /// time algorithm for four coloring, but it could not be used to
kpeter@828: /// implement an efficient algorithm. The five and six coloring can be
kpeter@828: /// made in linear time, but in this class, the five coloring has
deba@797: /// quadratic worst case time complexity. The two coloring (if
deba@797: /// possible) is solvable with a graph search algorithm and it is
deba@797: /// implemented in \ref bipartitePartitions() function in LEMON. To
kpeter@828: /// decide whether a planar graph is three colorable is NP-complete.
deba@797: ///
deba@797: /// This class contains member functions for calculate colorings
deba@797: /// with five and six colors. The six coloring algorithm is a simple
deba@797: /// greedy coloring on the backward minimum outgoing order of nodes.
kpeter@828: /// This order can be computed by selecting the node with least
kpeter@828: /// outgoing arcs to unprocessed nodes in each phase. This order
deba@797: /// guarantees that when a node is chosen for coloring it has at
deba@797: /// most five already colored adjacents. The five coloring algorithm
deba@797: /// use the same method, but if the greedy approach fails to color
deba@797: /// with five colors, i.e. the node has five already different
deba@797: /// colored neighbours, it swaps the colors in one of the connected
deba@797: /// two colored sets with the Kempe recoloring method.
deba@797: template <typename Graph>
deba@797: class PlanarColoring {
deba@797: public:
deba@797:
deba@797: TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@797:
kpeter@828: /// \brief The map type for storing color indices
deba@797: typedef typename Graph::template NodeMap<int> IndexMap;
kpeter@828: /// \brief The map type for storing colors
kpeter@828: ///
kpeter@828: /// The map type for storing colors.
kpeter@828: /// \see Palette, Color
deba@797: typedef ComposeMap<Palette, IndexMap> ColorMap;
deba@797:
deba@797: /// \brief Constructor
deba@797: ///
kpeter@828: /// Constructor.
kpeter@828: /// \pre The graph must be simple, i.e. it should not
kpeter@828: /// contain parallel or loop arcs.
deba@797: PlanarColoring(const Graph& graph)
deba@797: : _graph(graph), _color_map(graph), _palette(0) {
deba@797: _palette.add(Color(1,0,0));
deba@797: _palette.add(Color(0,1,0));
deba@797: _palette.add(Color(0,0,1));
deba@797: _palette.add(Color(1,1,0));
deba@797: _palette.add(Color(1,0,1));
deba@797: _palette.add(Color(0,1,1));
deba@797: }
deba@797:
kpeter@828: /// \brief Return the node map of color indices
deba@797: ///
kpeter@828: /// This function returns the node map of color indices. The values are
kpeter@828: /// in the range \c [0..4] or \c [0..5] according to the coloring method.
deba@797: IndexMap colorIndexMap() const {
deba@797: return _color_map;
deba@797: }
deba@797:
kpeter@828: /// \brief Return the node map of colors
deba@797: ///
kpeter@828: /// This function returns the node map of colors. The values are among
kpeter@828: /// five or six distinct \ref lemon::Color "colors".
deba@797: ColorMap colorMap() const {
deba@797: return composeMap(_palette, _color_map);
deba@797: }
deba@797:
kpeter@828: /// \brief Return the color index of the node
deba@797: ///
kpeter@828: /// This function returns the color index of the given node. The value is
kpeter@828: /// in the range \c [0..4] or \c [0..5] according to the coloring method.
deba@797: int colorIndex(const Node& node) const {
deba@797: return _color_map[node];
deba@797: }
deba@797:
kpeter@828: /// \brief Return the color of the node
deba@797: ///
kpeter@828: /// This function returns the color of the given node. The value is among
kpeter@828: /// five or six distinct \ref lemon::Color "colors".
deba@797: Color color(const Node& node) const {
deba@797: return _palette[_color_map[node]];
deba@797: }
deba@797:
deba@797:
kpeter@828: /// \brief Calculate a coloring with at most six colors
deba@797: ///
deba@797: /// This function calculates a coloring with at most six colors. The time
deba@797: /// complexity of this variant is linear in the size of the graph.
kpeter@828: /// \return \c true if the algorithm could color the graph with six colors.
kpeter@828: /// If the algorithm fails, then the graph is not planar.
kpeter@828: /// \note This function can return \c true if the graph is not
kpeter@828: /// planar, but it can be colored with at most six colors.
deba@797: bool runSixColoring() {
deba@797:
deba@797: typename Graph::template NodeMap<int> heap_index(_graph, -1);
deba@797: BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
deba@797:
deba@797: for (NodeIt n(_graph); n != INVALID; ++n) {
deba@797: _color_map[n] = -2;
deba@797: heap.push(n, countOutArcs(_graph, n));
deba@797: }
deba@797:
deba@797: std::vector<Node> order;
deba@797:
deba@797: while (!heap.empty()) {
deba@797: Node n = heap.top();
deba@797: heap.pop();
deba@797: _color_map[n] = -1;
deba@797: order.push_back(n);
deba@797: for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@797: Node t = _graph.runningNode(e);
deba@797: if (_color_map[t] == -2) {
deba@797: heap.decrease(t, heap[t] - 1);
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: for (int i = order.size() - 1; i >= 0; --i) {
deba@797: std::vector<bool> forbidden(6, false);
deba@797: for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
deba@797: Node t = _graph.runningNode(e);
deba@797: if (_color_map[t] != -1) {
deba@797: forbidden[_color_map[t]] = true;
deba@797: }
deba@797: }
deba@797: for (int k = 0; k < 6; ++k) {
deba@797: if (!forbidden[k]) {
deba@797: _color_map[order[i]] = k;
deba@797: break;
deba@797: }
deba@797: }
deba@797: if (_color_map[order[i]] == -1) {
deba@797: return false;
deba@797: }
deba@797: }
deba@797: return true;
deba@797: }
deba@797:
deba@797: private:
deba@797:
deba@797: bool recolor(const Node& u, const Node& v) {
deba@797: int ucolor = _color_map[u];
deba@797: int vcolor = _color_map[v];
deba@797: typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter;
deba@797: KempeFilter filter(_color_map, ucolor, vcolor);
deba@797:
deba@797: typedef FilterNodes<const Graph, const KempeFilter> KempeGraph;
deba@797: KempeGraph kempe_graph(_graph, filter);
deba@797:
deba@797: std::vector<Node> comp;
deba@797: Bfs<KempeGraph> bfs(kempe_graph);
deba@797: bfs.init();
deba@797: bfs.addSource(u);
deba@797: while (!bfs.emptyQueue()) {
deba@797: Node n = bfs.nextNode();
deba@797: if (n == v) return false;
deba@797: comp.push_back(n);
deba@797: bfs.processNextNode();
deba@797: }
deba@797:
deba@797: int scolor = ucolor + vcolor;
deba@797: for (int i = 0; i < static_cast<int>(comp.size()); ++i) {
deba@797: _color_map[comp[i]] = scolor - _color_map[comp[i]];
deba@797: }
deba@797:
deba@797: return true;
deba@797: }
deba@797:
deba@797: template <typename EmbeddingMap>
deba@797: void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) {
deba@797: std::vector<Node> nodes;
deba@797: nodes.reserve(4);
deba@797:
deba@797: for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) {
deba@797: Node t = _graph.target(e);
deba@797: if (_color_map[t] != -1) {
deba@797: nodes.push_back(t);
deba@797: if (nodes.size() == 4) break;
deba@797: }
deba@797: }
deba@797:
deba@797: int color = _color_map[nodes[0]];
deba@797: if (recolor(nodes[0], nodes[2])) {
deba@797: _color_map[node] = color;
deba@797: } else {
deba@797: color = _color_map[nodes[1]];
deba@797: recolor(nodes[1], nodes[3]);
deba@797: _color_map[node] = color;
deba@797: }
deba@797: }
deba@797:
deba@797: public:
deba@797:
kpeter@828: /// \brief Calculate a coloring with at most five colors
deba@797: ///
deba@797: /// This function calculates a coloring with at most five
deba@797: /// colors. The worst case time complexity of this variant is
deba@797: /// quadratic in the size of the graph.
kpeter@828: /// \param embedding This map should contain a valid combinatorical
kpeter@828: /// embedding, i.e. a valid cyclic order of the arcs.
kpeter@828: /// It can be computed using PlanarEmbedding.
deba@797: template <typename EmbeddingMap>
deba@797: void runFiveColoring(const EmbeddingMap& embedding) {
deba@797:
deba@797: typename Graph::template NodeMap<int> heap_index(_graph, -1);
deba@797: BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index);
deba@797:
deba@797: for (NodeIt n(_graph); n != INVALID; ++n) {
deba@797: _color_map[n] = -2;
deba@797: heap.push(n, countOutArcs(_graph, n));
deba@797: }
deba@797:
deba@797: std::vector<Node> order;
deba@797:
deba@797: while (!heap.empty()) {
deba@797: Node n = heap.top();
deba@797: heap.pop();
deba@797: _color_map[n] = -1;
deba@797: order.push_back(n);
deba@797: for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@797: Node t = _graph.runningNode(e);
deba@797: if (_color_map[t] == -2) {
deba@797: heap.decrease(t, heap[t] - 1);
deba@797: }
deba@797: }
deba@797: }
deba@797:
deba@797: for (int i = order.size() - 1; i >= 0; --i) {
deba@797: std::vector<bool> forbidden(5, false);
deba@797: for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
deba@797: Node t = _graph.runningNode(e);
deba@797: if (_color_map[t] != -1) {
deba@797: forbidden[_color_map[t]] = true;
deba@797: }
deba@797: }
deba@797: for (int k = 0; k < 5; ++k) {
deba@797: if (!forbidden[k]) {
deba@797: _color_map[order[i]] = k;
deba@797: break;
deba@797: }
deba@797: }
deba@797: if (_color_map[order[i]] == -1) {
deba@797: kempeRecoloring(order[i], embedding);
deba@797: }
deba@797: }
deba@797: }
deba@797:
kpeter@828: /// \brief Calculate a coloring with at most five colors
deba@797: ///
deba@797: /// This function calculates a coloring with at most five
deba@797: /// colors. The worst case time complexity of this variant is
deba@797: /// quadratic in the size of the graph.
kpeter@828: /// \return \c true if the graph is planar.
deba@797: bool runFiveColoring() {
deba@797: PlanarEmbedding<Graph> pe(_graph);
deba@797: if (!pe.run()) return false;
deba@797:
deba@797: runFiveColoring(pe.embeddingMap());
deba@797: return true;
deba@797: }
deba@797:
deba@797: private:
deba@797:
deba@797: const Graph& _graph;
deba@797: IndexMap _color_map;
deba@797: Palette _palette;
deba@797: };
deba@797:
deba@797: }
deba@797:
deba@797: #endif