[2391] | 1 | /* -*- C++ -*- |
---|
| 2 | * |
---|
| 3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
| 4 | * |
---|
| 5 | * Copyright (C) 2003-2007 |
---|
| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
| 8 | * |
---|
| 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. |
---|
| 12 | * |
---|
| 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 |
---|
| 15 | * purpose. |
---|
| 16 | * |
---|
| 17 | */ |
---|
| 18 | |
---|
[2390] | 19 | #include <lemon/list_graph.h> |
---|
| 20 | #include <lemon/graph_utils.h> |
---|
| 21 | #include <lemon/random.h> |
---|
| 22 | #include <lemon/dim2.h> |
---|
| 23 | #include <lemon/bfs.h> |
---|
| 24 | #include <lemon/counter.h> |
---|
| 25 | #include <lemon/suurballe.h> |
---|
| 26 | #include <lemon/graph_to_eps.h> |
---|
| 27 | #include <lemon/graph_writer.h> |
---|
| 28 | #include <lemon/arg_parser.h> |
---|
| 29 | #include <cmath> |
---|
| 30 | #include <algorithm> |
---|
| 31 | #include <lemon/unionfind.h> |
---|
| 32 | |
---|
| 33 | using namespace lemon; |
---|
| 34 | |
---|
| 35 | typedef dim2::Point<double> Point; |
---|
| 36 | |
---|
| 37 | UGRAPH_TYPEDEFS(ListUGraph); |
---|
| 38 | |
---|
| 39 | int N; |
---|
| 40 | int girth; |
---|
| 41 | |
---|
| 42 | ListUGraph g; |
---|
| 43 | |
---|
| 44 | std::vector<Node> nodes; |
---|
| 45 | ListUGraph::NodeMap<Point> coords(g); |
---|
| 46 | |
---|
| 47 | int tsp_impr_num=0; |
---|
| 48 | |
---|
| 49 | const double EPSILON=1e-8; |
---|
| 50 | bool tsp_improve(Node u, Node v) |
---|
| 51 | { |
---|
| 52 | double luv=std::sqrt((coords[v]-coords[u]).normSquare()); |
---|
| 53 | Node u2=u; |
---|
| 54 | Node v2=v; |
---|
| 55 | do { |
---|
| 56 | Node n; |
---|
| 57 | for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e); |
---|
| 58 | u2=v2; |
---|
| 59 | v2=n; |
---|
| 60 | if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON> |
---|
| 61 | std::sqrt((coords[u]-coords[u2]).normSquare())+ |
---|
| 62 | std::sqrt((coords[v]-coords[v2]).normSquare())) |
---|
| 63 | { |
---|
| 64 | g.erase(findUEdge(g,u,v)); |
---|
| 65 | g.erase(findUEdge(g,u2,v2)); |
---|
| 66 | g.addEdge(u2,u); |
---|
| 67 | g.addEdge(v,v2); |
---|
| 68 | tsp_impr_num++; |
---|
| 69 | return true; |
---|
| 70 | } |
---|
| 71 | } while(v2!=u); |
---|
| 72 | return false; |
---|
| 73 | } |
---|
| 74 | |
---|
| 75 | bool tsp_improve(Node u) |
---|
| 76 | { |
---|
| 77 | for(IncEdgeIt e(g,u);e!=INVALID;++e) |
---|
| 78 | if(tsp_improve(u,g.runningNode(e))) return true; |
---|
| 79 | return false; |
---|
| 80 | } |
---|
| 81 | |
---|
| 82 | void tsp_improve() |
---|
| 83 | { |
---|
| 84 | bool b; |
---|
| 85 | do { |
---|
| 86 | b=false; |
---|
| 87 | for(NodeIt n(g);n!=INVALID;++n) |
---|
| 88 | if(tsp_improve(n)) b=true; |
---|
| 89 | } while(b); |
---|
| 90 | } |
---|
| 91 | |
---|
| 92 | void tsp() |
---|
| 93 | { |
---|
| 94 | for(int i=0;i<N;i++) g.addEdge(nodes[i],nodes[(i+1)%N]); |
---|
| 95 | tsp_improve(); |
---|
| 96 | } |
---|
| 97 | |
---|
| 98 | class Line |
---|
| 99 | { |
---|
| 100 | public: |
---|
| 101 | Point a; |
---|
| 102 | Point b; |
---|
| 103 | Line(Point _a,Point _b) :a(_a),b(_b) {} |
---|
| 104 | Line(Node _a,Node _b) : a(coords[_a]),b(coords[_b]) {} |
---|
| 105 | Line(const Edge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
---|
| 106 | Line(const UEdge &e) : a(coords[g.source(e)]),b(coords[g.target(e)]) {} |
---|
| 107 | }; |
---|
| 108 | |
---|
| 109 | inline std::ostream& operator<<(std::ostream &os, const Line &l) |
---|
| 110 | { |
---|
| 111 | os << l.a << "->" << l.b; |
---|
| 112 | return os; |
---|
| 113 | } |
---|
| 114 | |
---|
| 115 | bool cross(Line a, Line b) |
---|
| 116 | { |
---|
| 117 | Point ao=rot90(a.b-a.a); |
---|
| 118 | Point bo=rot90(b.b-b.a); |
---|
| 119 | return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 && |
---|
| 120 | (bo*(a.a-b.a))*(bo*(a.b-b.a))<0; |
---|
| 121 | } |
---|
| 122 | |
---|
| 123 | struct Pedge |
---|
| 124 | { |
---|
| 125 | Node a; |
---|
| 126 | Node b; |
---|
| 127 | double len; |
---|
| 128 | }; |
---|
| 129 | |
---|
| 130 | bool pedgeLess(Pedge a,Pedge b) |
---|
| 131 | { |
---|
| 132 | return a.len<b.len; |
---|
| 133 | } |
---|
| 134 | |
---|
| 135 | std::vector<UEdge> edges; |
---|
| 136 | |
---|
| 137 | void triangle() |
---|
| 138 | { |
---|
| 139 | Counter cnt("Number of edges added: "); |
---|
| 140 | std::vector<Pedge> pedges; |
---|
| 141 | for(NodeIt n(g);n!=INVALID;++n) |
---|
| 142 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
---|
| 143 | { |
---|
| 144 | Pedge p; |
---|
| 145 | p.a=n; |
---|
| 146 | p.b=m; |
---|
| 147 | p.len=(coords[m]-coords[n]).normSquare(); |
---|
| 148 | pedges.push_back(p); |
---|
| 149 | } |
---|
| 150 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
---|
| 151 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
---|
| 152 | { |
---|
| 153 | Line li(pi->a,pi->b); |
---|
| 154 | UEdgeIt e(g); |
---|
| 155 | for(;e!=INVALID && !cross(e,li);++e) ; |
---|
| 156 | UEdge ne; |
---|
| 157 | if(e==INVALID) { |
---|
| 158 | ne=g.addEdge(pi->a,pi->b); |
---|
| 159 | edges.push_back(ne); |
---|
| 160 | cnt++; |
---|
| 161 | } |
---|
| 162 | } |
---|
| 163 | } |
---|
| 164 | |
---|
| 165 | void sparse(int d) |
---|
| 166 | { |
---|
| 167 | Counter cnt("Number of edges removed: "); |
---|
| 168 | Bfs<ListUGraph> bfs(g); |
---|
| 169 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
---|
| 170 | ei!=edges.rend();++ei) |
---|
| 171 | { |
---|
| 172 | Node a=g.source(*ei); |
---|
| 173 | Node b=g.target(*ei); |
---|
| 174 | g.erase(*ei); |
---|
| 175 | bfs.run(a,b); |
---|
| 176 | if(bfs.predEdge(b)==INVALID || bfs.dist(b)>d) |
---|
| 177 | g.addEdge(a,b); |
---|
| 178 | else cnt++; |
---|
| 179 | } |
---|
| 180 | } |
---|
| 181 | |
---|
| 182 | void sparse2(int d) |
---|
| 183 | { |
---|
| 184 | Counter cnt("Number of edges removed: "); |
---|
| 185 | for(std::vector<UEdge>::reverse_iterator ei=edges.rbegin(); |
---|
| 186 | ei!=edges.rend();++ei) |
---|
| 187 | { |
---|
| 188 | Node a=g.source(*ei); |
---|
| 189 | Node b=g.target(*ei); |
---|
| 190 | g.erase(*ei); |
---|
| 191 | ConstMap<Edge,int> cegy(1); |
---|
| 192 | Suurballe<ListUGraph,ConstMap<Edge,int> > sur(g,cegy,a,b); |
---|
| 193 | int k=sur.run(2); |
---|
| 194 | if(k<2 || sur.totalLength()>d) |
---|
| 195 | g.addEdge(a,b); |
---|
| 196 | else cnt++; |
---|
| 197 | // else std::cout << "Remove edge " << g.id(a) << "-" << g.id(b) << '\n'; |
---|
| 198 | } |
---|
| 199 | } |
---|
| 200 | |
---|
| 201 | void sparseTriangle(int d) |
---|
| 202 | { |
---|
| 203 | Counter cnt("Number of edges added: "); |
---|
| 204 | std::vector<Pedge> pedges; |
---|
| 205 | for(NodeIt n(g);n!=INVALID;++n) |
---|
| 206 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
---|
| 207 | { |
---|
| 208 | Pedge p; |
---|
| 209 | p.a=n; |
---|
| 210 | p.b=m; |
---|
| 211 | p.len=(coords[m]-coords[n]).normSquare(); |
---|
| 212 | pedges.push_back(p); |
---|
| 213 | } |
---|
| 214 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
---|
| 215 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
---|
| 216 | { |
---|
| 217 | Line li(pi->a,pi->b); |
---|
| 218 | UEdgeIt e(g); |
---|
| 219 | for(;e!=INVALID && !cross(e,li);++e) ; |
---|
| 220 | UEdge ne; |
---|
| 221 | if(e==INVALID) { |
---|
| 222 | ConstMap<Edge,int> cegy(1); |
---|
| 223 | Suurballe<ListUGraph,ConstMap<Edge,int> > |
---|
| 224 | sur(g,cegy,pi->a,pi->b); |
---|
| 225 | int k=sur.run(2); |
---|
| 226 | if(k<2 || sur.totalLength()>d) |
---|
| 227 | { |
---|
| 228 | ne=g.addEdge(pi->a,pi->b); |
---|
| 229 | edges.push_back(ne); |
---|
| 230 | cnt++; |
---|
| 231 | } |
---|
| 232 | } |
---|
| 233 | } |
---|
| 234 | } |
---|
| 235 | |
---|
| 236 | void minTree() { |
---|
| 237 | std::vector<Pedge> pedges; |
---|
| 238 | for(NodeIt n(g);n!=INVALID;++n) |
---|
| 239 | for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) |
---|
| 240 | { |
---|
| 241 | Pedge p; |
---|
| 242 | p.a=n; |
---|
| 243 | p.b=m; |
---|
| 244 | p.len=(coords[m]-coords[n]).normSquare(); |
---|
| 245 | pedges.push_back(p); |
---|
| 246 | } |
---|
| 247 | std::sort(pedges.begin(),pedges.end(),pedgeLess); |
---|
| 248 | ListUGraph::NodeMap<int> comp(g); |
---|
| 249 | UnionFind<ListUGraph::NodeMap<int> > uf(comp); |
---|
| 250 | for (NodeIt it(g); it != INVALID; ++it) |
---|
| 251 | uf.insert(it); |
---|
| 252 | |
---|
| 253 | int en=0; |
---|
| 254 | for(std::vector<Pedge>::iterator pi=pedges.begin();pi!=pedges.end();++pi) |
---|
| 255 | { |
---|
| 256 | if ( uf.join(pi->a,pi->b) ) { |
---|
| 257 | g.addEdge(pi->a,pi->b); |
---|
| 258 | en++; |
---|
| 259 | if(en>=N-1) return; |
---|
| 260 | } |
---|
| 261 | } |
---|
| 262 | } |
---|
| 263 | |
---|
| 264 | |
---|
| 265 | |
---|
| 266 | int main(int argc,char **argv) |
---|
| 267 | { |
---|
| 268 | ArgParser ap(argc,argv); |
---|
| 269 | |
---|
| 270 | bool eps; |
---|
| 271 | bool disc_d, square_d, gauss_d; |
---|
| 272 | bool tsp_a,two_a,tree_a; |
---|
| 273 | int num_of_cities=1; |
---|
| 274 | double area=1; |
---|
| 275 | N=100; |
---|
| 276 | girth=10; |
---|
| 277 | std::string ndist("disc"); |
---|
| 278 | ap.option("n", "Number of nodes (default is 100)", N) |
---|
| 279 | .option("g", "Girth parameter (default is 10)", girth) |
---|
| 280 | .option("cities", "Number of cities (default is 1)", num_of_cities) |
---|
| 281 | .option("area", "Full relative area of the cities (default is 1)", area) |
---|
| 282 | .option("disc", "Nodes are evenly distributed on a unit disc (default)",disc_d) |
---|
| 283 | .optionGroup("dist", "disc") |
---|
| 284 | .option("square", "Nodes are evenly distributed on a unit square", square_d) |
---|
| 285 | .optionGroup("dist", "square") |
---|
| 286 | .option("gauss", |
---|
| 287 | "Nodes are located according to a two-dim gauss distribution", |
---|
| 288 | gauss_d) |
---|
| 289 | .optionGroup("dist", "gauss") |
---|
| 290 | // .mandatoryGroup("dist") |
---|
| 291 | .onlyOneGroup("dist") |
---|
| 292 | .option("eps", "Also generate .eps output (prefix.eps)",eps) |
---|
| 293 | .option("2con", "Create a two connected planar graph",two_a) |
---|
| 294 | .optionGroup("alg","2con") |
---|
| 295 | .option("tree", "Create a min. cost spanning tree",tree_a) |
---|
| 296 | .optionGroup("alg","tree") |
---|
| 297 | .option("tsp", "Create a TSP tour",tsp_a) |
---|
| 298 | .optionGroup("alg","tsp") |
---|
| 299 | .onlyOneGroup("alg") |
---|
| 300 | .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'") |
---|
| 301 | .run(); |
---|
| 302 | |
---|
| 303 | std::string prefix; |
---|
| 304 | switch(ap.files().size()) |
---|
| 305 | { |
---|
| 306 | case 0: |
---|
| 307 | prefix="lgf-gen-out"; |
---|
| 308 | break; |
---|
| 309 | case 1: |
---|
| 310 | prefix=ap.files()[0]; |
---|
| 311 | break; |
---|
| 312 | default: |
---|
| 313 | std::cerr << "\nAt most one prefix can be given\n\n"; |
---|
| 314 | exit(1); |
---|
| 315 | } |
---|
| 316 | |
---|
| 317 | double sum_sizes=0; |
---|
| 318 | std::vector<double> sizes; |
---|
| 319 | std::vector<double> cum_sizes; |
---|
| 320 | for(int s=0;s<num_of_cities;s++) |
---|
| 321 | { |
---|
| 322 | // sum_sizes+=rnd.exponential(); |
---|
| 323 | double d=rnd(); |
---|
| 324 | sum_sizes+=d; |
---|
| 325 | sizes.push_back(d); |
---|
| 326 | cum_sizes.push_back(sum_sizes); |
---|
| 327 | } |
---|
| 328 | int i=0; |
---|
| 329 | for(int s=0;s<num_of_cities;s++) |
---|
| 330 | { |
---|
| 331 | Point center=(num_of_cities==1?Point(0,0):rnd.disc()); |
---|
| 332 | if(gauss_d) |
---|
| 333 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
---|
| 334 | Node n=g.addNode(); |
---|
| 335 | nodes.push_back(n); |
---|
| 336 | coords[n]=center+rnd.gauss2()*area* |
---|
| 337 | std::sqrt(sizes[s]/sum_sizes); |
---|
| 338 | } |
---|
| 339 | else if(square_d) |
---|
| 340 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
---|
| 341 | Node n=g.addNode(); |
---|
| 342 | nodes.push_back(n); |
---|
| 343 | coords[n]=center+Point(rnd()*2-1,rnd()*2-1)*area* |
---|
| 344 | std::sqrt(sizes[s]/sum_sizes); |
---|
| 345 | } |
---|
| 346 | else if(disc_d || true) |
---|
| 347 | for(;i<N*(cum_sizes[s]/sum_sizes);i++) { |
---|
| 348 | Node n=g.addNode(); |
---|
| 349 | nodes.push_back(n); |
---|
| 350 | coords[n]=center+rnd.disc()*area* |
---|
| 351 | std::sqrt(sizes[s]/sum_sizes); |
---|
| 352 | } |
---|
| 353 | } |
---|
| 354 | |
---|
| 355 | if(tsp_a) { |
---|
| 356 | tsp(); |
---|
| 357 | std::cout << "#2-opt improvements: " << tsp_impr_num << std::endl; |
---|
| 358 | } |
---|
| 359 | else if(two_a) { |
---|
| 360 | std::cout << "Make triangles\n"; |
---|
| 361 | // triangle(); |
---|
| 362 | sparseTriangle(girth); |
---|
| 363 | std::cout << "Make it sparser\n"; |
---|
| 364 | sparse2(girth); |
---|
| 365 | } |
---|
| 366 | else if(tree_a) { |
---|
| 367 | minTree(); |
---|
| 368 | } |
---|
| 369 | |
---|
| 370 | |
---|
| 371 | std::cout << "Number of nodes : " << countNodes(g) << std::endl; |
---|
| 372 | std::cout << "Number of edges : " << countUEdges(g) << std::endl; |
---|
| 373 | double tlen=0; |
---|
| 374 | for(UEdgeIt e(g);e!=INVALID;++e) |
---|
| 375 | tlen+=sqrt((coords[g.source(e)]-coords[g.target(e)]).normSquare()); |
---|
| 376 | std::cout << "Total edge length : " << tlen << std::endl; |
---|
| 377 | if(eps) |
---|
| 378 | graphToEps(g,prefix+".eps"). |
---|
| 379 | scale(600).nodeScale(.2).edgeWidthScale(.001).preScale(false). |
---|
| 380 | coords(coords).run(); |
---|
| 381 | |
---|
| 382 | UGraphWriter<ListUGraph>(prefix+".lgf",g). |
---|
| 383 | writeNodeMap("coordinates_x",scaleMap(xMap(coords),600)). |
---|
| 384 | writeNodeMap("coordinates_y",scaleMap(yMap(coords),600)). |
---|
| 385 | run(); |
---|
| 386 | } |
---|
| 387 | |
---|