Update the server and the repository names to lemon.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
21 ///\brief Special plane graph generator.
23 ///Graph generator application for various types of plane graphs.
27 /// ./tools/lgf-gen [-2con|-tree|-tsp|-tsp2|-dela] [-disc|-square|-gauss]
28 /// [-rand|-seed int] [--help|-h|-help] [-area num] [-cities int] [-dir]
29 /// [-eps] [-g int] [-n int] [prefix]
32 /// Prefix of the output files. Default is 'lgf-gen-out'
34 /// Print a short help message
36 /// Create a two connected planar graph
38 /// Full relative area of the cities (default is 1)
40 /// Number of cities (default is 1)
42 /// Delaunay triangulation graph
44 /// Directed graph is generated (each edges are replaced by two directed ones)
46 /// Nodes are evenly distributed on a unit disc (default)
48 /// Also generate .eps output (prefix.eps)
50 /// Girth parameter (default is 10)
52 /// Nodes are located according to a two-dim gauss distribution
54 /// Number of nodes (default is 100)
56 /// Use time seed for random number generator
60 /// Nodes are evenly distributed on a unit square
62 /// Create a min. cost spanning tree
66 /// Create a TSP tour (tree based)
68 /// \image html plane_tree.png
69 /// \image latex plane_tree.eps "Eucledian spanning tree" width=\textwidth
73 #include <lemon/list_graph.h>
74 #include <lemon/graph_utils.h>
75 #include <lemon/random.h>
76 #include <lemon/dim2.h>
77 #include <lemon/bfs.h>
78 #include <lemon/counter.h>
79 #include <lemon/suurballe.h>
80 #include <lemon/graph_to_eps.h>
81 #include <lemon/graph_writer.h>
82 #include <lemon/arg_parser.h>
83 #include <lemon/euler.h>
86 #include <lemon/kruskal.h>
87 #include <lemon/time_measure.h>
89 using namespace lemon;
91 typedef dim2::Point<double> Point;
93 UGRAPH_TYPEDEFS(ListUGraph);
102 std::vector<Node> nodes;
103 ListUGraph::NodeMap<Point> coords(g);
108 for(UEdgeIt e(g);e!=INVALID;++e)
109 tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare());
115 const double EPSILON=1e-8;
116 bool tsp_improve(Node u, Node v)
118 double luv=std::sqrt((coords[v]-coords[u]).normSquare());
123 for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e);
126 if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON>
127 std::sqrt((coords[u]-coords[u2]).normSquare())+
128 std::sqrt((coords[v]-coords[v2]).normSquare()))
130 g.erase(findUEdge(g,u,v));
131 g.erase(findUEdge(g,u2,v2));
141 bool tsp_improve(Node u)
143 for(IncEdgeIt e(g,u);e!=INVALID;++e)
144 if(tsp_improve(u,g.runningNode(e))) return true;
153 for(NodeIt n(g);n!=INVALID;++n)
154 if(tsp_improve(n)) b=true;
160 for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]);
169 Line(Point _a,Point _b) :a(_a),b(_b) {}
170 Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {}
171 Line(const Edge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {}
172 Line(const UEdge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {}
175 inline std::ostream& operator<<(std::ostream &os, const Line &l)
177 os << l.a << "->" << l.b;
181 bool cross(Line a, Line b)
183 Point ao=rot90(a.b-a.a);
184 Point bo=rot90(b.b-b.a);
185 return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 &&
186 (bo*(a.a-b.a))*(bo*(a.b-b.a))<0;
196 bool pedgeLess(Pedge a,Pedge b)
201 std::vector<UEdge> edges;
203 namespace _delaunay_bits {
206 int prev, curr, next;
208 Part(int p, int c, int n) : prev(p), curr(c), next(n) {}
211 inline std::ostream& operator<<(std::ostream& os, const Part& part) {
212 os << '(' << part.prev << ',' << part.curr << ',' << part.next << ')';
216 inline double circle_point(const Point& p, const Point& q, const Point& r) {
217 double a = p.x * (q.y - r.y) + q.x * (r.y - p.y) + r.x * (p.y - q.y);
218 if (a == 0) return std::numeric_limits<double>::quiet_NaN();
220 double d = (p.x * p.x + p.y * p.y) * (q.y - r.y) +
221 (q.x * q.x + q.y * q.y) * (r.y - p.y) +
222 (r.x * r.x + r.y * r.y) * (p.y - q.y);
224 double e = (p.x * p.x + p.y * p.y) * (q.x - r.x) +
225 (q.x * q.x + q.y * q.y) * (r.x - p.x) +
226 (r.x * r.x + r.y * r.y) * (p.x - q.x);
228 double f = (p.x * p.x + p.y * p.y) * (q.x * r.y - r.x * q.y) +
229 (q.x * q.x + q.y * q.y) * (r.x * p.y - p.x * r.y) +
230 (r.x * r.x + r.y * r.y) * (p.x * q.y - q.x * p.y);
232 return d / (2 * a) + sqrt((d * d + e * e) / (4 * a * a) + f / a);
235 inline bool circle_form(const Point& p, const Point& q, const Point& r) {
236 return rot90(q - p) * (r - q) < 0.0;
239 inline double intersection(const Point& p, const Point& q, double sx) {
240 const double epsilon = 1e-8;
242 if (p.x == q.x) return (p.y + q.y) / 2.0;
244 if (sx < p.x + epsilon) return p.y;
245 if (sx < q.x + epsilon) return q.y;
247 double a = q.x - p.x;
248 double b = (q.x - sx) * p.y - (p.x - sx) * q.y;
249 double d = (q.x - sx) * (p.x - sx) * (p - q).normSquare();
250 return (b - sqrt(d)) / a;
256 YLess(const std::vector<Point>& points, double& sweep)
257 : _points(points), _sweep(sweep) {}
259 bool operator()(const Part& l, const Part& r) const {
260 const double epsilon = 1e-8;
262 // std::cerr << l << " vs " << r << std::endl;
263 double lbx = l.prev != -1 ?
264 intersection(_points[l.prev], _points[l.curr], _sweep) :
265 - std::numeric_limits<double>::infinity();
266 double rbx = r.prev != -1 ?
267 intersection(_points[r.prev], _points[r.curr], _sweep) :
268 - std::numeric_limits<double>::infinity();
269 double lex = l.next != -1 ?
270 intersection(_points[l.curr], _points[l.next], _sweep) :
271 std::numeric_limits<double>::infinity();
272 double rex = r.next != -1 ?
273 intersection(_points[r.curr], _points[r.next], _sweep) :
274 std::numeric_limits<double>::infinity();
276 if (lbx > lex) std::swap(lbx, lex);
277 if (rbx > rex) std::swap(rbx, rex);
279 if (lex < epsilon + rex && lbx + epsilon < rex) return true;
280 if (rex < epsilon + lex && rbx + epsilon < lex) return false;
284 const std::vector<Point>& _points;
290 typedef std::multimap<double, BeachIt> SpikeHeap;
292 typedef std::multimap<Part, SpikeHeap::iterator, YLess> Beach;
297 BeachIt(Beach::iterator iter) : it(iter) {}
302 inline void delaunay() {
303 Counter cnt("Number of edges added: ");
305 using namespace _delaunay_bits;
307 typedef _delaunay_bits::Part Part;
308 typedef std::vector<std::pair<double, int> > SiteHeap;
311 std::vector<Point> points;
312 std::vector<Node> nodes;
314 for (NodeIt it(g); it != INVALID; ++it) {
316 points.push_back(coords[it]);
319 SiteHeap siteheap(points.size());
324 for (int i = 0; i < int(siteheap.size()); ++i) {
325 siteheap[i] = std::make_pair(points[i].x, i);
328 std::sort(siteheap.begin(), siteheap.end());
329 sweep = siteheap.front().first;
331 YLess yless(points, sweep);
336 std::set<std::pair<int, int> > edges;
342 while (siteindex < int(siteheap.size()) &&
343 siteheap[0].first == siteheap[siteindex].first) {
344 front.push_back(std::make_pair(points[siteheap[siteindex].second].y,
345 siteheap[siteindex].second));
349 std::sort(front.begin(), front.end());
351 for (int i = 0; i < int(front.size()); ++i) {
352 int prev = (i == 0 ? -1 : front[i - 1].second);
353 int curr = front[i].second;
354 int next = (i + 1 == int(front.size()) ? -1 : front[i + 1].second);
356 beach.insert(std::make_pair(Part(prev, curr, next),
361 while (siteindex < int(points.size()) || !spikeheap.empty()) {
363 SpikeHeap::iterator spit = spikeheap.begin();
365 if (siteindex < int(points.size()) &&
366 (spit == spikeheap.end() || siteheap[siteindex].first < spit->first)) {
367 int site = siteheap[siteindex].second;
368 sweep = siteheap[siteindex].first;
370 Beach::iterator bit = beach.upper_bound(Part(site, site, site));
372 if (bit->second != spikeheap.end()) {
373 spikeheap.erase(bit->second);
376 int prev = bit->first.prev;
377 int curr = bit->first.curr;
378 int next = bit->first.next;
382 SpikeHeap::iterator pit = spikeheap.end();
384 circle_form(points[prev], points[curr], points[site])) {
385 double x = circle_point(points[prev], points[curr], points[site]);
386 pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
388 beach.insert(std::make_pair(Part(prev, curr, site), pit));
390 beach.insert(std::make_pair(Part(prev, curr, site), pit));
393 beach.insert(std::make_pair(Part(curr, site, curr), spikeheap.end()));
395 SpikeHeap::iterator nit = spikeheap.end();
397 circle_form(points[site], points[curr],points[next])) {
398 double x = circle_point(points[site], points[curr], points[next]);
399 nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
401 beach.insert(std::make_pair(Part(site, curr, next), nit));
403 beach.insert(std::make_pair(Part(site, curr, next), nit));
410 Beach::iterator bit = spit->second.it;
412 int prev = bit->first.prev;
413 int curr = bit->first.curr;
414 int next = bit->first.next;
417 std::pair<int, int> edge;
420 std::make_pair(prev, curr) : std::make_pair(curr, prev);
422 if (edges.find(edge) == edges.end()) {
424 g.addEdge(nodes[prev], nodes[curr]);
429 std::make_pair(curr, next) : std::make_pair(next, curr);
431 if (edges.find(edge) == edges.end()) {
433 g.addEdge(nodes[curr], nodes[next]);
438 Beach::iterator pbit = bit; --pbit;
439 int ppv = pbit->first.prev;
440 Beach::iterator nbit = bit; ++nbit;
441 int nnt = nbit->first.next;
443 if (bit->second != spikeheap.end()) spikeheap.erase(bit->second);
444 if (pbit->second != spikeheap.end()) spikeheap.erase(pbit->second);
445 if (nbit->second != spikeheap.end()) spikeheap.erase(nbit->second);
451 SpikeHeap::iterator pit = spikeheap.end();
452 if (ppv != -1 && ppv != next &&
453 circle_form(points[ppv], points[prev], points[next])) {
454 double x = circle_point(points[ppv], points[prev], points[next]);
455 if (x < sweep) x = sweep;
456 pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
458 beach.insert(std::make_pair(Part(ppv, prev, next), pit));
460 beach.insert(std::make_pair(Part(ppv, prev, next), pit));
463 SpikeHeap::iterator nit = spikeheap.end();
464 if (nnt != -1 && prev != nnt &&
465 circle_form(points[prev], points[next], points[nnt])) {
466 double x = circle_point(points[prev], points[next], points[nnt]);
467 if (x < sweep) x = sweep;
468 nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
470 beach.insert(std::make_pair(Part(prev, next, nnt), nit));
472 beach.insert(std::make_pair(Part(prev, next, nnt), nit));
478 for (Beach::iterator it = beach.begin(); it != beach.end(); ++it) {
479 int curr = it->first.curr;
480 int next = it->first.next;
482 if (next == -1) continue;
484 std::pair<int, int> edge;
487 std::make_pair(curr, next) : std::make_pair(next, curr);
489 if (edges.find(edge) == edges.end()) {
491 g.addEdge(nodes[curr], nodes[next]);
499 Counter cnt("Number of edges removed: ");
500 Bfs<ListUGraph> bfs(g);
501 for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin();
502 ei!=edges.rend();++ei)
504 Node a=g.source(*ei);
505 Node b=g.target(*ei);
508 if(bfs.predEdge(b)==INVALID || bfs.dist(b)>d)
516 Counter cnt("Number of edges removed: ");
517 for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin();
518 ei!=edges.rend();++ei)
520 Node a=g.source(*ei);
521 Node b=g.target(*ei);
523 ConstMap<Edge,int> cegy(1);
524 Suurballe<ListUGraph,ConstMap<Edge,int> > sur(g,cegy,a,b);
526 if(k<2 || sur.totalLength()>d)
529 // else std::cout << "Remove edge " << g.id(a) << "-" << g.id(b) << '\n';
533 void sparseTriangle(int d)
535 Counter cnt("Number of edges added: ");
536 std::vector<Pedge> pedges;
537 for(NodeIt n(g);n!=INVALID;++n)
538 for(NodeIt m=++(NodeIt(n));m!=INVALID;++m)
543 p.len=(coords[m]-coords[n]).normSquare();
546 std::sort(pedges.begin(),pedges.end(),pedgeLess);
547 for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi)
549 Line li(pi->a,pi->b);
551 for(;e!=INVALID && !cross(e,li);++e) ;
554 ConstMap<Edge,int> cegy(1);
555 Suurballe<ListUGraph,ConstMap<Edge,int> >
556 sur(g,cegy,pi->a,pi->b);
558 if(k<2 || sur.totalLength()>d)
560 ne=g.addEdge(pi->a,pi->b);
568 template <typename UGraph, typename CoordMap>
569 class LengthSquareMap {
571 typedef typename UGraph::UEdge Key;
572 typedef typename CoordMap::Value::Value Value;
574 LengthSquareMap(const UGraph& ugraph, const CoordMap& coords)
575 : _ugraph(ugraph), _coords(coords) {}
577 Value operator[](const Key& key) const {
578 return (_coords[_ugraph.target(key)] -
579 _coords[_ugraph.source(key)]).normSquare();
584 const UGraph& _ugraph;
585 const CoordMap& _coords;
589 std::vector<Pedge> pedges;
591 std::cout << T.realTime() << "s: Creating delaunay triangulation...\n";
593 std::cout << T.realTime() << "s: Calculating spanning tree...\n";
594 LengthSquareMap<ListUGraph, ListUGraph::NodeMap<Point> > ls(g, coords);
595 ListUGraph::UEdgeMap<bool> tree(g);
596 kruskal(g, ls, tree);
597 std::cout << T.realTime() << "s: Removing non tree edges...\n";
598 std::vector<UEdge> remove;
599 for (UEdgeIt e(g); e != INVALID; ++e) {
600 if (!tree[e]) remove.push_back(e);
602 for(int i = 0; i < int(remove.size()); ++i) {
605 std::cout << T.realTime() << "s: Done\n";
610 std::cout << "Find a tree..." << std::endl;
614 std::cout << "Total edge length (tree) : " << totalLen() << std::endl;
616 std::cout << "Make it Euler..." << std::endl;
619 std::vector<Node> leafs;
620 for(NodeIt n(g);n!=INVALID;++n)
621 if(countIncEdges(g,n)%2==1) leafs.push_back(n);
623 // for(unsigned int i=0;i<leafs.size();i+=2)
624 // g.addEdge(leafs[i],leafs[i+1]);
626 std::vector<Pedge> pedges;
627 for(unsigned int i=0;i<leafs.size()-1;i++)
628 for(unsigned int j=i+1;j<leafs.size();j++)
635 p.len=(coords[m]-coords[n]).normSquare();
638 std::sort(pedges.begin(),pedges.end(),pedgeLess);
639 for(unsigned int i=0;i<pedges.size();i++)
640 if(countIncEdges(g,pedges[i].a)%2 &&
641 countIncEdges(g,pedges[i].b)%2)
642 g.addEdge(pedges[i].a,pedges[i].b);
645 for(NodeIt n(g);n!=INVALID;++n)
646 if(countIncEdges(g,n)%2 || countIncEdges(g,n)==0 )
647 std::cout << "GEBASZ!!!" << std::endl;
649 for(UEdgeIt e(g);e!=INVALID;++e)
650 if(g.source(e)==g.target(e))
651 std::cout << "LOOP GEBASZ!!!" << std::endl;
653 std::cout << "Number of edges : " << countUEdges(g) << std::endl;
655 std::cout << "Total edge length (euler) : " << totalLen() << std::endl;
657 ListUGraph::UEdgeMap<Edge> enext(g);
659 UEulerIt<ListUGraph> e(g);
662 // std::cout << "Tour edge: " << g.id(UEdge(e)) << std::endl;
663 for(++e;e!=INVALID;++e)
665 // std::cout << "Tour edge: " << g.id(UEdge(e)) << std::endl;
672 std::cout << "Creating a tour from that..." << std::endl;
674 int nnum = countNodes(g);
675 int ednum = countUEdges(g);
677 for(Edge p=enext[UEdgeIt(g)];ednum>nnum;p=enext[p])
679 // std::cout << "Checking edge " << g.id(p) << std::endl;
683 Node n1=g.oppositeNode(n2,e);
684 Node n3=g.oppositeNode(n2,f);
685 if(countIncEdges(g,n2)>2)
687 // std::cout << "Remove an Edge" << std::endl;
693 Edge ne=g.direct(g.addEdge(n1,n3),n1);
705 std::cout << "Total edge length (tour) : " << totalLen() << std::endl;
707 std::cout << "2-opt the tour..." << std::endl;
711 std::cout << "Total edge length (2-opt tour) : " << totalLen() << std::endl;
715 int main(int argc,const char **argv)
717 ArgParser ap(argc,argv);
720 bool disc_d, square_d, gauss_d;
721 // bool tsp_a,two_a,tree_a;
726 std::string ndist("disc");
727 ap.refOption("n", "Number of nodes (default is 100)", N)
728 .intOption("g", "Girth parameter (default is 10)", 10)
729 .refOption("cities", "Number of cities (default is 1)", num_of_cities)
730 .refOption("area", "Full relative area of the cities (default is 1)", area)
731 .refOption("disc", "Nodes are evenly distributed on a unit disc (default)",disc_d)
732 .optionGroup("dist", "disc")
733 .refOption("square", "Nodes are evenly distributed on a unit square", square_d)
734 .optionGroup("dist", "square")
736 "Nodes are located according to a two-dim gauss distribution",
738 .optionGroup("dist", "gauss")
739 // .mandatoryGroup("dist")
740 .onlyOneGroup("dist")
741 .boolOption("eps", "Also generate .eps output (prefix.eps)")
742 .boolOption("dir", "Directed graph is generated (each edges are replaced by two directed ones)")
743 .boolOption("2con", "Create a two connected planar graph")
744 .optionGroup("alg","2con")
745 .boolOption("tree", "Create a min. cost spanning tree")
746 .optionGroup("alg","tree")
747 .boolOption("tsp", "Create a TSP tour")
748 .optionGroup("alg","tsp")
749 .boolOption("tsp2", "Create a TSP tour (tree based)")
750 .optionGroup("alg","tsp2")
751 .boolOption("dela", "Delaunay triangulation graph")
752 .optionGroup("alg","dela")
754 .boolOption("rand", "Use time seed for random number generator")
755 .optionGroup("rand", "rand")
756 .intOption("seed", "Random seed", -1)
757 .optionGroup("rand", "seed")
758 .onlyOneGroup("rand")
759 .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'")
764 std::cout << "Random number seed: " << seed << std::endl;
767 if (ap.given("seed")) {
768 int seed = ap["seed"];
769 std::cout << "Random number seed: " << seed << std::endl;
774 switch(ap.files().size())
777 prefix="lgf-gen-out";
780 prefix=ap.files()[0];
783 std::cerr << "\nAt most one prefix can be given\n\n";
788 std::vector<double> sizes;
789 std::vector<double> cum_sizes;
790 for(int s=0;s<num_of_cities;s++)
792 // sum_sizes+=rnd.exponential();
796 cum_sizes.push_back(sum_sizes);
799 for(int s=0;s<num_of_cities;s++)
801 Point center=(num_of_cities==1?Point(0,0):rnd.disc());
803 for(;i<N*(cum_sizes[s]/sum_sizes);i++) {
806 coords[n]=center+rnd.gauss2()*area*
807 std::sqrt(sizes[s]/sum_sizes);
810 for(;i<N*(cum_sizes[s]/sum_sizes);i++) {
813 coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area*
814 std::sqrt(sizes[s]/sum_sizes);
816 else if(disc_d || true)
817 for(;i<N*(cum_sizes[s]/sum_sizes);i++) {
820 coords[n]=center+rnd.disc()*area*
821 std::sqrt(sizes[s]/sum_sizes);
825 // for (ListUGraph::NodeIt n(g); n != INVALID; ++n) {
826 // std::cerr << coords[n] << std::endl;
831 std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl;
835 std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl;
837 else if(ap["2con"]) {
838 std::cout << "Make triangles\n";
840 sparseTriangle(ap["g"]);
841 std::cout << "Make it sparser\n";
844 else if(ap["tree"]) {
847 else if(ap["dela"]) {
852 std::cout << "Number of nodes : " << countNodes(g) << std::endl;
853 std::cout << "Number of edges : " << countUEdges(g) << std::endl;
855 for(UEdgeIt e(g);e!=INVALID;++e)
856 tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare());
857 std::cout << "Total edge length : " << tlen << std::endl;
860 graphToEps(g,prefix+".eps").scaleToA4().
861 scale(600).nodeScale(.2).edgeWidthScale(.001).preScale(false).
862 coords(coords).run();
865 GraphWriter<ListUGraph>(prefix+".lgf",g).
866 writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)).
867 writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)).
869 else UGraphWriter<ListUGraph>(prefix+".lgf",g).
870 writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)).
871 writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)).