1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
3 * This file is a part of LEMON, a generic C++ optimization library.
5 * Copyright (C) 2003-2009
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 digraph generator.
23 /// Graph generator application for various types of plane graphs.
29 /// for more info on the usage.
35 #include <lemon/list_graph.h>
36 #include <lemon/random.h>
37 #include <lemon/dim2.h>
38 #include <lemon/bfs.h>
39 #include <lemon/counter.h>
40 #include <lemon/suurballe.h>
41 #include <lemon/graph_to_eps.h>
42 #include <lemon/lgf_writer.h>
43 #include <lemon/arg_parser.h>
44 #include <lemon/euler.h>
45 #include <lemon/math.h>
46 #include <lemon/kruskal.h>
47 #include <lemon/time_measure.h>
49 using namespace lemon;
51 typedef dim2::Point<double> Point;
53 GRAPH_TYPEDEFS(ListGraph);
62 std::vector<Node> nodes;
63 ListGraph::NodeMap<Point> coords(g);
68 for(EdgeIt e(g);e!=INVALID;++e)
69 tlen+=sqrt((coords[g.v(e)]-coords[g.u(e)]).normSquare());
75 const double EPSILON=1e-8;
76 bool tsp_improve(Node u, Node v)
78 double luv=std::sqrt((coords[v]-coords[u]).normSquare());
83 for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e) { }
86 if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON>
87 std::sqrt((coords[u]-coords[u2]).normSquare())+
88 std::sqrt((coords[v]-coords[v2]).normSquare()))
90 g.erase(findEdge(g,u,v));
91 g.erase(findEdge(g,u2,v2));
101 bool tsp_improve(Node u)
103 for(IncEdgeIt e(g,u);e!=INVALID;++e)
104 if(tsp_improve(u,g.runningNode(e))) return true;
113 for(NodeIt n(g);n!=INVALID;++n)
114 if(tsp_improve(n)) b=true;
120 for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]);
129 Line(Point _a,Point _b) :a(_a),b(_b) {}
130 Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {}
131 Line(const Arc &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {}
132 Line(const Edge &e) : a(coords[g.u(e)]),b(coords[g.v(e)]) {}
135 inline std::ostream& operator<<(std::ostream &os, const Line &l)
137 os << l.a << "->" << l.b;
141 bool cross(Line a, Line b)
143 Point ao=rot90(a.b-a.a);
144 Point bo=rot90(b.b-b.a);
145 return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 &&
146 (bo*(a.a-b.a))*(bo*(a.b-b.a))<0;
156 bool pedgeLess(Parc a,Parc b)
161 std::vector<Edge> arcs;
163 namespace _delaunay_bits {
166 int prev, curr, next;
168 Part(int p, int c, int n) : prev(p), curr(c), next(n) {}
171 inline std::ostream& operator<<(std::ostream& os, const Part& part) {
172 os << '(' << part.prev << ',' << part.curr << ',' << part.next << ')';
176 inline double circle_point(const Point& p, const Point& q, const Point& r) {
177 double a = p.x * (q.y - r.y) + q.x * (r.y - p.y) + r.x * (p.y - q.y);
178 if (a == 0) return std::numeric_limits<double>::quiet_NaN();
180 double d = (p.x * p.x + p.y * p.y) * (q.y - r.y) +
181 (q.x * q.x + q.y * q.y) * (r.y - p.y) +
182 (r.x * r.x + r.y * r.y) * (p.y - q.y);
184 double e = (p.x * p.x + p.y * p.y) * (q.x - r.x) +
185 (q.x * q.x + q.y * q.y) * (r.x - p.x) +
186 (r.x * r.x + r.y * r.y) * (p.x - q.x);
188 double f = (p.x * p.x + p.y * p.y) * (q.x * r.y - r.x * q.y) +
189 (q.x * q.x + q.y * q.y) * (r.x * p.y - p.x * r.y) +
190 (r.x * r.x + r.y * r.y) * (p.x * q.y - q.x * p.y);
192 return d / (2 * a) + sqrt((d * d + e * e) / (4 * a * a) + f / a);
195 inline bool circle_form(const Point& p, const Point& q, const Point& r) {
196 return rot90(q - p) * (r - q) < 0.0;
199 inline double intersection(const Point& p, const Point& q, double sx) {
200 const double epsilon = 1e-8;
202 if (p.x == q.x) return (p.y + q.y) / 2.0;
204 if (sx < p.x + epsilon) return p.y;
205 if (sx < q.x + epsilon) return q.y;
207 double a = q.x - p.x;
208 double b = (q.x - sx) * p.y - (p.x - sx) * q.y;
209 double d = (q.x - sx) * (p.x - sx) * (p - q).normSquare();
210 return (b - sqrt(d)) / a;
216 YLess(const std::vector<Point>& points, double& sweep)
217 : _points(points), _sweep(sweep) {}
219 bool operator()(const Part& l, const Part& r) const {
220 const double epsilon = 1e-8;
222 // std::cerr << l << " vs " << r << std::endl;
223 double lbx = l.prev != -1 ?
224 intersection(_points[l.prev], _points[l.curr], _sweep) :
225 - std::numeric_limits<double>::infinity();
226 double rbx = r.prev != -1 ?
227 intersection(_points[r.prev], _points[r.curr], _sweep) :
228 - std::numeric_limits<double>::infinity();
229 double lex = l.next != -1 ?
230 intersection(_points[l.curr], _points[l.next], _sweep) :
231 std::numeric_limits<double>::infinity();
232 double rex = r.next != -1 ?
233 intersection(_points[r.curr], _points[r.next], _sweep) :
234 std::numeric_limits<double>::infinity();
236 if (lbx > lex) std::swap(lbx, lex);
237 if (rbx > rex) std::swap(rbx, rex);
239 if (lex < epsilon + rex && lbx + epsilon < rex) return true;
240 if (rex < epsilon + lex && rbx + epsilon < lex) return false;
244 const std::vector<Point>& _points;
250 typedef std::multimap<double, BeachIt> SpikeHeap;
252 typedef std::multimap<Part, SpikeHeap::iterator, YLess> Beach;
257 BeachIt(Beach::iterator iter) : it(iter) {}
262 inline void delaunay() {
263 Counter cnt("Number of arcs added: ");
265 using namespace _delaunay_bits;
267 typedef _delaunay_bits::Part Part;
268 typedef std::vector<std::pair<double, int> > SiteHeap;
271 std::vector<Point> points;
272 std::vector<Node> nodes;
274 for (NodeIt it(g); it != INVALID; ++it) {
276 points.push_back(coords[it]);
279 SiteHeap siteheap(points.size());
284 for (int i = 0; i < int(siteheap.size()); ++i) {
285 siteheap[i] = std::make_pair(points[i].x, i);
288 std::sort(siteheap.begin(), siteheap.end());
289 sweep = siteheap.front().first;
291 YLess yless(points, sweep);
296 std::set<std::pair<int, int> > arcs;
302 while (siteindex < int(siteheap.size()) &&
303 siteheap[0].first == siteheap[siteindex].first) {
304 front.push_back(std::make_pair(points[siteheap[siteindex].second].y,
305 siteheap[siteindex].second));
309 std::sort(front.begin(), front.end());
311 for (int i = 0; i < int(front.size()); ++i) {
312 int prev = (i == 0 ? -1 : front[i - 1].second);
313 int curr = front[i].second;
314 int next = (i + 1 == int(front.size()) ? -1 : front[i + 1].second);
316 beach.insert(std::make_pair(Part(prev, curr, next),
321 while (siteindex < int(points.size()) || !spikeheap.empty()) {
323 SpikeHeap::iterator spit = spikeheap.begin();
325 if (siteindex < int(points.size()) &&
326 (spit == spikeheap.end() || siteheap[siteindex].first < spit->first)) {
327 int site = siteheap[siteindex].second;
328 sweep = siteheap[siteindex].first;
330 Beach::iterator bit = beach.upper_bound(Part(site, site, site));
332 if (bit->second != spikeheap.end()) {
333 spikeheap.erase(bit->second);
336 int prev = bit->first.prev;
337 int curr = bit->first.curr;
338 int next = bit->first.next;
342 SpikeHeap::iterator pit = spikeheap.end();
344 circle_form(points[prev], points[curr], points[site])) {
345 double x = circle_point(points[prev], points[curr], points[site]);
346 pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
348 beach.insert(std::make_pair(Part(prev, curr, site), pit));
350 beach.insert(std::make_pair(Part(prev, curr, site), pit));
353 beach.insert(std::make_pair(Part(curr, site, curr), spikeheap.end()));
355 SpikeHeap::iterator nit = spikeheap.end();
357 circle_form(points[site], points[curr],points[next])) {
358 double x = circle_point(points[site], points[curr], points[next]);
359 nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
361 beach.insert(std::make_pair(Part(site, curr, next), nit));
363 beach.insert(std::make_pair(Part(site, curr, next), nit));
370 Beach::iterator bit = spit->second.it;
372 int prev = bit->first.prev;
373 int curr = bit->first.curr;
374 int next = bit->first.next;
377 std::pair<int, int> arc;
380 std::make_pair(prev, curr) : std::make_pair(curr, prev);
382 if (arcs.find(arc) == arcs.end()) {
384 g.addEdge(nodes[prev], nodes[curr]);
389 std::make_pair(curr, next) : std::make_pair(next, curr);
391 if (arcs.find(arc) == arcs.end()) {
393 g.addEdge(nodes[curr], nodes[next]);
398 Beach::iterator pbit = bit; --pbit;
399 int ppv = pbit->first.prev;
400 Beach::iterator nbit = bit; ++nbit;
401 int nnt = nbit->first.next;
403 if (bit->second != spikeheap.end()) spikeheap.erase(bit->second);
404 if (pbit->second != spikeheap.end()) spikeheap.erase(pbit->second);
405 if (nbit->second != spikeheap.end()) spikeheap.erase(nbit->second);
411 SpikeHeap::iterator pit = spikeheap.end();
412 if (ppv != -1 && ppv != next &&
413 circle_form(points[ppv], points[prev], points[next])) {
414 double x = circle_point(points[ppv], points[prev], points[next]);
415 if (x < sweep) x = sweep;
416 pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
418 beach.insert(std::make_pair(Part(ppv, prev, next), pit));
420 beach.insert(std::make_pair(Part(ppv, prev, next), pit));
423 SpikeHeap::iterator nit = spikeheap.end();
424 if (nnt != -1 && prev != nnt &&
425 circle_form(points[prev], points[next], points[nnt])) {
426 double x = circle_point(points[prev], points[next], points[nnt]);
427 if (x < sweep) x = sweep;
428 nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end())));
430 beach.insert(std::make_pair(Part(prev, next, nnt), nit));
432 beach.insert(std::make_pair(Part(prev, next, nnt), nit));
438 for (Beach::iterator it = beach.begin(); it != beach.end(); ++it) {
439 int curr = it->first.curr;
440 int next = it->first.next;
442 if (next == -1) continue;
444 std::pair<int, int> arc;
447 std::make_pair(curr, next) : std::make_pair(next, curr);
449 if (arcs.find(arc) == arcs.end()) {
451 g.addEdge(nodes[curr], nodes[next]);
459 Counter cnt("Number of arcs removed: ");
460 Bfs<ListGraph> bfs(g);
461 for(std::vector<Edge>::reverse_iterator ei=arcs.rbegin();
462 ei!=arcs.rend();++ei)
468 if(bfs.predArc(b)==INVALID || bfs.dist(b)>d)
476 Counter cnt("Number of arcs removed: ");
477 for(std::vector<Edge>::reverse_iterator ei=arcs.rbegin();
478 ei!=arcs.rend();++ei)
483 ConstMap<Arc,int> cegy(1);
484 Suurballe<ListGraph,ConstMap<Arc,int> > sur(g,cegy,a,b);
486 if(k<2 || sur.totalLength()>d)
489 // else std::cout << "Remove arc " << g.id(a) << "-" << g.id(b) << '\n';
493 void sparseTriangle(int d)
495 Counter cnt("Number of arcs added: ");
496 std::vector<Parc> pedges;
497 for(NodeIt n(g);n!=INVALID;++n)
498 for(NodeIt m=++(NodeIt(n));m!=INVALID;++m)
503 p.len=(coords[m]-coords[n]).normSquare();
506 std::sort(pedges.begin(),pedges.end(),pedgeLess);
507 for(std::vector<Parc>::iterator pi=pedges.begin();pi!=pedges.end();++pi)
509 Line li(pi->a,pi->b);
511 for(;e!=INVALID && !cross(e,li);++e) ;
514 ConstMap<Arc,int> cegy(1);
515 Suurballe<ListGraph,ConstMap<Arc,int> >
516 sur(g,cegy,pi->a,pi->b);
518 if(k<2 || sur.totalLength()>d)
520 ne=g.addEdge(pi->a,pi->b);
528 template <typename Graph, typename CoordMap>
529 class LengthSquareMap {
531 typedef typename Graph::Edge Key;
532 typedef typename CoordMap::Value::Value Value;
534 LengthSquareMap(const Graph& graph, const CoordMap& coords)
535 : _graph(graph), _coords(coords) {}
537 Value operator[](const Key& key) const {
538 return (_coords[_graph.v(key)] -
539 _coords[_graph.u(key)]).normSquare();
545 const CoordMap& _coords;
549 std::vector<Parc> pedges;
551 std::cout << T.realTime() << "s: Creating delaunay triangulation...\n";
553 std::cout << T.realTime() << "s: Calculating spanning tree...\n";
554 LengthSquareMap<ListGraph, ListGraph::NodeMap<Point> > ls(g, coords);
555 ListGraph::EdgeMap<bool> tree(g);
556 kruskal(g, ls, tree);
557 std::cout << T.realTime() << "s: Removing non tree arcs...\n";
558 std::vector<Edge> remove;
559 for (EdgeIt e(g); e != INVALID; ++e) {
560 if (!tree[e]) remove.push_back(e);
562 for(int i = 0; i < int(remove.size()); ++i) {
565 std::cout << T.realTime() << "s: Done\n";
570 std::cout << "Find a tree..." << std::endl;
574 std::cout << "Total arc length (tree) : " << totalLen() << std::endl;
576 std::cout << "Make it Euler..." << std::endl;
579 std::vector<Node> leafs;
580 for(NodeIt n(g);n!=INVALID;++n)
581 if(countIncEdges(g,n)%2==1) leafs.push_back(n);
583 // for(unsigned int i=0;i<leafs.size();i+=2)
584 // g.addArc(leafs[i],leafs[i+1]);
586 std::vector<Parc> pedges;
587 for(unsigned int i=0;i<leafs.size()-1;i++)
588 for(unsigned int j=i+1;j<leafs.size();j++)
595 p.len=(coords[m]-coords[n]).normSquare();
598 std::sort(pedges.begin(),pedges.end(),pedgeLess);
599 for(unsigned int i=0;i<pedges.size();i++)
600 if(countIncEdges(g,pedges[i].a)%2 &&
601 countIncEdges(g,pedges[i].b)%2)
602 g.addEdge(pedges[i].a,pedges[i].b);
605 for(NodeIt n(g);n!=INVALID;++n)
606 if(countIncEdges(g,n)%2 || countIncEdges(g,n)==0 )
607 std::cout << "GEBASZ!!!" << std::endl;
609 for(EdgeIt e(g);e!=INVALID;++e)
611 std::cout << "LOOP GEBASZ!!!" << std::endl;
613 std::cout << "Number of arcs : " << countEdges(g) << std::endl;
615 std::cout << "Total arc length (euler) : " << totalLen() << std::endl;
617 ListGraph::EdgeMap<Arc> enext(g);
619 EulerIt<ListGraph> e(g);
622 // std::cout << "Tour arc: " << g.id(Edge(e)) << std::endl;
623 for(++e;e!=INVALID;++e)
625 // std::cout << "Tour arc: " << g.id(Edge(e)) << std::endl;
632 std::cout << "Creating a tour from that..." << std::endl;
634 int nnum = countNodes(g);
635 int ednum = countEdges(g);
637 for(Arc p=enext[EdgeIt(g)];ednum>nnum;p=enext[p])
639 // std::cout << "Checking arc " << g.id(p) << std::endl;
643 Node n1=g.oppositeNode(n2,e);
644 Node n3=g.oppositeNode(n2,f);
645 if(countIncEdges(g,n2)>2)
647 // std::cout << "Remove an Arc" << std::endl;
653 Arc ne=g.direct(g.addEdge(n1,n3),n1);
665 std::cout << "Total arc length (tour) : " << totalLen() << std::endl;
667 std::cout << "2-opt the tour..." << std::endl;
671 std::cout << "Total arc length (2-opt tour) : " << totalLen() << std::endl;
675 int main(int argc,const char **argv)
677 ArgParser ap(argc,argv);
680 bool disc_d, square_d, gauss_d;
681 // bool tsp_a,two_a,tree_a;
686 std::string ndist("disc");
687 ap.refOption("n", "Number of nodes (default is 100)", N)
688 .intOption("g", "Girth parameter (default is 10)", 10)
689 .refOption("cities", "Number of cities (default is 1)", num_of_cities)
690 .refOption("area", "Full relative area of the cities (default is 1)", area)
691 .refOption("disc", "Nodes are evenly distributed on a unit disc (default)",disc_d)
692 .optionGroup("dist", "disc")
693 .refOption("square", "Nodes are evenly distributed on a unit square", square_d)
694 .optionGroup("dist", "square")
696 "Nodes are located according to a two-dim gauss distribution",
698 .optionGroup("dist", "gauss")
699 // .mandatoryGroup("dist")
700 .onlyOneGroup("dist")
701 .boolOption("eps", "Also generate .eps output (prefix.eps)")
702 .boolOption("dir", "Directed digraph is generated (each arcs are replaced by two directed ones)")
703 .boolOption("2con", "Create a two connected planar digraph")
704 .optionGroup("alg","2con")
705 .boolOption("tree", "Create a min. cost spanning tree")
706 .optionGroup("alg","tree")
707 .boolOption("tsp", "Create a TSP tour")
708 .optionGroup("alg","tsp")
709 .boolOption("tsp2", "Create a TSP tour (tree based)")
710 .optionGroup("alg","tsp2")
711 .boolOption("dela", "Delaunay triangulation digraph")
712 .optionGroup("alg","dela")
714 .boolOption("rand", "Use time seed for random number generator")
715 .optionGroup("rand", "rand")
716 .intOption("seed", "Random seed", -1)
717 .optionGroup("rand", "seed")
718 .onlyOneGroup("rand")
719 .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'")
724 std::cout << "Random number seed: " << seed << std::endl;
727 if (ap.given("seed")) {
728 int seed = ap["seed"];
729 std::cout << "Random number seed: " << seed << std::endl;
734 switch(ap.files().size())
737 prefix="lgf-gen-out";
740 prefix=ap.files()[0];
743 std::cerr << "\nAt most one prefix can be given\n\n";
748 std::vector<double> sizes;
749 std::vector<double> cum_sizes;
750 for(int s=0;s<num_of_cities;s++)
752 // sum_sizes+=rnd.exponential();
756 cum_sizes.push_back(sum_sizes);
759 for(int s=0;s<num_of_cities;s++)
761 Point center=(num_of_cities==1?Point(0,0):rnd.disc());
763 for(;i<N*(cum_sizes[s]/sum_sizes);i++) {
766 coords[n]=center+rnd.gauss2()*area*
767 std::sqrt(sizes[s]/sum_sizes);
770 for(;i<N*(cum_sizes[s]/sum_sizes);i++) {
773 coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area*
774 std::sqrt(sizes[s]/sum_sizes);
776 else if(disc_d || true)
777 for(;i<N*(cum_sizes[s]/sum_sizes);i++) {
780 coords[n]=center+rnd.disc()*area*
781 std::sqrt(sizes[s]/sum_sizes);
785 // for (ListGraph::NodeIt n(g); n != INVALID; ++n) {
786 // std::cerr << coords[n] << std::endl;
791 std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl;
795 std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl;
797 else if(ap["2con"]) {
798 std::cout << "Make triangles\n";
800 sparseTriangle(ap["g"]);
801 std::cout << "Make it sparser\n";
804 else if(ap["tree"]) {
807 else if(ap["dela"]) {
812 std::cout << "Number of nodes : " << countNodes(g) << std::endl;
813 std::cout << "Number of arcs : " << countEdges(g) << std::endl;
815 for(EdgeIt e(g);e!=INVALID;++e)
816 tlen+=sqrt((coords[g.v(e)]-coords[g.u(e)]).normSquare());
817 std::cout << "Total arc length : " << tlen << std::endl;
820 graphToEps(g,prefix+".eps").scaleToA4().
821 scale(600).nodeScale(.005).arcWidthScale(.001).preScale(false).
822 coords(coords).run();
825 DigraphWriter<ListGraph>(g,prefix+".lgf").
826 nodeMap("coordinates_x",scaleMap(xMap(coords),600)).
827 nodeMap("coordinates_y",scaleMap(yMap(coords),600)).
829 else GraphWriter<ListGraph>(g,prefix+".lgf").
830 nodeMap("coordinates_x",scaleMap(xMap(coords),600)).
831 nodeMap("coordinates_y",scaleMap(yMap(coords),600)).