r896:5fd7fafc4470
Thu, 11 Feb 2010 07:40:29
[Not Reviewed]
0 comments (0 inline)
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| ... | ... |
@@ -329,589 +329,596 @@ |
| 329 | 329 |
} |
| 330 | 330 |
|
| 331 | 331 |
if (parent != root) {
|
| 332 | 332 |
na = nb = order_map[parent]; |
| 333 | 333 |
da = true; db = false; |
| 334 | 334 |
} else {
|
| 335 | 335 |
break; |
| 336 | 336 |
} |
| 337 | 337 |
} |
| 338 | 338 |
} |
| 339 | 339 |
} |
| 340 | 340 |
|
| 341 | 341 |
void walkDown(int rn, int rorder, NodeData& node_data, |
| 342 | 342 |
OrderList& order_list, ChildLists& child_lists, |
| 343 | 343 |
AncestorMap& ancestor_map, LowMap& low_map, |
| 344 | 344 |
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
| 345 | 345 |
|
| 346 | 346 |
std::vector<std::pair<int, bool> > merge_stack; |
| 347 | 347 |
|
| 348 | 348 |
for (int di = 0; di < 2; ++di) {
|
| 349 | 349 |
bool rd = di == 0; |
| 350 | 350 |
int pn = rn; |
| 351 | 351 |
int n = rd ? node_data[rn].next : node_data[rn].prev; |
| 352 | 352 |
|
| 353 | 353 |
while (n != rn) {
|
| 354 | 354 |
|
| 355 | 355 |
Node node = order_list[n]; |
| 356 | 356 |
|
| 357 | 357 |
if (embed_arc[node]) {
|
| 358 | 358 |
|
| 359 | 359 |
// Merging components on the critical path |
| 360 | 360 |
while (!merge_stack.empty()) {
|
| 361 | 361 |
|
| 362 | 362 |
// Component root |
| 363 | 363 |
int cn = merge_stack.back().first; |
| 364 | 364 |
bool cd = merge_stack.back().second; |
| 365 | 365 |
merge_stack.pop_back(); |
| 366 | 366 |
|
| 367 | 367 |
// Parent of component |
| 368 | 368 |
int dn = merge_stack.back().first; |
| 369 | 369 |
bool dd = merge_stack.back().second; |
| 370 | 370 |
merge_stack.pop_back(); |
| 371 | 371 |
|
| 372 | 372 |
Node parent = order_list[dn]; |
| 373 | 373 |
|
| 374 | 374 |
// Erasing from merge_roots |
| 375 | 375 |
merge_roots[parent].pop_front(); |
| 376 | 376 |
|
| 377 | 377 |
Node child = order_list[cn - order_list.size()]; |
| 378 | 378 |
|
| 379 | 379 |
// Erasing from child_lists |
| 380 | 380 |
if (child_lists[child].prev != INVALID) {
|
| 381 | 381 |
child_lists[child_lists[child].prev].next = |
| 382 | 382 |
child_lists[child].next; |
| 383 | 383 |
} else {
|
| 384 | 384 |
child_lists[parent].first = child_lists[child].next; |
| 385 | 385 |
} |
| 386 | 386 |
|
| 387 | 387 |
if (child_lists[child].next != INVALID) {
|
| 388 | 388 |
child_lists[child_lists[child].next].prev = |
| 389 | 389 |
child_lists[child].prev; |
| 390 | 390 |
} |
| 391 | 391 |
|
| 392 | 392 |
// Merging external faces |
| 393 | 393 |
{
|
| 394 | 394 |
int en = cn; |
| 395 | 395 |
cn = cd ? node_data[cn].prev : node_data[cn].next; |
| 396 | 396 |
cd = node_data[cn].next == en; |
| 397 | 397 |
|
| 398 | 398 |
} |
| 399 | 399 |
|
| 400 | 400 |
if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
| 401 | 401 |
if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
| 402 | 402 |
|
| 403 | 403 |
} |
| 404 | 404 |
|
| 405 | 405 |
bool d = pn == node_data[n].prev; |
| 406 | 406 |
|
| 407 | 407 |
if (node_data[n].prev == node_data[n].next && |
| 408 | 408 |
node_data[n].inverted) {
|
| 409 | 409 |
d = !d; |
| 410 | 410 |
} |
| 411 | 411 |
|
| 412 | 412 |
// Embedding arc into external face |
| 413 | 413 |
if (rd) node_data[rn].next = n; else node_data[rn].prev = n; |
| 414 | 414 |
if (d) node_data[n].prev = rn; else node_data[n].next = rn; |
| 415 | 415 |
pn = rn; |
| 416 | 416 |
|
| 417 | 417 |
embed_arc[order_list[n]] = false; |
| 418 | 418 |
} |
| 419 | 419 |
|
| 420 | 420 |
if (!merge_roots[node].empty()) {
|
| 421 | 421 |
|
| 422 | 422 |
bool d = pn == node_data[n].prev; |
| 423 | 423 |
|
| 424 | 424 |
merge_stack.push_back(std::make_pair(n, d)); |
| 425 | 425 |
|
| 426 | 426 |
int rn = merge_roots[node].front(); |
| 427 | 427 |
|
| 428 | 428 |
int xn = node_data[rn].next; |
| 429 | 429 |
Node xnode = order_list[xn]; |
| 430 | 430 |
|
| 431 | 431 |
int yn = node_data[rn].prev; |
| 432 | 432 |
Node ynode = order_list[yn]; |
| 433 | 433 |
|
| 434 | 434 |
bool rd; |
| 435 | 435 |
if (!external(xnode, rorder, child_lists, |
| 436 | 436 |
ancestor_map, low_map)) {
|
| 437 | 437 |
rd = true; |
| 438 | 438 |
} else if (!external(ynode, rorder, child_lists, |
| 439 | 439 |
ancestor_map, low_map)) {
|
| 440 | 440 |
rd = false; |
| 441 | 441 |
} else if (pertinent(xnode, embed_arc, merge_roots)) {
|
| 442 | 442 |
rd = true; |
| 443 | 443 |
} else {
|
| 444 | 444 |
rd = false; |
| 445 | 445 |
} |
| 446 | 446 |
|
| 447 | 447 |
merge_stack.push_back(std::make_pair(rn, rd)); |
| 448 | 448 |
|
| 449 | 449 |
pn = rn; |
| 450 | 450 |
n = rd ? xn : yn; |
| 451 | 451 |
|
| 452 | 452 |
} else if (!external(node, rorder, child_lists, |
| 453 | 453 |
ancestor_map, low_map)) {
|
| 454 | 454 |
int nn = (node_data[n].next != pn ? |
| 455 | 455 |
node_data[n].next : node_data[n].prev); |
| 456 | 456 |
|
| 457 | 457 |
bool nd = n == node_data[nn].prev; |
| 458 | 458 |
|
| 459 | 459 |
if (nd) node_data[nn].prev = pn; |
| 460 | 460 |
else node_data[nn].next = pn; |
| 461 | 461 |
|
| 462 | 462 |
if (n == node_data[pn].prev) node_data[pn].prev = nn; |
| 463 | 463 |
else node_data[pn].next = nn; |
| 464 | 464 |
|
| 465 | 465 |
node_data[nn].inverted = |
| 466 | 466 |
(node_data[nn].prev == node_data[nn].next && nd != rd); |
| 467 | 467 |
|
| 468 | 468 |
n = nn; |
| 469 | 469 |
} |
| 470 | 470 |
else break; |
| 471 | 471 |
|
| 472 | 472 |
} |
| 473 | 473 |
|
| 474 | 474 |
if (!merge_stack.empty() || n == rn) {
|
| 475 | 475 |
break; |
| 476 | 476 |
} |
| 477 | 477 |
} |
| 478 | 478 |
} |
| 479 | 479 |
|
| 480 | 480 |
void initFace(const Node& node, NodeData& node_data, |
| 481 | 481 |
const OrderMap& order_map, const OrderList& order_list) {
|
| 482 | 482 |
int n = order_map[node]; |
| 483 | 483 |
int rn = n + order_list.size(); |
| 484 | 484 |
|
| 485 | 485 |
node_data[n].next = node_data[n].prev = rn; |
| 486 | 486 |
node_data[rn].next = node_data[rn].prev = n; |
| 487 | 487 |
|
| 488 | 488 |
node_data[n].visited = order_list.size(); |
| 489 | 489 |
node_data[rn].visited = order_list.size(); |
| 490 | 490 |
|
| 491 | 491 |
} |
| 492 | 492 |
|
| 493 | 493 |
bool external(const Node& node, int rorder, |
| 494 | 494 |
ChildLists& child_lists, AncestorMap& ancestor_map, |
| 495 | 495 |
LowMap& low_map) {
|
| 496 | 496 |
Node child = child_lists[node].first; |
| 497 | 497 |
|
| 498 | 498 |
if (child != INVALID) {
|
| 499 | 499 |
if (low_map[child] < rorder) return true; |
| 500 | 500 |
} |
| 501 | 501 |
|
| 502 | 502 |
if (ancestor_map[node] < rorder) return true; |
| 503 | 503 |
|
| 504 | 504 |
return false; |
| 505 | 505 |
} |
| 506 | 506 |
|
| 507 | 507 |
bool pertinent(const Node& node, const EmbedArc& embed_arc, |
| 508 | 508 |
const MergeRoots& merge_roots) {
|
| 509 | 509 |
return !merge_roots[node].empty() || embed_arc[node]; |
| 510 | 510 |
} |
| 511 | 511 |
|
| 512 | 512 |
}; |
| 513 | 513 |
|
| 514 | 514 |
} |
| 515 | 515 |
|
| 516 | 516 |
/// \ingroup planar |
| 517 | 517 |
/// |
| 518 | 518 |
/// \brief Planarity checking of an undirected simple graph |
| 519 | 519 |
/// |
| 520 | 520 |
/// This function implements the Boyer-Myrvold algorithm for |
| 521 |
/// planarity checking of an undirected graph. It is a simplified |
|
| 521 |
/// planarity checking of an undirected simple graph. It is a simplified |
|
| 522 | 522 |
/// version of the PlanarEmbedding algorithm class because neither |
| 523 |
/// the embedding nor the |
|
| 523 |
/// the embedding nor the Kuratowski subdivisons are computed. |
|
| 524 | 524 |
template <typename GR> |
| 525 | 525 |
bool checkPlanarity(const GR& graph) {
|
| 526 | 526 |
_planarity_bits::PlanarityChecking<GR> pc(graph); |
| 527 | 527 |
return pc.run(); |
| 528 | 528 |
} |
| 529 | 529 |
|
| 530 | 530 |
/// \ingroup planar |
| 531 | 531 |
/// |
| 532 | 532 |
/// \brief Planar embedding of an undirected simple graph |
| 533 | 533 |
/// |
| 534 | 534 |
/// This class implements the Boyer-Myrvold algorithm for planar |
| 535 |
/// embedding of an undirected graph. The planar embedding is an |
|
| 535 |
/// embedding of an undirected simple graph. The planar embedding is an |
|
| 536 | 536 |
/// ordering of the outgoing edges of the nodes, which is a possible |
| 537 | 537 |
/// configuration to draw the graph in the plane. If there is not |
| 538 |
/// such ordering then the graph contains a \f$ K_5 \f$ (full graph |
|
| 539 |
/// with 5 nodes) or a \f$ K_{3,3} \f$ (complete bipartite graph on
|
|
| 540 |
/// |
|
| 538 |
/// such ordering then the graph contains a K<sub>5</sub> (full graph |
|
| 539 |
/// with 5 nodes) or a K<sub>3,3</sub> (complete bipartite graph on |
|
| 540 |
/// 3 Red and 3 Blue nodes) subdivision. |
|
| 541 | 541 |
/// |
| 542 | 542 |
/// The current implementation calculates either an embedding or a |
| 543 |
/// Kuratowski subdivision. The running time of the algorithm is |
|
| 544 |
/// \f$ O(n) \f$. |
|
| 543 |
/// Kuratowski subdivision. The running time of the algorithm is O(n). |
|
| 544 |
/// |
|
| 545 |
/// \see PlanarDrawing, checkPlanarity() |
|
| 545 | 546 |
template <typename Graph> |
| 546 | 547 |
class PlanarEmbedding {
|
| 547 | 548 |
private: |
| 548 | 549 |
|
| 549 | 550 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 550 | 551 |
|
| 551 | 552 |
const Graph& _graph; |
| 552 | 553 |
typename Graph::template ArcMap<Arc> _embedding; |
| 553 | 554 |
|
| 554 | 555 |
typename Graph::template EdgeMap<bool> _kuratowski; |
| 555 | 556 |
|
| 556 | 557 |
private: |
| 557 | 558 |
|
| 558 | 559 |
typedef typename Graph::template NodeMap<Arc> PredMap; |
| 559 | 560 |
|
| 560 | 561 |
typedef typename Graph::template EdgeMap<bool> TreeMap; |
| 561 | 562 |
|
| 562 | 563 |
typedef typename Graph::template NodeMap<int> OrderMap; |
| 563 | 564 |
typedef std::vector<Node> OrderList; |
| 564 | 565 |
|
| 565 | 566 |
typedef typename Graph::template NodeMap<int> LowMap; |
| 566 | 567 |
typedef typename Graph::template NodeMap<int> AncestorMap; |
| 567 | 568 |
|
| 568 | 569 |
typedef _planarity_bits::NodeDataNode<Graph> NodeDataNode; |
| 569 | 570 |
typedef std::vector<NodeDataNode> NodeData; |
| 570 | 571 |
|
| 571 | 572 |
typedef _planarity_bits::ChildListNode<Graph> ChildListNode; |
| 572 | 573 |
typedef typename Graph::template NodeMap<ChildListNode> ChildLists; |
| 573 | 574 |
|
| 574 | 575 |
typedef typename Graph::template NodeMap<std::list<int> > MergeRoots; |
| 575 | 576 |
|
| 576 | 577 |
typedef typename Graph::template NodeMap<Arc> EmbedArc; |
| 577 | 578 |
|
| 578 | 579 |
typedef _planarity_bits::ArcListNode<Graph> ArcListNode; |
| 579 | 580 |
typedef typename Graph::template ArcMap<ArcListNode> ArcLists; |
| 580 | 581 |
|
| 581 | 582 |
typedef typename Graph::template NodeMap<bool> FlipMap; |
| 582 | 583 |
|
| 583 | 584 |
typedef typename Graph::template NodeMap<int> TypeMap; |
| 584 | 585 |
|
| 585 | 586 |
enum IsolatorNodeType {
|
| 586 | 587 |
HIGHX = 6, LOWX = 7, |
| 587 | 588 |
HIGHY = 8, LOWY = 9, |
| 588 | 589 |
ROOT = 10, PERTINENT = 11, |
| 589 | 590 |
INTERNAL = 12 |
| 590 | 591 |
}; |
| 591 | 592 |
|
| 592 | 593 |
public: |
| 593 | 594 |
|
| 594 |
/// \brief The map for |
|
| 595 |
/// \brief The map type for storing the embedding |
|
| 596 |
/// |
|
| 597 |
/// The map type for storing the embedding. |
|
| 598 |
/// \see embeddingMap() |
|
| 595 | 599 |
typedef typename Graph::template ArcMap<Arc> EmbeddingMap; |
| 596 | 600 |
|
| 597 | 601 |
/// \brief Constructor |
| 598 | 602 |
/// |
| 599 |
/// \note The graph should be simple, i.e. parallel and loop arc |
|
| 600 |
/// free. |
|
| 603 |
/// Constructor. |
|
| 604 |
/// \pre The graph must be simple, i.e. it should not |
|
| 605 |
/// contain parallel or loop arcs. |
|
| 601 | 606 |
PlanarEmbedding(const Graph& graph) |
| 602 | 607 |
: _graph(graph), _embedding(_graph), _kuratowski(graph, false) {}
|
| 603 | 608 |
|
| 604 |
/// \brief |
|
| 609 |
/// \brief Run the algorithm. |
|
| 605 | 610 |
/// |
| 606 |
/// Runs the algorithm. |
|
| 607 |
/// \param kuratowski If the parameter is false, then the |
|
| 611 |
/// This function runs the algorithm. |
|
| 612 |
/// \param kuratowski If this parameter is set to \c false, then the |
|
| 608 | 613 |
/// algorithm does not compute a Kuratowski subdivision. |
| 609 |
///\return |
|
| 614 |
/// \return \c true if the graph is planar. |
|
| 610 | 615 |
bool run(bool kuratowski = true) {
|
| 611 | 616 |
typedef _planarity_bits::PlanarityVisitor<Graph> Visitor; |
| 612 | 617 |
|
| 613 | 618 |
PredMap pred_map(_graph, INVALID); |
| 614 | 619 |
TreeMap tree_map(_graph, false); |
| 615 | 620 |
|
| 616 | 621 |
OrderMap order_map(_graph, -1); |
| 617 | 622 |
OrderList order_list; |
| 618 | 623 |
|
| 619 | 624 |
AncestorMap ancestor_map(_graph, -1); |
| 620 | 625 |
LowMap low_map(_graph, -1); |
| 621 | 626 |
|
| 622 | 627 |
Visitor visitor(_graph, pred_map, tree_map, |
| 623 | 628 |
order_map, order_list, ancestor_map, low_map); |
| 624 | 629 |
DfsVisit<Graph, Visitor> visit(_graph, visitor); |
| 625 | 630 |
visit.run(); |
| 626 | 631 |
|
| 627 | 632 |
ChildLists child_lists(_graph); |
| 628 | 633 |
createChildLists(tree_map, order_map, low_map, child_lists); |
| 629 | 634 |
|
| 630 | 635 |
NodeData node_data(2 * order_list.size()); |
| 631 | 636 |
|
| 632 | 637 |
EmbedArc embed_arc(_graph, INVALID); |
| 633 | 638 |
|
| 634 | 639 |
MergeRoots merge_roots(_graph); |
| 635 | 640 |
|
| 636 | 641 |
ArcLists arc_lists(_graph); |
| 637 | 642 |
|
| 638 | 643 |
FlipMap flip_map(_graph, false); |
| 639 | 644 |
|
| 640 | 645 |
for (int i = order_list.size() - 1; i >= 0; --i) {
|
| 641 | 646 |
|
| 642 | 647 |
Node node = order_list[i]; |
| 643 | 648 |
|
| 644 | 649 |
node_data[i].first = INVALID; |
| 645 | 650 |
|
| 646 | 651 |
Node source = node; |
| 647 | 652 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
| 648 | 653 |
Node target = _graph.target(e); |
| 649 | 654 |
|
| 650 | 655 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
| 651 | 656 |
initFace(target, arc_lists, node_data, |
| 652 | 657 |
pred_map, order_map, order_list); |
| 653 | 658 |
} |
| 654 | 659 |
} |
| 655 | 660 |
|
| 656 | 661 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
| 657 | 662 |
Node target = _graph.target(e); |
| 658 | 663 |
|
| 659 | 664 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
| 660 | 665 |
embed_arc[target] = e; |
| 661 | 666 |
walkUp(target, source, i, pred_map, low_map, |
| 662 | 667 |
order_map, order_list, node_data, merge_roots); |
| 663 | 668 |
} |
| 664 | 669 |
} |
| 665 | 670 |
|
| 666 | 671 |
for (typename MergeRoots::Value::iterator it = |
| 667 | 672 |
merge_roots[node].begin(); it != merge_roots[node].end(); ++it) {
|
| 668 | 673 |
int rn = *it; |
| 669 | 674 |
walkDown(rn, i, node_data, arc_lists, flip_map, order_list, |
| 670 | 675 |
child_lists, ancestor_map, low_map, embed_arc, merge_roots); |
| 671 | 676 |
} |
| 672 | 677 |
merge_roots[node].clear(); |
| 673 | 678 |
|
| 674 | 679 |
for (OutArcIt e(_graph, node); e != INVALID; ++e) {
|
| 675 | 680 |
Node target = _graph.target(e); |
| 676 | 681 |
|
| 677 | 682 |
if (order_map[source] < order_map[target] && !tree_map[e]) {
|
| 678 | 683 |
if (embed_arc[target] != INVALID) {
|
| 679 | 684 |
if (kuratowski) {
|
| 680 | 685 |
isolateKuratowski(e, node_data, arc_lists, flip_map, |
| 681 | 686 |
order_map, order_list, pred_map, child_lists, |
| 682 | 687 |
ancestor_map, low_map, |
| 683 | 688 |
embed_arc, merge_roots); |
| 684 | 689 |
} |
| 685 | 690 |
return false; |
| 686 | 691 |
} |
| 687 | 692 |
} |
| 688 | 693 |
} |
| 689 | 694 |
} |
| 690 | 695 |
|
| 691 | 696 |
for (int i = 0; i < int(order_list.size()); ++i) {
|
| 692 | 697 |
|
| 693 | 698 |
mergeRemainingFaces(order_list[i], node_data, order_list, order_map, |
| 694 | 699 |
child_lists, arc_lists); |
| 695 | 700 |
storeEmbedding(order_list[i], node_data, order_map, pred_map, |
| 696 | 701 |
arc_lists, flip_map); |
| 697 | 702 |
} |
| 698 | 703 |
|
| 699 | 704 |
return true; |
| 700 | 705 |
} |
| 701 | 706 |
|
| 702 |
/// \brief |
|
| 707 |
/// \brief Give back the successor of an arc |
|
| 703 | 708 |
/// |
| 704 |
/// |
|
| 709 |
/// This function gives back the successor of an arc. It makes |
|
| 705 | 710 |
/// possible to query the cyclic order of the outgoing arcs from |
| 706 | 711 |
/// a node. |
| 707 | 712 |
Arc next(const Arc& arc) const {
|
| 708 | 713 |
return _embedding[arc]; |
| 709 | 714 |
} |
| 710 | 715 |
|
| 711 |
/// \brief |
|
| 716 |
/// \brief Give back the calculated embedding map |
|
| 712 | 717 |
/// |
| 713 |
/// The returned map contains the successor of each arc in the |
|
| 714 |
/// graph. |
|
| 718 |
/// This function gives back the calculated embedding map, which |
|
| 719 |
/// contains the successor of each arc in the cyclic order of the |
|
| 720 |
/// outgoing arcs of its source node. |
|
| 715 | 721 |
const EmbeddingMap& embeddingMap() const {
|
| 716 | 722 |
return _embedding; |
| 717 | 723 |
} |
| 718 | 724 |
|
| 719 |
/// \brief Gives back true if the undirected arc is in the |
|
| 720 |
/// kuratowski subdivision |
|
| 725 |
/// \brief Give back \c true if the given edge is in the Kuratowski |
|
| 726 |
/// subdivision |
|
| 721 | 727 |
/// |
| 722 |
/// Gives back true if the undirected arc is in the kuratowski |
|
| 723 |
/// subdivision |
|
| 724 |
/// \note The \c run() had to be called with true value. |
|
| 725 |
bool kuratowski(const Edge& edge) {
|
|
| 728 |
/// This function gives back \c true if the given edge is in the found |
|
| 729 |
/// Kuratowski subdivision. |
|
| 730 |
/// \pre The \c run() function must be called with \c true parameter |
|
| 731 |
/// before using this function. |
|
| 732 |
bool kuratowski(const Edge& edge) const {
|
|
| 726 | 733 |
return _kuratowski[edge]; |
| 727 | 734 |
} |
| 728 | 735 |
|
| 729 | 736 |
private: |
| 730 | 737 |
|
| 731 | 738 |
void createChildLists(const TreeMap& tree_map, const OrderMap& order_map, |
| 732 | 739 |
const LowMap& low_map, ChildLists& child_lists) {
|
| 733 | 740 |
|
| 734 | 741 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 735 | 742 |
Node source = n; |
| 736 | 743 |
|
| 737 | 744 |
std::vector<Node> targets; |
| 738 | 745 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 739 | 746 |
Node target = _graph.target(e); |
| 740 | 747 |
|
| 741 | 748 |
if (order_map[source] < order_map[target] && tree_map[e]) {
|
| 742 | 749 |
targets.push_back(target); |
| 743 | 750 |
} |
| 744 | 751 |
} |
| 745 | 752 |
|
| 746 | 753 |
if (targets.size() == 0) {
|
| 747 | 754 |
child_lists[source].first = INVALID; |
| 748 | 755 |
} else if (targets.size() == 1) {
|
| 749 | 756 |
child_lists[source].first = targets[0]; |
| 750 | 757 |
child_lists[targets[0]].prev = INVALID; |
| 751 | 758 |
child_lists[targets[0]].next = INVALID; |
| 752 | 759 |
} else {
|
| 753 | 760 |
radixSort(targets.begin(), targets.end(), mapToFunctor(low_map)); |
| 754 | 761 |
for (int i = 1; i < int(targets.size()); ++i) {
|
| 755 | 762 |
child_lists[targets[i]].prev = targets[i - 1]; |
| 756 | 763 |
child_lists[targets[i - 1]].next = targets[i]; |
| 757 | 764 |
} |
| 758 | 765 |
child_lists[targets.back()].next = INVALID; |
| 759 | 766 |
child_lists[targets.front()].prev = INVALID; |
| 760 | 767 |
child_lists[source].first = targets.front(); |
| 761 | 768 |
} |
| 762 | 769 |
} |
| 763 | 770 |
} |
| 764 | 771 |
|
| 765 | 772 |
void walkUp(const Node& node, Node root, int rorder, |
| 766 | 773 |
const PredMap& pred_map, const LowMap& low_map, |
| 767 | 774 |
const OrderMap& order_map, const OrderList& order_list, |
| 768 | 775 |
NodeData& node_data, MergeRoots& merge_roots) {
|
| 769 | 776 |
|
| 770 | 777 |
int na, nb; |
| 771 | 778 |
bool da, db; |
| 772 | 779 |
|
| 773 | 780 |
na = nb = order_map[node]; |
| 774 | 781 |
da = true; db = false; |
| 775 | 782 |
|
| 776 | 783 |
while (true) {
|
| 777 | 784 |
|
| 778 | 785 |
if (node_data[na].visited == rorder) break; |
| 779 | 786 |
if (node_data[nb].visited == rorder) break; |
| 780 | 787 |
|
| 781 | 788 |
node_data[na].visited = rorder; |
| 782 | 789 |
node_data[nb].visited = rorder; |
| 783 | 790 |
|
| 784 | 791 |
int rn = -1; |
| 785 | 792 |
|
| 786 | 793 |
if (na >= int(order_list.size())) {
|
| 787 | 794 |
rn = na; |
| 788 | 795 |
} else if (nb >= int(order_list.size())) {
|
| 789 | 796 |
rn = nb; |
| 790 | 797 |
} |
| 791 | 798 |
|
| 792 | 799 |
if (rn == -1) {
|
| 793 | 800 |
int nn; |
| 794 | 801 |
|
| 795 | 802 |
nn = da ? node_data[na].prev : node_data[na].next; |
| 796 | 803 |
da = node_data[nn].prev != na; |
| 797 | 804 |
na = nn; |
| 798 | 805 |
|
| 799 | 806 |
nn = db ? node_data[nb].prev : node_data[nb].next; |
| 800 | 807 |
db = node_data[nn].prev != nb; |
| 801 | 808 |
nb = nn; |
| 802 | 809 |
|
| 803 | 810 |
} else {
|
| 804 | 811 |
|
| 805 | 812 |
Node rep = order_list[rn - order_list.size()]; |
| 806 | 813 |
Node parent = _graph.source(pred_map[rep]); |
| 807 | 814 |
|
| 808 | 815 |
if (low_map[rep] < rorder) {
|
| 809 | 816 |
merge_roots[parent].push_back(rn); |
| 810 | 817 |
} else {
|
| 811 | 818 |
merge_roots[parent].push_front(rn); |
| 812 | 819 |
} |
| 813 | 820 |
|
| 814 | 821 |
if (parent != root) {
|
| 815 | 822 |
na = nb = order_map[parent]; |
| 816 | 823 |
da = true; db = false; |
| 817 | 824 |
} else {
|
| 818 | 825 |
break; |
| 819 | 826 |
} |
| 820 | 827 |
} |
| 821 | 828 |
} |
| 822 | 829 |
} |
| 823 | 830 |
|
| 824 | 831 |
void walkDown(int rn, int rorder, NodeData& node_data, |
| 825 | 832 |
ArcLists& arc_lists, FlipMap& flip_map, |
| 826 | 833 |
OrderList& order_list, ChildLists& child_lists, |
| 827 | 834 |
AncestorMap& ancestor_map, LowMap& low_map, |
| 828 | 835 |
EmbedArc& embed_arc, MergeRoots& merge_roots) {
|
| 829 | 836 |
|
| 830 | 837 |
std::vector<std::pair<int, bool> > merge_stack; |
| 831 | 838 |
|
| 832 | 839 |
for (int di = 0; di < 2; ++di) {
|
| 833 | 840 |
bool rd = di == 0; |
| 834 | 841 |
int pn = rn; |
| 835 | 842 |
int n = rd ? node_data[rn].next : node_data[rn].prev; |
| 836 | 843 |
|
| 837 | 844 |
while (n != rn) {
|
| 838 | 845 |
|
| 839 | 846 |
Node node = order_list[n]; |
| 840 | 847 |
|
| 841 | 848 |
if (embed_arc[node] != INVALID) {
|
| 842 | 849 |
|
| 843 | 850 |
// Merging components on the critical path |
| 844 | 851 |
while (!merge_stack.empty()) {
|
| 845 | 852 |
|
| 846 | 853 |
// Component root |
| 847 | 854 |
int cn = merge_stack.back().first; |
| 848 | 855 |
bool cd = merge_stack.back().second; |
| 849 | 856 |
merge_stack.pop_back(); |
| 850 | 857 |
|
| 851 | 858 |
// Parent of component |
| 852 | 859 |
int dn = merge_stack.back().first; |
| 853 | 860 |
bool dd = merge_stack.back().second; |
| 854 | 861 |
merge_stack.pop_back(); |
| 855 | 862 |
|
| 856 | 863 |
Node parent = order_list[dn]; |
| 857 | 864 |
|
| 858 | 865 |
// Erasing from merge_roots |
| 859 | 866 |
merge_roots[parent].pop_front(); |
| 860 | 867 |
|
| 861 | 868 |
Node child = order_list[cn - order_list.size()]; |
| 862 | 869 |
|
| 863 | 870 |
// Erasing from child_lists |
| 864 | 871 |
if (child_lists[child].prev != INVALID) {
|
| 865 | 872 |
child_lists[child_lists[child].prev].next = |
| 866 | 873 |
child_lists[child].next; |
| 867 | 874 |
} else {
|
| 868 | 875 |
child_lists[parent].first = child_lists[child].next; |
| 869 | 876 |
} |
| 870 | 877 |
|
| 871 | 878 |
if (child_lists[child].next != INVALID) {
|
| 872 | 879 |
child_lists[child_lists[child].next].prev = |
| 873 | 880 |
child_lists[child].prev; |
| 874 | 881 |
} |
| 875 | 882 |
|
| 876 | 883 |
// Merging arcs + flipping |
| 877 | 884 |
Arc de = node_data[dn].first; |
| 878 | 885 |
Arc ce = node_data[cn].first; |
| 879 | 886 |
|
| 880 | 887 |
flip_map[order_list[cn - order_list.size()]] = cd != dd; |
| 881 | 888 |
if (cd != dd) {
|
| 882 | 889 |
std::swap(arc_lists[ce].prev, arc_lists[ce].next); |
| 883 | 890 |
ce = arc_lists[ce].prev; |
| 884 | 891 |
std::swap(arc_lists[ce].prev, arc_lists[ce].next); |
| 885 | 892 |
} |
| 886 | 893 |
|
| 887 | 894 |
{
|
| 888 | 895 |
Arc dne = arc_lists[de].next; |
| 889 | 896 |
Arc cne = arc_lists[ce].next; |
| 890 | 897 |
|
| 891 | 898 |
arc_lists[de].next = cne; |
| 892 | 899 |
arc_lists[ce].next = dne; |
| 893 | 900 |
|
| 894 | 901 |
arc_lists[dne].prev = ce; |
| 895 | 902 |
arc_lists[cne].prev = de; |
| 896 | 903 |
} |
| 897 | 904 |
|
| 898 | 905 |
if (dd) {
|
| 899 | 906 |
node_data[dn].first = ce; |
| 900 | 907 |
} |
| 901 | 908 |
|
| 902 | 909 |
// Merging external faces |
| 903 | 910 |
{
|
| 904 | 911 |
int en = cn; |
| 905 | 912 |
cn = cd ? node_data[cn].prev : node_data[cn].next; |
| 906 | 913 |
cd = node_data[cn].next == en; |
| 907 | 914 |
|
| 908 | 915 |
if (node_data[cn].prev == node_data[cn].next && |
| 909 | 916 |
node_data[cn].inverted) {
|
| 910 | 917 |
cd = !cd; |
| 911 | 918 |
} |
| 912 | 919 |
} |
| 913 | 920 |
|
| 914 | 921 |
if (cd) node_data[cn].next = dn; else node_data[cn].prev = dn; |
| 915 | 922 |
if (dd) node_data[dn].prev = cn; else node_data[dn].next = cn; |
| 916 | 923 |
|
| 917 | 924 |
} |
| ... | ... |
@@ -1870,868 +1877,879 @@ |
| 1870 | 1877 |
std::vector<typename Graph::Arc> arcs; |
| 1871 | 1878 |
for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
|
| 1872 | 1879 |
arcs.push_back(e); |
| 1873 | 1880 |
} |
| 1874 | 1881 |
|
| 1875 | 1882 |
IterableBoolMap<Graph, typename Graph::Node> visited(graph, false); |
| 1876 | 1883 |
|
| 1877 | 1884 |
for (int i = 0; i < int(arcs.size()); ++i) {
|
| 1878 | 1885 |
typename Graph::Arc pp = arcs[i]; |
| 1879 | 1886 |
if (processed[pp]) continue; |
| 1880 | 1887 |
|
| 1881 | 1888 |
typename Graph::Arc e = embedding[graph.oppositeArc(pp)]; |
| 1882 | 1889 |
processed[e] = true; |
| 1883 | 1890 |
visited.set(graph.source(e), true); |
| 1884 | 1891 |
|
| 1885 | 1892 |
typename Graph::Arc p = e, l = e; |
| 1886 | 1893 |
e = embedding[graph.oppositeArc(e)]; |
| 1887 | 1894 |
|
| 1888 | 1895 |
while (e != l) {
|
| 1889 | 1896 |
processed[e] = true; |
| 1890 | 1897 |
|
| 1891 | 1898 |
if (visited[graph.source(e)]) {
|
| 1892 | 1899 |
|
| 1893 | 1900 |
typename Graph::Arc n = |
| 1894 | 1901 |
graph.direct(graph.addEdge(graph.source(p), |
| 1895 | 1902 |
graph.target(e)), true); |
| 1896 | 1903 |
embedding[n] = p; |
| 1897 | 1904 |
embedding[graph.oppositeArc(pp)] = n; |
| 1898 | 1905 |
|
| 1899 | 1906 |
embedding[graph.oppositeArc(n)] = |
| 1900 | 1907 |
embedding[graph.oppositeArc(e)]; |
| 1901 | 1908 |
embedding[graph.oppositeArc(e)] = |
| 1902 | 1909 |
graph.oppositeArc(n); |
| 1903 | 1910 |
|
| 1904 | 1911 |
p = n; |
| 1905 | 1912 |
e = embedding[graph.oppositeArc(n)]; |
| 1906 | 1913 |
} else {
|
| 1907 | 1914 |
visited.set(graph.source(e), true); |
| 1908 | 1915 |
pp = p; |
| 1909 | 1916 |
p = e; |
| 1910 | 1917 |
e = embedding[graph.oppositeArc(e)]; |
| 1911 | 1918 |
} |
| 1912 | 1919 |
} |
| 1913 | 1920 |
visited.setAll(false); |
| 1914 | 1921 |
} |
| 1915 | 1922 |
} |
| 1916 | 1923 |
|
| 1917 | 1924 |
|
| 1918 | 1925 |
template <typename Graph, typename EmbeddingMap> |
| 1919 | 1926 |
void makeMaxPlanar(Graph& graph, EmbeddingMap& embedding) {
|
| 1920 | 1927 |
|
| 1921 | 1928 |
typename Graph::template NodeMap<int> degree(graph); |
| 1922 | 1929 |
|
| 1923 | 1930 |
for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
|
| 1924 | 1931 |
degree[n] = countIncEdges(graph, n); |
| 1925 | 1932 |
} |
| 1926 | 1933 |
|
| 1927 | 1934 |
typename Graph::template ArcMap<bool> processed(graph); |
| 1928 | 1935 |
IterableBoolMap<Graph, typename Graph::Node> visited(graph, false); |
| 1929 | 1936 |
|
| 1930 | 1937 |
std::vector<typename Graph::Arc> arcs; |
| 1931 | 1938 |
for (typename Graph::ArcIt e(graph); e != INVALID; ++e) {
|
| 1932 | 1939 |
arcs.push_back(e); |
| 1933 | 1940 |
} |
| 1934 | 1941 |
|
| 1935 | 1942 |
for (int i = 0; i < int(arcs.size()); ++i) {
|
| 1936 | 1943 |
typename Graph::Arc e = arcs[i]; |
| 1937 | 1944 |
|
| 1938 | 1945 |
if (processed[e]) continue; |
| 1939 | 1946 |
processed[e] = true; |
| 1940 | 1947 |
|
| 1941 | 1948 |
typename Graph::Arc mine = e; |
| 1942 | 1949 |
int mind = degree[graph.source(e)]; |
| 1943 | 1950 |
|
| 1944 | 1951 |
int face_size = 1; |
| 1945 | 1952 |
|
| 1946 | 1953 |
typename Graph::Arc l = e; |
| 1947 | 1954 |
e = embedding[graph.oppositeArc(e)]; |
| 1948 | 1955 |
while (l != e) {
|
| 1949 | 1956 |
processed[e] = true; |
| 1950 | 1957 |
|
| 1951 | 1958 |
++face_size; |
| 1952 | 1959 |
|
| 1953 | 1960 |
if (degree[graph.source(e)] < mind) {
|
| 1954 | 1961 |
mine = e; |
| 1955 | 1962 |
mind = degree[graph.source(e)]; |
| 1956 | 1963 |
} |
| 1957 | 1964 |
|
| 1958 | 1965 |
e = embedding[graph.oppositeArc(e)]; |
| 1959 | 1966 |
} |
| 1960 | 1967 |
|
| 1961 | 1968 |
if (face_size < 4) {
|
| 1962 | 1969 |
continue; |
| 1963 | 1970 |
} |
| 1964 | 1971 |
|
| 1965 | 1972 |
typename Graph::Node s = graph.source(mine); |
| 1966 | 1973 |
for (typename Graph::OutArcIt e(graph, s); e != INVALID; ++e) {
|
| 1967 | 1974 |
visited.set(graph.target(e), true); |
| 1968 | 1975 |
} |
| 1969 | 1976 |
|
| 1970 | 1977 |
typename Graph::Arc oppe = INVALID; |
| 1971 | 1978 |
|
| 1972 | 1979 |
e = embedding[graph.oppositeArc(mine)]; |
| 1973 | 1980 |
e = embedding[graph.oppositeArc(e)]; |
| 1974 | 1981 |
while (graph.target(e) != s) {
|
| 1975 | 1982 |
if (visited[graph.source(e)]) {
|
| 1976 | 1983 |
oppe = e; |
| 1977 | 1984 |
break; |
| 1978 | 1985 |
} |
| 1979 | 1986 |
e = embedding[graph.oppositeArc(e)]; |
| 1980 | 1987 |
} |
| 1981 | 1988 |
visited.setAll(false); |
| 1982 | 1989 |
|
| 1983 | 1990 |
if (oppe == INVALID) {
|
| 1984 | 1991 |
|
| 1985 | 1992 |
e = embedding[graph.oppositeArc(mine)]; |
| 1986 | 1993 |
typename Graph::Arc pn = mine, p = e; |
| 1987 | 1994 |
|
| 1988 | 1995 |
e = embedding[graph.oppositeArc(e)]; |
| 1989 | 1996 |
while (graph.target(e) != s) {
|
| 1990 | 1997 |
typename Graph::Arc n = |
| 1991 | 1998 |
graph.direct(graph.addEdge(s, graph.source(e)), true); |
| 1992 | 1999 |
|
| 1993 | 2000 |
embedding[n] = pn; |
| 1994 | 2001 |
embedding[graph.oppositeArc(n)] = e; |
| 1995 | 2002 |
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
| 1996 | 2003 |
|
| 1997 | 2004 |
pn = n; |
| 1998 | 2005 |
|
| 1999 | 2006 |
p = e; |
| 2000 | 2007 |
e = embedding[graph.oppositeArc(e)]; |
| 2001 | 2008 |
} |
| 2002 | 2009 |
|
| 2003 | 2010 |
embedding[graph.oppositeArc(e)] = pn; |
| 2004 | 2011 |
|
| 2005 | 2012 |
} else {
|
| 2006 | 2013 |
|
| 2007 | 2014 |
mine = embedding[graph.oppositeArc(mine)]; |
| 2008 | 2015 |
s = graph.source(mine); |
| 2009 | 2016 |
oppe = embedding[graph.oppositeArc(oppe)]; |
| 2010 | 2017 |
typename Graph::Node t = graph.source(oppe); |
| 2011 | 2018 |
|
| 2012 | 2019 |
typename Graph::Arc ce = graph.direct(graph.addEdge(s, t), true); |
| 2013 | 2020 |
embedding[ce] = mine; |
| 2014 | 2021 |
embedding[graph.oppositeArc(ce)] = oppe; |
| 2015 | 2022 |
|
| 2016 | 2023 |
typename Graph::Arc pn = ce, p = oppe; |
| 2017 | 2024 |
e = embedding[graph.oppositeArc(oppe)]; |
| 2018 | 2025 |
while (graph.target(e) != s) {
|
| 2019 | 2026 |
typename Graph::Arc n = |
| 2020 | 2027 |
graph.direct(graph.addEdge(s, graph.source(e)), true); |
| 2021 | 2028 |
|
| 2022 | 2029 |
embedding[n] = pn; |
| 2023 | 2030 |
embedding[graph.oppositeArc(n)] = e; |
| 2024 | 2031 |
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
| 2025 | 2032 |
|
| 2026 | 2033 |
pn = n; |
| 2027 | 2034 |
|
| 2028 | 2035 |
p = e; |
| 2029 | 2036 |
e = embedding[graph.oppositeArc(e)]; |
| 2030 | 2037 |
|
| 2031 | 2038 |
} |
| 2032 | 2039 |
embedding[graph.oppositeArc(e)] = pn; |
| 2033 | 2040 |
|
| 2034 | 2041 |
pn = graph.oppositeArc(ce), p = mine; |
| 2035 | 2042 |
e = embedding[graph.oppositeArc(mine)]; |
| 2036 | 2043 |
while (graph.target(e) != t) {
|
| 2037 | 2044 |
typename Graph::Arc n = |
| 2038 | 2045 |
graph.direct(graph.addEdge(t, graph.source(e)), true); |
| 2039 | 2046 |
|
| 2040 | 2047 |
embedding[n] = pn; |
| 2041 | 2048 |
embedding[graph.oppositeArc(n)] = e; |
| 2042 | 2049 |
embedding[graph.oppositeArc(p)] = graph.oppositeArc(n); |
| 2043 | 2050 |
|
| 2044 | 2051 |
pn = n; |
| 2045 | 2052 |
|
| 2046 | 2053 |
p = e; |
| 2047 | 2054 |
e = embedding[graph.oppositeArc(e)]; |
| 2048 | 2055 |
|
| 2049 | 2056 |
} |
| 2050 | 2057 |
embedding[graph.oppositeArc(e)] = pn; |
| 2051 | 2058 |
} |
| 2052 | 2059 |
} |
| 2053 | 2060 |
} |
| 2054 | 2061 |
|
| 2055 | 2062 |
} |
| 2056 | 2063 |
|
| 2057 | 2064 |
/// \ingroup planar |
| 2058 | 2065 |
/// |
| 2059 | 2066 |
/// \brief Schnyder's planar drawing algorithm |
| 2060 | 2067 |
/// |
| 2061 | 2068 |
/// The planar drawing algorithm calculates positions for the nodes |
| 2062 |
/// in the plane which coordinates satisfy that if the arcs are |
|
| 2063 |
/// represented with straight lines then they will not intersect |
|
| 2069 |
/// in the plane. These coordinates satisfy that if the edges are |
|
| 2070 |
/// represented with straight lines, then they will not intersect |
|
| 2064 | 2071 |
/// each other. |
| 2065 | 2072 |
/// |
| 2066 |
/// Scnyder's algorithm embeds the graph on \c (n-2,n-2) size grid, |
|
| 2067 |
/// i.e. each node will be located in the \c [0,n-2]x[0,n-2] square. |
|
| 2073 |
/// Scnyder's algorithm embeds the graph on an \c (n-2)x(n-2) size grid, |
|
| 2074 |
/// i.e. each node will be located in the \c [0..n-2]x[0..n-2] square. |
|
| 2068 | 2075 |
/// The time complexity of the algorithm is O(n). |
| 2076 |
/// |
|
| 2077 |
/// \see PlanarEmbedding |
|
| 2069 | 2078 |
template <typename Graph> |
| 2070 | 2079 |
class PlanarDrawing {
|
| 2071 | 2080 |
public: |
| 2072 | 2081 |
|
| 2073 | 2082 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 2074 | 2083 |
|
| 2075 |
/// \brief The point type for |
|
| 2084 |
/// \brief The point type for storing coordinates |
|
| 2076 | 2085 |
typedef dim2::Point<int> Point; |
| 2077 |
/// \brief The map type for |
|
| 2086 |
/// \brief The map type for storing the coordinates of the nodes |
|
| 2078 | 2087 |
typedef typename Graph::template NodeMap<Point> PointMap; |
| 2079 | 2088 |
|
| 2080 | 2089 |
|
| 2081 | 2090 |
/// \brief Constructor |
| 2082 | 2091 |
/// |
| 2083 | 2092 |
/// Constructor |
| 2084 |
/// \pre The graph |
|
| 2093 |
/// \pre The graph must be simple, i.e. it should not |
|
| 2094 |
/// contain parallel or loop arcs. |
|
| 2085 | 2095 |
PlanarDrawing(const Graph& graph) |
| 2086 | 2096 |
: _graph(graph), _point_map(graph) {}
|
| 2087 | 2097 |
|
| 2088 | 2098 |
private: |
| 2089 | 2099 |
|
| 2090 | 2100 |
template <typename AuxGraph, typename AuxEmbeddingMap> |
| 2091 | 2101 |
void drawing(const AuxGraph& graph, |
| 2092 | 2102 |
const AuxEmbeddingMap& next, |
| 2093 | 2103 |
PointMap& point_map) {
|
| 2094 | 2104 |
TEMPLATE_GRAPH_TYPEDEFS(AuxGraph); |
| 2095 | 2105 |
|
| 2096 | 2106 |
typename AuxGraph::template ArcMap<Arc> prev(graph); |
| 2097 | 2107 |
|
| 2098 | 2108 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2099 | 2109 |
Arc e = OutArcIt(graph, n); |
| 2100 | 2110 |
|
| 2101 | 2111 |
Arc p = e, l = e; |
| 2102 | 2112 |
|
| 2103 | 2113 |
e = next[e]; |
| 2104 | 2114 |
while (e != l) {
|
| 2105 | 2115 |
prev[e] = p; |
| 2106 | 2116 |
p = e; |
| 2107 | 2117 |
e = next[e]; |
| 2108 | 2118 |
} |
| 2109 | 2119 |
prev[e] = p; |
| 2110 | 2120 |
} |
| 2111 | 2121 |
|
| 2112 | 2122 |
Node anode, bnode, cnode; |
| 2113 | 2123 |
|
| 2114 | 2124 |
{
|
| 2115 | 2125 |
Arc e = ArcIt(graph); |
| 2116 | 2126 |
anode = graph.source(e); |
| 2117 | 2127 |
bnode = graph.target(e); |
| 2118 | 2128 |
cnode = graph.target(next[graph.oppositeArc(e)]); |
| 2119 | 2129 |
} |
| 2120 | 2130 |
|
| 2121 | 2131 |
IterableBoolMap<AuxGraph, Node> proper(graph, false); |
| 2122 | 2132 |
typename AuxGraph::template NodeMap<int> conn(graph, -1); |
| 2123 | 2133 |
|
| 2124 | 2134 |
conn[anode] = conn[bnode] = -2; |
| 2125 | 2135 |
{
|
| 2126 | 2136 |
for (OutArcIt e(graph, anode); e != INVALID; ++e) {
|
| 2127 | 2137 |
Node m = graph.target(e); |
| 2128 | 2138 |
if (conn[m] == -1) {
|
| 2129 | 2139 |
conn[m] = 1; |
| 2130 | 2140 |
} |
| 2131 | 2141 |
} |
| 2132 | 2142 |
conn[cnode] = 2; |
| 2133 | 2143 |
|
| 2134 | 2144 |
for (OutArcIt e(graph, bnode); e != INVALID; ++e) {
|
| 2135 | 2145 |
Node m = graph.target(e); |
| 2136 | 2146 |
if (conn[m] == -1) {
|
| 2137 | 2147 |
conn[m] = 1; |
| 2138 | 2148 |
} else if (conn[m] != -2) {
|
| 2139 | 2149 |
conn[m] += 1; |
| 2140 | 2150 |
Arc pe = graph.oppositeArc(e); |
| 2141 | 2151 |
if (conn[graph.target(next[pe])] == -2) {
|
| 2142 | 2152 |
conn[m] -= 1; |
| 2143 | 2153 |
} |
| 2144 | 2154 |
if (conn[graph.target(prev[pe])] == -2) {
|
| 2145 | 2155 |
conn[m] -= 1; |
| 2146 | 2156 |
} |
| 2147 | 2157 |
|
| 2148 | 2158 |
proper.set(m, conn[m] == 1); |
| 2149 | 2159 |
} |
| 2150 | 2160 |
} |
| 2151 | 2161 |
} |
| 2152 | 2162 |
|
| 2153 | 2163 |
|
| 2154 | 2164 |
typename AuxGraph::template ArcMap<int> angle(graph, -1); |
| 2155 | 2165 |
|
| 2156 | 2166 |
while (proper.trueNum() != 0) {
|
| 2157 | 2167 |
Node n = typename IterableBoolMap<AuxGraph, Node>::TrueIt(proper); |
| 2158 | 2168 |
proper.set(n, false); |
| 2159 | 2169 |
conn[n] = -2; |
| 2160 | 2170 |
|
| 2161 | 2171 |
for (OutArcIt e(graph, n); e != INVALID; ++e) {
|
| 2162 | 2172 |
Node m = graph.target(e); |
| 2163 | 2173 |
if (conn[m] == -1) {
|
| 2164 | 2174 |
conn[m] = 1; |
| 2165 | 2175 |
} else if (conn[m] != -2) {
|
| 2166 | 2176 |
conn[m] += 1; |
| 2167 | 2177 |
Arc pe = graph.oppositeArc(e); |
| 2168 | 2178 |
if (conn[graph.target(next[pe])] == -2) {
|
| 2169 | 2179 |
conn[m] -= 1; |
| 2170 | 2180 |
} |
| 2171 | 2181 |
if (conn[graph.target(prev[pe])] == -2) {
|
| 2172 | 2182 |
conn[m] -= 1; |
| 2173 | 2183 |
} |
| 2174 | 2184 |
|
| 2175 | 2185 |
proper.set(m, conn[m] == 1); |
| 2176 | 2186 |
} |
| 2177 | 2187 |
} |
| 2178 | 2188 |
|
| 2179 | 2189 |
{
|
| 2180 | 2190 |
Arc e = OutArcIt(graph, n); |
| 2181 | 2191 |
Arc p = e, l = e; |
| 2182 | 2192 |
|
| 2183 | 2193 |
e = next[e]; |
| 2184 | 2194 |
while (e != l) {
|
| 2185 | 2195 |
|
| 2186 | 2196 |
if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
|
| 2187 | 2197 |
Arc f = e; |
| 2188 | 2198 |
angle[f] = 0; |
| 2189 | 2199 |
f = next[graph.oppositeArc(f)]; |
| 2190 | 2200 |
angle[f] = 1; |
| 2191 | 2201 |
f = next[graph.oppositeArc(f)]; |
| 2192 | 2202 |
angle[f] = 2; |
| 2193 | 2203 |
} |
| 2194 | 2204 |
|
| 2195 | 2205 |
p = e; |
| 2196 | 2206 |
e = next[e]; |
| 2197 | 2207 |
} |
| 2198 | 2208 |
|
| 2199 | 2209 |
if (conn[graph.target(e)] == -2 && conn[graph.target(p)] == -2) {
|
| 2200 | 2210 |
Arc f = e; |
| 2201 | 2211 |
angle[f] = 0; |
| 2202 | 2212 |
f = next[graph.oppositeArc(f)]; |
| 2203 | 2213 |
angle[f] = 1; |
| 2204 | 2214 |
f = next[graph.oppositeArc(f)]; |
| 2205 | 2215 |
angle[f] = 2; |
| 2206 | 2216 |
} |
| 2207 | 2217 |
} |
| 2208 | 2218 |
} |
| 2209 | 2219 |
|
| 2210 | 2220 |
typename AuxGraph::template NodeMap<Node> apred(graph, INVALID); |
| 2211 | 2221 |
typename AuxGraph::template NodeMap<Node> bpred(graph, INVALID); |
| 2212 | 2222 |
typename AuxGraph::template NodeMap<Node> cpred(graph, INVALID); |
| 2213 | 2223 |
|
| 2214 | 2224 |
typename AuxGraph::template NodeMap<int> apredid(graph, -1); |
| 2215 | 2225 |
typename AuxGraph::template NodeMap<int> bpredid(graph, -1); |
| 2216 | 2226 |
typename AuxGraph::template NodeMap<int> cpredid(graph, -1); |
| 2217 | 2227 |
|
| 2218 | 2228 |
for (ArcIt e(graph); e != INVALID; ++e) {
|
| 2219 | 2229 |
if (angle[e] == angle[next[e]]) {
|
| 2220 | 2230 |
switch (angle[e]) {
|
| 2221 | 2231 |
case 2: |
| 2222 | 2232 |
apred[graph.target(e)] = graph.source(e); |
| 2223 | 2233 |
apredid[graph.target(e)] = graph.id(graph.source(e)); |
| 2224 | 2234 |
break; |
| 2225 | 2235 |
case 1: |
| 2226 | 2236 |
bpred[graph.target(e)] = graph.source(e); |
| 2227 | 2237 |
bpredid[graph.target(e)] = graph.id(graph.source(e)); |
| 2228 | 2238 |
break; |
| 2229 | 2239 |
case 0: |
| 2230 | 2240 |
cpred[graph.target(e)] = graph.source(e); |
| 2231 | 2241 |
cpredid[graph.target(e)] = graph.id(graph.source(e)); |
| 2232 | 2242 |
break; |
| 2233 | 2243 |
} |
| 2234 | 2244 |
} |
| 2235 | 2245 |
} |
| 2236 | 2246 |
|
| 2237 | 2247 |
cpred[anode] = INVALID; |
| 2238 | 2248 |
cpred[bnode] = INVALID; |
| 2239 | 2249 |
|
| 2240 | 2250 |
std::vector<Node> aorder, border, corder; |
| 2241 | 2251 |
|
| 2242 | 2252 |
{
|
| 2243 | 2253 |
typename AuxGraph::template NodeMap<bool> processed(graph, false); |
| 2244 | 2254 |
std::vector<Node> st; |
| 2245 | 2255 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2246 | 2256 |
if (!processed[n] && n != bnode && n != cnode) {
|
| 2247 | 2257 |
st.push_back(n); |
| 2248 | 2258 |
processed[n] = true; |
| 2249 | 2259 |
Node m = apred[n]; |
| 2250 | 2260 |
while (m != INVALID && !processed[m]) {
|
| 2251 | 2261 |
st.push_back(m); |
| 2252 | 2262 |
processed[m] = true; |
| 2253 | 2263 |
m = apred[m]; |
| 2254 | 2264 |
} |
| 2255 | 2265 |
while (!st.empty()) {
|
| 2256 | 2266 |
aorder.push_back(st.back()); |
| 2257 | 2267 |
st.pop_back(); |
| 2258 | 2268 |
} |
| 2259 | 2269 |
} |
| 2260 | 2270 |
} |
| 2261 | 2271 |
} |
| 2262 | 2272 |
|
| 2263 | 2273 |
{
|
| 2264 | 2274 |
typename AuxGraph::template NodeMap<bool> processed(graph, false); |
| 2265 | 2275 |
std::vector<Node> st; |
| 2266 | 2276 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2267 | 2277 |
if (!processed[n] && n != cnode && n != anode) {
|
| 2268 | 2278 |
st.push_back(n); |
| 2269 | 2279 |
processed[n] = true; |
| 2270 | 2280 |
Node m = bpred[n]; |
| 2271 | 2281 |
while (m != INVALID && !processed[m]) {
|
| 2272 | 2282 |
st.push_back(m); |
| 2273 | 2283 |
processed[m] = true; |
| 2274 | 2284 |
m = bpred[m]; |
| 2275 | 2285 |
} |
| 2276 | 2286 |
while (!st.empty()) {
|
| 2277 | 2287 |
border.push_back(st.back()); |
| 2278 | 2288 |
st.pop_back(); |
| 2279 | 2289 |
} |
| 2280 | 2290 |
} |
| 2281 | 2291 |
} |
| 2282 | 2292 |
} |
| 2283 | 2293 |
|
| 2284 | 2294 |
{
|
| 2285 | 2295 |
typename AuxGraph::template NodeMap<bool> processed(graph, false); |
| 2286 | 2296 |
std::vector<Node> st; |
| 2287 | 2297 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2288 | 2298 |
if (!processed[n] && n != anode && n != bnode) {
|
| 2289 | 2299 |
st.push_back(n); |
| 2290 | 2300 |
processed[n] = true; |
| 2291 | 2301 |
Node m = cpred[n]; |
| 2292 | 2302 |
while (m != INVALID && !processed[m]) {
|
| 2293 | 2303 |
st.push_back(m); |
| 2294 | 2304 |
processed[m] = true; |
| 2295 | 2305 |
m = cpred[m]; |
| 2296 | 2306 |
} |
| 2297 | 2307 |
while (!st.empty()) {
|
| 2298 | 2308 |
corder.push_back(st.back()); |
| 2299 | 2309 |
st.pop_back(); |
| 2300 | 2310 |
} |
| 2301 | 2311 |
} |
| 2302 | 2312 |
} |
| 2303 | 2313 |
} |
| 2304 | 2314 |
|
| 2305 | 2315 |
typename AuxGraph::template NodeMap<int> atree(graph, 0); |
| 2306 | 2316 |
for (int i = aorder.size() - 1; i >= 0; --i) {
|
| 2307 | 2317 |
Node n = aorder[i]; |
| 2308 | 2318 |
atree[n] = 1; |
| 2309 | 2319 |
for (OutArcIt e(graph, n); e != INVALID; ++e) {
|
| 2310 | 2320 |
if (apred[graph.target(e)] == n) {
|
| 2311 | 2321 |
atree[n] += atree[graph.target(e)]; |
| 2312 | 2322 |
} |
| 2313 | 2323 |
} |
| 2314 | 2324 |
} |
| 2315 | 2325 |
|
| 2316 | 2326 |
typename AuxGraph::template NodeMap<int> btree(graph, 0); |
| 2317 | 2327 |
for (int i = border.size() - 1; i >= 0; --i) {
|
| 2318 | 2328 |
Node n = border[i]; |
| 2319 | 2329 |
btree[n] = 1; |
| 2320 | 2330 |
for (OutArcIt e(graph, n); e != INVALID; ++e) {
|
| 2321 | 2331 |
if (bpred[graph.target(e)] == n) {
|
| 2322 | 2332 |
btree[n] += btree[graph.target(e)]; |
| 2323 | 2333 |
} |
| 2324 | 2334 |
} |
| 2325 | 2335 |
} |
| 2326 | 2336 |
|
| 2327 | 2337 |
typename AuxGraph::template NodeMap<int> apath(graph, 0); |
| 2328 | 2338 |
apath[bnode] = apath[cnode] = 1; |
| 2329 | 2339 |
typename AuxGraph::template NodeMap<int> apath_btree(graph, 0); |
| 2330 | 2340 |
apath_btree[bnode] = btree[bnode]; |
| 2331 | 2341 |
for (int i = 1; i < int(aorder.size()); ++i) {
|
| 2332 | 2342 |
Node n = aorder[i]; |
| 2333 | 2343 |
apath[n] = apath[apred[n]] + 1; |
| 2334 | 2344 |
apath_btree[n] = btree[n] + apath_btree[apred[n]]; |
| 2335 | 2345 |
} |
| 2336 | 2346 |
|
| 2337 | 2347 |
typename AuxGraph::template NodeMap<int> bpath_atree(graph, 0); |
| 2338 | 2348 |
bpath_atree[anode] = atree[anode]; |
| 2339 | 2349 |
for (int i = 1; i < int(border.size()); ++i) {
|
| 2340 | 2350 |
Node n = border[i]; |
| 2341 | 2351 |
bpath_atree[n] = atree[n] + bpath_atree[bpred[n]]; |
| 2342 | 2352 |
} |
| 2343 | 2353 |
|
| 2344 | 2354 |
typename AuxGraph::template NodeMap<int> cpath(graph, 0); |
| 2345 | 2355 |
cpath[anode] = cpath[bnode] = 1; |
| 2346 | 2356 |
typename AuxGraph::template NodeMap<int> cpath_atree(graph, 0); |
| 2347 | 2357 |
cpath_atree[anode] = atree[anode]; |
| 2348 | 2358 |
typename AuxGraph::template NodeMap<int> cpath_btree(graph, 0); |
| 2349 | 2359 |
cpath_btree[bnode] = btree[bnode]; |
| 2350 | 2360 |
for (int i = 1; i < int(corder.size()); ++i) {
|
| 2351 | 2361 |
Node n = corder[i]; |
| 2352 | 2362 |
cpath[n] = cpath[cpred[n]] + 1; |
| 2353 | 2363 |
cpath_atree[n] = atree[n] + cpath_atree[cpred[n]]; |
| 2354 | 2364 |
cpath_btree[n] = btree[n] + cpath_btree[cpred[n]]; |
| 2355 | 2365 |
} |
| 2356 | 2366 |
|
| 2357 | 2367 |
typename AuxGraph::template NodeMap<int> third(graph); |
| 2358 | 2368 |
for (NodeIt n(graph); n != INVALID; ++n) {
|
| 2359 | 2369 |
point_map[n].x = |
| 2360 | 2370 |
bpath_atree[n] + cpath_atree[n] - atree[n] - cpath[n] + 1; |
| 2361 | 2371 |
point_map[n].y = |
| 2362 | 2372 |
cpath_btree[n] + apath_btree[n] - btree[n] - apath[n] + 1; |
| 2363 | 2373 |
} |
| 2364 | 2374 |
|
| 2365 | 2375 |
} |
| 2366 | 2376 |
|
| 2367 | 2377 |
public: |
| 2368 | 2378 |
|
| 2369 |
/// \brief |
|
| 2379 |
/// \brief Calculate the node positions |
|
| 2370 | 2380 |
/// |
| 2371 |
/// This function calculates the node positions. |
|
| 2372 |
/// \return %True if the graph is planar. |
|
| 2381 |
/// This function calculates the node positions on the plane. |
|
| 2382 |
/// \return \c true if the graph is planar. |
|
| 2373 | 2383 |
bool run() {
|
| 2374 | 2384 |
PlanarEmbedding<Graph> pe(_graph); |
| 2375 | 2385 |
if (!pe.run()) return false; |
| 2376 | 2386 |
|
| 2377 | 2387 |
run(pe); |
| 2378 | 2388 |
return true; |
| 2379 | 2389 |
} |
| 2380 | 2390 |
|
| 2381 |
/// \brief |
|
| 2391 |
/// \brief Calculate the node positions according to a |
|
| 2382 | 2392 |
/// combinatorical embedding |
| 2383 | 2393 |
/// |
| 2384 |
/// This function calculates the node locations. The \c embedding |
|
| 2385 |
/// parameter should contain a valid combinatorical embedding, i.e. |
|
| 2386 |
/// |
|
| 2394 |
/// This function calculates the node positions on the plane. |
|
| 2395 |
/// The given \c embedding map should contain a valid combinatorical |
|
| 2396 |
/// embedding, i.e. a valid cyclic order of the arcs. |
|
| 2397 |
/// It can be computed using PlanarEmbedding. |
|
| 2387 | 2398 |
template <typename EmbeddingMap> |
| 2388 | 2399 |
void run(const EmbeddingMap& embedding) {
|
| 2389 | 2400 |
typedef SmartEdgeSet<Graph> AuxGraph; |
| 2390 | 2401 |
|
| 2391 | 2402 |
if (3 * countNodes(_graph) - 6 == countEdges(_graph)) {
|
| 2392 | 2403 |
drawing(_graph, embedding, _point_map); |
| 2393 | 2404 |
return; |
| 2394 | 2405 |
} |
| 2395 | 2406 |
|
| 2396 | 2407 |
AuxGraph aux_graph(_graph); |
| 2397 | 2408 |
typename AuxGraph::template ArcMap<typename AuxGraph::Arc> |
| 2398 | 2409 |
aux_embedding(aux_graph); |
| 2399 | 2410 |
|
| 2400 | 2411 |
{
|
| 2401 | 2412 |
|
| 2402 | 2413 |
typename Graph::template EdgeMap<typename AuxGraph::Edge> |
| 2403 | 2414 |
ref(_graph); |
| 2404 | 2415 |
|
| 2405 | 2416 |
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
| 2406 | 2417 |
ref[e] = aux_graph.addEdge(_graph.u(e), _graph.v(e)); |
| 2407 | 2418 |
} |
| 2408 | 2419 |
|
| 2409 | 2420 |
for (EdgeIt e(_graph); e != INVALID; ++e) {
|
| 2410 | 2421 |
Arc ee = embedding[_graph.direct(e, true)]; |
| 2411 | 2422 |
aux_embedding[aux_graph.direct(ref[e], true)] = |
| 2412 | 2423 |
aux_graph.direct(ref[ee], _graph.direction(ee)); |
| 2413 | 2424 |
ee = embedding[_graph.direct(e, false)]; |
| 2414 | 2425 |
aux_embedding[aux_graph.direct(ref[e], false)] = |
| 2415 | 2426 |
aux_graph.direct(ref[ee], _graph.direction(ee)); |
| 2416 | 2427 |
} |
| 2417 | 2428 |
} |
| 2418 | 2429 |
_planarity_bits::makeConnected(aux_graph, aux_embedding); |
| 2419 | 2430 |
_planarity_bits::makeBiNodeConnected(aux_graph, aux_embedding); |
| 2420 | 2431 |
_planarity_bits::makeMaxPlanar(aux_graph, aux_embedding); |
| 2421 | 2432 |
drawing(aux_graph, aux_embedding, _point_map); |
| 2422 | 2433 |
} |
| 2423 | 2434 |
|
| 2424 | 2435 |
/// \brief The coordinate of the given node |
| 2425 | 2436 |
/// |
| 2426 |
/// |
|
| 2437 |
/// This function returns the coordinate of the given node. |
|
| 2427 | 2438 |
Point operator[](const Node& node) const {
|
| 2428 | 2439 |
return _point_map[node]; |
| 2429 | 2440 |
} |
| 2430 | 2441 |
|
| 2431 |
/// \brief |
|
| 2442 |
/// \brief Return the grid embedding in a node map |
|
| 2432 | 2443 |
/// |
| 2433 |
/// |
|
| 2444 |
/// This function returns the grid embedding in a node map of |
|
| 2445 |
/// \c dim2::Point<int> coordinates. |
|
| 2434 | 2446 |
const PointMap& coords() const {
|
| 2435 | 2447 |
return _point_map; |
| 2436 | 2448 |
} |
| 2437 | 2449 |
|
| 2438 | 2450 |
private: |
| 2439 | 2451 |
|
| 2440 | 2452 |
const Graph& _graph; |
| 2441 | 2453 |
PointMap _point_map; |
| 2442 | 2454 |
|
| 2443 | 2455 |
}; |
| 2444 | 2456 |
|
| 2445 | 2457 |
namespace _planarity_bits {
|
| 2446 | 2458 |
|
| 2447 | 2459 |
template <typename ColorMap> |
| 2448 | 2460 |
class KempeFilter {
|
| 2449 | 2461 |
public: |
| 2450 | 2462 |
typedef typename ColorMap::Key Key; |
| 2451 | 2463 |
typedef bool Value; |
| 2452 | 2464 |
|
| 2453 | 2465 |
KempeFilter(const ColorMap& color_map, |
| 2454 | 2466 |
const typename ColorMap::Value& first, |
| 2455 | 2467 |
const typename ColorMap::Value& second) |
| 2456 | 2468 |
: _color_map(color_map), _first(first), _second(second) {}
|
| 2457 | 2469 |
|
| 2458 | 2470 |
Value operator[](const Key& key) const {
|
| 2459 | 2471 |
return _color_map[key] == _first || _color_map[key] == _second; |
| 2460 | 2472 |
} |
| 2461 | 2473 |
|
| 2462 | 2474 |
private: |
| 2463 | 2475 |
const ColorMap& _color_map; |
| 2464 | 2476 |
typename ColorMap::Value _first, _second; |
| 2465 | 2477 |
}; |
| 2466 | 2478 |
} |
| 2467 | 2479 |
|
| 2468 | 2480 |
/// \ingroup planar |
| 2469 | 2481 |
/// |
| 2470 | 2482 |
/// \brief Coloring planar graphs |
| 2471 | 2483 |
/// |
| 2472 | 2484 |
/// The graph coloring problem is the coloring of the graph nodes |
| 2473 |
/// that there are not adjacent nodes with the same color. The |
|
| 2474 |
/// planar graphs can be always colored with four colors, it is |
|
| 2475 |
/// |
|
| 2485 |
/// so that there are no adjacent nodes with the same color. The |
|
| 2486 |
/// planar graphs can always be colored with four colors, which is |
|
| 2487 |
/// proved by Appel and Haken. Their proofs provide a quadratic |
|
| 2476 | 2488 |
/// time algorithm for four coloring, but it could not be used to |
| 2477 |
/// implement efficient algorithm. The five and six coloring can be |
|
| 2478 |
/// made in linear time, but in this class the five coloring has |
|
| 2489 |
/// implement an efficient algorithm. The five and six coloring can be |
|
| 2490 |
/// made in linear time, but in this class, the five coloring has |
|
| 2479 | 2491 |
/// quadratic worst case time complexity. The two coloring (if |
| 2480 | 2492 |
/// possible) is solvable with a graph search algorithm and it is |
| 2481 | 2493 |
/// implemented in \ref bipartitePartitions() function in LEMON. To |
| 2482 |
/// decide whether the planar graph is three colorable is |
|
| 2483 |
/// NP-complete. |
|
| 2494 |
/// decide whether a planar graph is three colorable is NP-complete. |
|
| 2484 | 2495 |
/// |
| 2485 | 2496 |
/// This class contains member functions for calculate colorings |
| 2486 | 2497 |
/// with five and six colors. The six coloring algorithm is a simple |
| 2487 | 2498 |
/// greedy coloring on the backward minimum outgoing order of nodes. |
| 2488 |
/// This order can be computed as in each phase the node with least |
|
| 2489 |
/// outgoing arcs to unprocessed nodes is chosen. This order |
|
| 2499 |
/// This order can be computed by selecting the node with least |
|
| 2500 |
/// outgoing arcs to unprocessed nodes in each phase. This order |
|
| 2490 | 2501 |
/// guarantees that when a node is chosen for coloring it has at |
| 2491 | 2502 |
/// most five already colored adjacents. The five coloring algorithm |
| 2492 | 2503 |
/// use the same method, but if the greedy approach fails to color |
| 2493 | 2504 |
/// with five colors, i.e. the node has five already different |
| 2494 | 2505 |
/// colored neighbours, it swaps the colors in one of the connected |
| 2495 | 2506 |
/// two colored sets with the Kempe recoloring method. |
| 2496 | 2507 |
template <typename Graph> |
| 2497 | 2508 |
class PlanarColoring {
|
| 2498 | 2509 |
public: |
| 2499 | 2510 |
|
| 2500 | 2511 |
TEMPLATE_GRAPH_TYPEDEFS(Graph); |
| 2501 | 2512 |
|
| 2502 |
/// \brief The map type for |
|
| 2513 |
/// \brief The map type for storing color indices |
|
| 2503 | 2514 |
typedef typename Graph::template NodeMap<int> IndexMap; |
| 2504 |
/// \brief The map type for |
|
| 2515 |
/// \brief The map type for storing colors |
|
| 2516 |
/// |
|
| 2517 |
/// The map type for storing colors. |
|
| 2518 |
/// \see Palette, Color |
|
| 2505 | 2519 |
typedef ComposeMap<Palette, IndexMap> ColorMap; |
| 2506 | 2520 |
|
| 2507 | 2521 |
/// \brief Constructor |
| 2508 | 2522 |
/// |
| 2509 |
/// Constructor |
|
| 2510 |
/// \pre The graph should be simple, i.e. loop and parallel arc free. |
|
| 2523 |
/// Constructor. |
|
| 2524 |
/// \pre The graph must be simple, i.e. it should not |
|
| 2525 |
/// contain parallel or loop arcs. |
|
| 2511 | 2526 |
PlanarColoring(const Graph& graph) |
| 2512 | 2527 |
: _graph(graph), _color_map(graph), _palette(0) {
|
| 2513 | 2528 |
_palette.add(Color(1,0,0)); |
| 2514 | 2529 |
_palette.add(Color(0,1,0)); |
| 2515 | 2530 |
_palette.add(Color(0,0,1)); |
| 2516 | 2531 |
_palette.add(Color(1,1,0)); |
| 2517 | 2532 |
_palette.add(Color(1,0,1)); |
| 2518 | 2533 |
_palette.add(Color(0,1,1)); |
| 2519 | 2534 |
} |
| 2520 | 2535 |
|
| 2521 |
/// \brief |
|
| 2536 |
/// \brief Return the node map of color indices |
|
| 2522 | 2537 |
/// |
| 2523 |
/// Returns the \e NodeMap of color indexes. The values are in the |
|
| 2524 |
/// range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2538 |
/// This function returns the node map of color indices. The values are |
|
| 2539 |
/// in the range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2525 | 2540 |
IndexMap colorIndexMap() const {
|
| 2526 | 2541 |
return _color_map; |
| 2527 | 2542 |
} |
| 2528 | 2543 |
|
| 2529 |
/// \brief |
|
| 2544 |
/// \brief Return the node map of colors |
|
| 2530 | 2545 |
/// |
| 2531 |
/// Returns the \e NodeMap of colors. The values are five or six |
|
| 2532 |
/// distinct \ref lemon::Color "colors". |
|
| 2546 |
/// This function returns the node map of colors. The values are among |
|
| 2547 |
/// five or six distinct \ref lemon::Color "colors". |
|
| 2533 | 2548 |
ColorMap colorMap() const {
|
| 2534 | 2549 |
return composeMap(_palette, _color_map); |
| 2535 | 2550 |
} |
| 2536 | 2551 |
|
| 2537 |
/// \brief |
|
| 2552 |
/// \brief Return the color index of the node |
|
| 2538 | 2553 |
/// |
| 2539 |
/// Returns the color index of the node. The values are in the |
|
| 2540 |
/// range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2554 |
/// This function returns the color index of the given node. The value is |
|
| 2555 |
/// in the range \c [0..4] or \c [0..5] according to the coloring method. |
|
| 2541 | 2556 |
int colorIndex(const Node& node) const {
|
| 2542 | 2557 |
return _color_map[node]; |
| 2543 | 2558 |
} |
| 2544 | 2559 |
|
| 2545 |
/// \brief |
|
| 2560 |
/// \brief Return the color of the node |
|
| 2546 | 2561 |
/// |
| 2547 |
/// Returns the color of the node. The values are five or six |
|
| 2548 |
/// distinct \ref lemon::Color "colors". |
|
| 2562 |
/// This function returns the color of the given node. The value is among |
|
| 2563 |
/// five or six distinct \ref lemon::Color "colors". |
|
| 2549 | 2564 |
Color color(const Node& node) const {
|
| 2550 | 2565 |
return _palette[_color_map[node]]; |
| 2551 | 2566 |
} |
| 2552 | 2567 |
|
| 2553 | 2568 |
|
| 2554 |
/// \brief |
|
| 2569 |
/// \brief Calculate a coloring with at most six colors |
|
| 2555 | 2570 |
/// |
| 2556 | 2571 |
/// This function calculates a coloring with at most six colors. The time |
| 2557 | 2572 |
/// complexity of this variant is linear in the size of the graph. |
| 2558 |
/// \return %True when the algorithm could color the graph with six color. |
|
| 2559 |
/// If the algorithm fails, then the graph could not be planar. |
|
| 2560 |
/// \note This function can return true if the graph is not |
|
| 2561 |
/// planar but it can be colored with 6 colors. |
|
| 2573 |
/// \return \c true if the algorithm could color the graph with six colors. |
|
| 2574 |
/// If the algorithm fails, then the graph is not planar. |
|
| 2575 |
/// \note This function can return \c true if the graph is not |
|
| 2576 |
/// planar, but it can be colored with at most six colors. |
|
| 2562 | 2577 |
bool runSixColoring() {
|
| 2563 | 2578 |
|
| 2564 | 2579 |
typename Graph::template NodeMap<int> heap_index(_graph, -1); |
| 2565 | 2580 |
BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
| 2566 | 2581 |
|
| 2567 | 2582 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 2568 | 2583 |
_color_map[n] = -2; |
| 2569 | 2584 |
heap.push(n, countOutArcs(_graph, n)); |
| 2570 | 2585 |
} |
| 2571 | 2586 |
|
| 2572 | 2587 |
std::vector<Node> order; |
| 2573 | 2588 |
|
| 2574 | 2589 |
while (!heap.empty()) {
|
| 2575 | 2590 |
Node n = heap.top(); |
| 2576 | 2591 |
heap.pop(); |
| 2577 | 2592 |
_color_map[n] = -1; |
| 2578 | 2593 |
order.push_back(n); |
| 2579 | 2594 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 2580 | 2595 |
Node t = _graph.runningNode(e); |
| 2581 | 2596 |
if (_color_map[t] == -2) {
|
| 2582 | 2597 |
heap.decrease(t, heap[t] - 1); |
| 2583 | 2598 |
} |
| 2584 | 2599 |
} |
| 2585 | 2600 |
} |
| 2586 | 2601 |
|
| 2587 | 2602 |
for (int i = order.size() - 1; i >= 0; --i) {
|
| 2588 | 2603 |
std::vector<bool> forbidden(6, false); |
| 2589 | 2604 |
for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
|
| 2590 | 2605 |
Node t = _graph.runningNode(e); |
| 2591 | 2606 |
if (_color_map[t] != -1) {
|
| 2592 | 2607 |
forbidden[_color_map[t]] = true; |
| 2593 | 2608 |
} |
| 2594 | 2609 |
} |
| 2595 | 2610 |
for (int k = 0; k < 6; ++k) {
|
| 2596 | 2611 |
if (!forbidden[k]) {
|
| 2597 | 2612 |
_color_map[order[i]] = k; |
| 2598 | 2613 |
break; |
| 2599 | 2614 |
} |
| 2600 | 2615 |
} |
| 2601 | 2616 |
if (_color_map[order[i]] == -1) {
|
| 2602 | 2617 |
return false; |
| 2603 | 2618 |
} |
| 2604 | 2619 |
} |
| 2605 | 2620 |
return true; |
| 2606 | 2621 |
} |
| 2607 | 2622 |
|
| 2608 | 2623 |
private: |
| 2609 | 2624 |
|
| 2610 | 2625 |
bool recolor(const Node& u, const Node& v) {
|
| 2611 | 2626 |
int ucolor = _color_map[u]; |
| 2612 | 2627 |
int vcolor = _color_map[v]; |
| 2613 | 2628 |
typedef _planarity_bits::KempeFilter<IndexMap> KempeFilter; |
| 2614 | 2629 |
KempeFilter filter(_color_map, ucolor, vcolor); |
| 2615 | 2630 |
|
| 2616 | 2631 |
typedef FilterNodes<const Graph, const KempeFilter> KempeGraph; |
| 2617 | 2632 |
KempeGraph kempe_graph(_graph, filter); |
| 2618 | 2633 |
|
| 2619 | 2634 |
std::vector<Node> comp; |
| 2620 | 2635 |
Bfs<KempeGraph> bfs(kempe_graph); |
| 2621 | 2636 |
bfs.init(); |
| 2622 | 2637 |
bfs.addSource(u); |
| 2623 | 2638 |
while (!bfs.emptyQueue()) {
|
| 2624 | 2639 |
Node n = bfs.nextNode(); |
| 2625 | 2640 |
if (n == v) return false; |
| 2626 | 2641 |
comp.push_back(n); |
| 2627 | 2642 |
bfs.processNextNode(); |
| 2628 | 2643 |
} |
| 2629 | 2644 |
|
| 2630 | 2645 |
int scolor = ucolor + vcolor; |
| 2631 | 2646 |
for (int i = 0; i < static_cast<int>(comp.size()); ++i) {
|
| 2632 | 2647 |
_color_map[comp[i]] = scolor - _color_map[comp[i]]; |
| 2633 | 2648 |
} |
| 2634 | 2649 |
|
| 2635 | 2650 |
return true; |
| 2636 | 2651 |
} |
| 2637 | 2652 |
|
| 2638 | 2653 |
template <typename EmbeddingMap> |
| 2639 | 2654 |
void kempeRecoloring(const Node& node, const EmbeddingMap& embedding) {
|
| 2640 | 2655 |
std::vector<Node> nodes; |
| 2641 | 2656 |
nodes.reserve(4); |
| 2642 | 2657 |
|
| 2643 | 2658 |
for (Arc e = OutArcIt(_graph, node); e != INVALID; e = embedding[e]) {
|
| 2644 | 2659 |
Node t = _graph.target(e); |
| 2645 | 2660 |
if (_color_map[t] != -1) {
|
| 2646 | 2661 |
nodes.push_back(t); |
| 2647 | 2662 |
if (nodes.size() == 4) break; |
| 2648 | 2663 |
} |
| 2649 | 2664 |
} |
| 2650 | 2665 |
|
| 2651 | 2666 |
int color = _color_map[nodes[0]]; |
| 2652 | 2667 |
if (recolor(nodes[0], nodes[2])) {
|
| 2653 | 2668 |
_color_map[node] = color; |
| 2654 | 2669 |
} else {
|
| 2655 | 2670 |
color = _color_map[nodes[1]]; |
| 2656 | 2671 |
recolor(nodes[1], nodes[3]); |
| 2657 | 2672 |
_color_map[node] = color; |
| 2658 | 2673 |
} |
| 2659 | 2674 |
} |
| 2660 | 2675 |
|
| 2661 | 2676 |
public: |
| 2662 | 2677 |
|
| 2663 |
/// \brief |
|
| 2678 |
/// \brief Calculate a coloring with at most five colors |
|
| 2664 | 2679 |
/// |
| 2665 | 2680 |
/// This function calculates a coloring with at most five |
| 2666 | 2681 |
/// colors. The worst case time complexity of this variant is |
| 2667 | 2682 |
/// quadratic in the size of the graph. |
| 2683 |
/// \param embedding This map should contain a valid combinatorical |
|
| 2684 |
/// embedding, i.e. a valid cyclic order of the arcs. |
|
| 2685 |
/// It can be computed using PlanarEmbedding. |
|
| 2668 | 2686 |
template <typename EmbeddingMap> |
| 2669 | 2687 |
void runFiveColoring(const EmbeddingMap& embedding) {
|
| 2670 | 2688 |
|
| 2671 | 2689 |
typename Graph::template NodeMap<int> heap_index(_graph, -1); |
| 2672 | 2690 |
BucketHeap<typename Graph::template NodeMap<int> > heap(heap_index); |
| 2673 | 2691 |
|
| 2674 | 2692 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
| 2675 | 2693 |
_color_map[n] = -2; |
| 2676 | 2694 |
heap.push(n, countOutArcs(_graph, n)); |
| 2677 | 2695 |
} |
| 2678 | 2696 |
|
| 2679 | 2697 |
std::vector<Node> order; |
| 2680 | 2698 |
|
| 2681 | 2699 |
while (!heap.empty()) {
|
| 2682 | 2700 |
Node n = heap.top(); |
| 2683 | 2701 |
heap.pop(); |
| 2684 | 2702 |
_color_map[n] = -1; |
| 2685 | 2703 |
order.push_back(n); |
| 2686 | 2704 |
for (OutArcIt e(_graph, n); e != INVALID; ++e) {
|
| 2687 | 2705 |
Node t = _graph.runningNode(e); |
| 2688 | 2706 |
if (_color_map[t] == -2) {
|
| 2689 | 2707 |
heap.decrease(t, heap[t] - 1); |
| 2690 | 2708 |
} |
| 2691 | 2709 |
} |
| 2692 | 2710 |
} |
| 2693 | 2711 |
|
| 2694 | 2712 |
for (int i = order.size() - 1; i >= 0; --i) {
|
| 2695 | 2713 |
std::vector<bool> forbidden(5, false); |
| 2696 | 2714 |
for (OutArcIt e(_graph, order[i]); e != INVALID; ++e) {
|
| 2697 | 2715 |
Node t = _graph.runningNode(e); |
| 2698 | 2716 |
if (_color_map[t] != -1) {
|
| 2699 | 2717 |
forbidden[_color_map[t]] = true; |
| 2700 | 2718 |
} |
| 2701 | 2719 |
} |
| 2702 | 2720 |
for (int k = 0; k < 5; ++k) {
|
| 2703 | 2721 |
if (!forbidden[k]) {
|
| 2704 | 2722 |
_color_map[order[i]] = k; |
| 2705 | 2723 |
break; |
| 2706 | 2724 |
} |
| 2707 | 2725 |
} |
| 2708 | 2726 |
if (_color_map[order[i]] == -1) {
|
| 2709 | 2727 |
kempeRecoloring(order[i], embedding); |
| 2710 | 2728 |
} |
| 2711 | 2729 |
} |
| 2712 | 2730 |
} |
| 2713 | 2731 |
|
| 2714 |
/// \brief |
|
| 2732 |
/// \brief Calculate a coloring with at most five colors |
|
| 2715 | 2733 |
/// |
| 2716 | 2734 |
/// This function calculates a coloring with at most five |
| 2717 | 2735 |
/// colors. The worst case time complexity of this variant is |
| 2718 | 2736 |
/// quadratic in the size of the graph. |
| 2719 |
/// \return |
|
| 2737 |
/// \return \c true if the graph is planar. |
|
| 2720 | 2738 |
bool runFiveColoring() {
|
| 2721 | 2739 |
PlanarEmbedding<Graph> pe(_graph); |
| 2722 | 2740 |
if (!pe.run()) return false; |
| 2723 | 2741 |
|
| 2724 | 2742 |
runFiveColoring(pe.embeddingMap()); |
| 2725 | 2743 |
return true; |
| 2726 | 2744 |
} |
| 2727 | 2745 |
|
| 2728 | 2746 |
private: |
| 2729 | 2747 |
|
| 2730 | 2748 |
const Graph& _graph; |
| 2731 | 2749 |
IndexMap _color_map; |
| 2732 | 2750 |
Palette _palette; |
| 2733 | 2751 |
}; |
| 2734 | 2752 |
|
| 2735 | 2753 |
} |
| 2736 | 2754 |
|
| 2737 | 2755 |
#endif |
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