diff --git a/tools/lgf-gen.cc b/tools/lgf-gen.cc new file mode 100644 --- /dev/null +++ b/tools/lgf-gen.cc @@ -0,0 +1,834 @@ +/* -*- mode: C++; indent-tabs-mode: nil; -*- + * + * This file is a part of LEMON, a generic C++ optimization library. + * + * Copyright (C) 2003-2009 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport + * (Egervary Research Group on Combinatorial Optimization, EGRES). + * + * Permission to use, modify and distribute this software is granted + * provided that this copyright notice appears in all copies. For + * precise terms see the accompanying LICENSE file. + * + * This software is provided "AS IS" with no warranty of any kind, + * express or implied, and with no claim as to its suitability for any + * purpose. + * + */ + +/// \ingroup tools +/// \file +/// \brief Special plane graph generator. +/// +/// Graph generator application for various types of plane graphs. +/// +/// See +/// \code +/// lgf-gen --help +/// \endcode +/// for more information on the usage. + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +using namespace lemon; + +typedef dim2::Point Point; + +GRAPH_TYPEDEFS(ListGraph); + +bool progress=true; + +int N; +// int girth; + +ListGraph g; + +std::vector nodes; +ListGraph::NodeMap coords(g); + + +double totalLen(){ + double tlen=0; + for(EdgeIt e(g);e!=INVALID;++e) + tlen+=std::sqrt((coords[g.v(e)]-coords[g.u(e)]).normSquare()); + return tlen; +} + +int tsp_impr_num=0; + +const double EPSILON=1e-8; +bool tsp_improve(Node u, Node v) +{ + double luv=std::sqrt((coords[v]-coords[u]).normSquare()); + Node u2=u; + Node v2=v; + do { + Node n; + for(IncEdgeIt e(g,v2);(n=g.runningNode(e))==u2;++e) { } + u2=v2; + v2=n; + if(luv+std::sqrt((coords[v2]-coords[u2]).normSquare())-EPSILON> + std::sqrt((coords[u]-coords[u2]).normSquare())+ + std::sqrt((coords[v]-coords[v2]).normSquare())) + { + g.erase(findEdge(g,u,v)); + g.erase(findEdge(g,u2,v2)); + g.addEdge(u2,u); + g.addEdge(v,v2); + tsp_impr_num++; + return true; + } + } while(v2!=u); + return false; +} + +bool tsp_improve(Node u) +{ + for(IncEdgeIt e(g,u);e!=INVALID;++e) + if(tsp_improve(u,g.runningNode(e))) return true; + return false; +} + +void tsp_improve() +{ + bool b; + do { + b=false; + for(NodeIt n(g);n!=INVALID;++n) + if(tsp_improve(n)) b=true; + } while(b); +} + +void tsp() +{ + for(int i=0;i" << l.b; + return os; +} + +bool cross(Line a, Line b) +{ + Point ao=rot90(a.b-a.a); + Point bo=rot90(b.b-b.a); + return (ao*(b.a-a.a))*(ao*(b.b-a.a))<0 && + (bo*(a.a-b.a))*(bo*(a.b-b.a))<0; +} + +struct Parc +{ + Node a; + Node b; + double len; +}; + +bool pedgeLess(Parc a,Parc b) +{ + return a.len arcs; + +namespace _delaunay_bits { + + struct Part { + int prev, curr, next; + + Part(int p, int c, int n) : prev(p), curr(c), next(n) {} + }; + + inline std::ostream& operator<<(std::ostream& os, const Part& part) { + os << '(' << part.prev << ',' << part.curr << ',' << part.next << ')'; + return os; + } + + inline double circle_point(const Point& p, const Point& q, const Point& r) { + double a = p.x * (q.y - r.y) + q.x * (r.y - p.y) + r.x * (p.y - q.y); + if (a == 0) return std::numeric_limits::quiet_NaN(); + + double d = (p.x * p.x + p.y * p.y) * (q.y - r.y) + + (q.x * q.x + q.y * q.y) * (r.y - p.y) + + (r.x * r.x + r.y * r.y) * (p.y - q.y); + + double e = (p.x * p.x + p.y * p.y) * (q.x - r.x) + + (q.x * q.x + q.y * q.y) * (r.x - p.x) + + (r.x * r.x + r.y * r.y) * (p.x - q.x); + + double f = (p.x * p.x + p.y * p.y) * (q.x * r.y - r.x * q.y) + + (q.x * q.x + q.y * q.y) * (r.x * p.y - p.x * r.y) + + (r.x * r.x + r.y * r.y) * (p.x * q.y - q.x * p.y); + + return d / (2 * a) + std::sqrt((d * d + e * e) / (4 * a * a) + f / a); + } + + inline bool circle_form(const Point& p, const Point& q, const Point& r) { + return rot90(q - p) * (r - q) < 0.0; + } + + inline double intersection(const Point& p, const Point& q, double sx) { + const double epsilon = 1e-8; + + if (p.x == q.x) return (p.y + q.y) / 2.0; + + if (sx < p.x + epsilon) return p.y; + if (sx < q.x + epsilon) return q.y; + + double a = q.x - p.x; + double b = (q.x - sx) * p.y - (p.x - sx) * q.y; + double d = (q.x - sx) * (p.x - sx) * (p - q).normSquare(); + return (b - std::sqrt(d)) / a; + } + + struct YLess { + + + YLess(const std::vector& points, double& sweep) + : _points(points), _sweep(sweep) {} + + bool operator()(const Part& l, const Part& r) const { + const double epsilon = 1e-8; + + // std::cerr << l << " vs " << r << std::endl; + double lbx = l.prev != -1 ? + intersection(_points[l.prev], _points[l.curr], _sweep) : + - std::numeric_limits::infinity(); + double rbx = r.prev != -1 ? + intersection(_points[r.prev], _points[r.curr], _sweep) : + - std::numeric_limits::infinity(); + double lex = l.next != -1 ? + intersection(_points[l.curr], _points[l.next], _sweep) : + std::numeric_limits::infinity(); + double rex = r.next != -1 ? + intersection(_points[r.curr], _points[r.next], _sweep) : + std::numeric_limits::infinity(); + + if (lbx > lex) std::swap(lbx, lex); + if (rbx > rex) std::swap(rbx, rex); + + if (lex < epsilon + rex && lbx + epsilon < rex) return true; + if (rex < epsilon + lex && rbx + epsilon < lex) return false; + return lex < rex; + } + + const std::vector& _points; + double& _sweep; + }; + + struct BeachIt; + + typedef std::multimap SpikeHeap; + + typedef std::multimap Beach; + + struct BeachIt { + Beach::iterator it; + + BeachIt(Beach::iterator iter) : it(iter) {} + }; + +} + +inline void delaunay() { + Counter cnt("Number of arcs added: "); + + using namespace _delaunay_bits; + + typedef _delaunay_bits::Part Part; + typedef std::vector > SiteHeap; + + + std::vector points; + std::vector nodes; + + for (NodeIt it(g); it != INVALID; ++it) { + nodes.push_back(it); + points.push_back(coords[it]); + } + + SiteHeap siteheap(points.size()); + + double sweep; + + + for (int i = 0; i < int(siteheap.size()); ++i) { + siteheap[i] = std::make_pair(points[i].x, i); + } + + std::sort(siteheap.begin(), siteheap.end()); + sweep = siteheap.front().first; + + YLess yless(points, sweep); + Beach beach(yless); + + SpikeHeap spikeheap; + + std::set > arcs; + + int siteindex = 0; + { + SiteHeap front; + + while (siteindex < int(siteheap.size()) && + siteheap[0].first == siteheap[siteindex].first) { + front.push_back(std::make_pair(points[siteheap[siteindex].second].y, + siteheap[siteindex].second)); + ++siteindex; + } + + std::sort(front.begin(), front.end()); + + for (int i = 0; i < int(front.size()); ++i) { + int prev = (i == 0 ? -1 : front[i - 1].second); + int curr = front[i].second; + int next = (i + 1 == int(front.size()) ? -1 : front[i + 1].second); + + beach.insert(std::make_pair(Part(prev, curr, next), + spikeheap.end())); + } + } + + while (siteindex < int(points.size()) || !spikeheap.empty()) { + + SpikeHeap::iterator spit = spikeheap.begin(); + + if (siteindex < int(points.size()) && + (spit == spikeheap.end() || siteheap[siteindex].first < spit->first)) { + int site = siteheap[siteindex].second; + sweep = siteheap[siteindex].first; + + Beach::iterator bit = beach.upper_bound(Part(site, site, site)); + + if (bit->second != spikeheap.end()) { + spikeheap.erase(bit->second); + } + + int prev = bit->first.prev; + int curr = bit->first.curr; + int next = bit->first.next; + + beach.erase(bit); + + SpikeHeap::iterator pit = spikeheap.end(); + if (prev != -1 && + circle_form(points[prev], points[curr], points[site])) { + double x = circle_point(points[prev], points[curr], points[site]); + pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end()))); + pit->second.it = + beach.insert(std::make_pair(Part(prev, curr, site), pit)); + } else { + beach.insert(std::make_pair(Part(prev, curr, site), pit)); + } + + beach.insert(std::make_pair(Part(curr, site, curr), spikeheap.end())); + + SpikeHeap::iterator nit = spikeheap.end(); + if (next != -1 && + circle_form(points[site], points[curr],points[next])) { + double x = circle_point(points[site], points[curr], points[next]); + nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end()))); + nit->second.it = + beach.insert(std::make_pair(Part(site, curr, next), nit)); + } else { + beach.insert(std::make_pair(Part(site, curr, next), nit)); + } + + ++siteindex; + } else { + sweep = spit->first; + + Beach::iterator bit = spit->second.it; + + int prev = bit->first.prev; + int curr = bit->first.curr; + int next = bit->first.next; + + { + std::pair arc; + + arc = prev < curr ? + std::make_pair(prev, curr) : std::make_pair(curr, prev); + + if (arcs.find(arc) == arcs.end()) { + arcs.insert(arc); + g.addEdge(nodes[prev], nodes[curr]); + ++cnt; + } + + arc = curr < next ? + std::make_pair(curr, next) : std::make_pair(next, curr); + + if (arcs.find(arc) == arcs.end()) { + arcs.insert(arc); + g.addEdge(nodes[curr], nodes[next]); + ++cnt; + } + } + + Beach::iterator pbit = bit; --pbit; + int ppv = pbit->first.prev; + Beach::iterator nbit = bit; ++nbit; + int nnt = nbit->first.next; + + if (bit->second != spikeheap.end()) spikeheap.erase(bit->second); + if (pbit->second != spikeheap.end()) spikeheap.erase(pbit->second); + if (nbit->second != spikeheap.end()) spikeheap.erase(nbit->second); + + beach.erase(nbit); + beach.erase(bit); + beach.erase(pbit); + + SpikeHeap::iterator pit = spikeheap.end(); + if (ppv != -1 && ppv != next && + circle_form(points[ppv], points[prev], points[next])) { + double x = circle_point(points[ppv], points[prev], points[next]); + if (x < sweep) x = sweep; + pit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end()))); + pit->second.it = + beach.insert(std::make_pair(Part(ppv, prev, next), pit)); + } else { + beach.insert(std::make_pair(Part(ppv, prev, next), pit)); + } + + SpikeHeap::iterator nit = spikeheap.end(); + if (nnt != -1 && prev != nnt && + circle_form(points[prev], points[next], points[nnt])) { + double x = circle_point(points[prev], points[next], points[nnt]); + if (x < sweep) x = sweep; + nit = spikeheap.insert(std::make_pair(x, BeachIt(beach.end()))); + nit->second.it = + beach.insert(std::make_pair(Part(prev, next, nnt), nit)); + } else { + beach.insert(std::make_pair(Part(prev, next, nnt), nit)); + } + + } + } + + for (Beach::iterator it = beach.begin(); it != beach.end(); ++it) { + int curr = it->first.curr; + int next = it->first.next; + + if (next == -1) continue; + + std::pair arc; + + arc = curr < next ? + std::make_pair(curr, next) : std::make_pair(next, curr); + + if (arcs.find(arc) == arcs.end()) { + arcs.insert(arc); + g.addEdge(nodes[curr], nodes[next]); + ++cnt; + } + } +} + +void sparse(int d) +{ + Counter cnt("Number of arcs removed: "); + Bfs bfs(g); + for(std::vector::reverse_iterator ei=arcs.rbegin(); + ei!=arcs.rend();++ei) + { + Node a=g.u(*ei); + Node b=g.v(*ei); + g.erase(*ei); + bfs.run(a,b); + if(bfs.predArc(b)==INVALID || bfs.dist(b)>d) + g.addEdge(a,b); + else cnt++; + } +} + +void sparse2(int d) +{ + Counter cnt("Number of arcs removed: "); + for(std::vector::reverse_iterator ei=arcs.rbegin(); + ei!=arcs.rend();++ei) + { + Node a=g.u(*ei); + Node b=g.v(*ei); + g.erase(*ei); + ConstMap cegy(1); + Suurballe > sur(g,cegy); + int k=sur.run(a,b,2); + if(k<2 || sur.totalLength()>d) + g.addEdge(a,b); + else cnt++; +// else std::cout << "Remove arc " << g.id(a) << "-" << g.id(b) << '\n'; + } +} + +void sparseTriangle(int d) +{ + Counter cnt("Number of arcs added: "); + std::vector pedges; + for(NodeIt n(g);n!=INVALID;++n) + for(NodeIt m=++(NodeIt(n));m!=INVALID;++m) + { + Parc p; + p.a=n; + p.b=m; + p.len=(coords[m]-coords[n]).normSquare(); + pedges.push_back(p); + } + std::sort(pedges.begin(),pedges.end(),pedgeLess); + for(std::vector::iterator pi=pedges.begin();pi!=pedges.end();++pi) + { + Line li(pi->a,pi->b); + EdgeIt e(g); + for(;e!=INVALID && !cross(e,li);++e) ; + Edge ne; + if(e==INVALID) { + ConstMap cegy(1); + Suurballe > sur(g,cegy); + int k=sur.run(pi->a,pi->b,2); + if(k<2 || sur.totalLength()>d) + { + ne=g.addEdge(pi->a,pi->b); + arcs.push_back(ne); + cnt++; + } + } + } +} + +template +class LengthSquareMap { +public: + typedef typename Graph::Edge Key; + typedef typename CoordMap::Value::Value Value; + + LengthSquareMap(const Graph& graph, const CoordMap& coords) + : _graph(graph), _coords(coords) {} + + Value operator[](const Key& key) const { + return (_coords[_graph.v(key)] - + _coords[_graph.u(key)]).normSquare(); + } + +private: + + const Graph& _graph; + const CoordMap& _coords; +}; + +void minTree() { + std::vector pedges; + Timer T; + std::cout << T.realTime() << "s: Creating delaunay triangulation...\n"; + delaunay(); + std::cout << T.realTime() << "s: Calculating spanning tree...\n"; + LengthSquareMap > ls(g, coords); + ListGraph::EdgeMap tree(g); + kruskal(g, ls, tree); + std::cout << T.realTime() << "s: Removing non tree arcs...\n"; + std::vector remove; + for (EdgeIt e(g); e != INVALID; ++e) { + if (!tree[e]) remove.push_back(e); + } + for(int i = 0; i < int(remove.size()); ++i) { + g.erase(remove[i]); + } + std::cout << T.realTime() << "s: Done\n"; +} + +void tsp2() +{ + std::cout << "Find a tree..." << std::endl; + + minTree(); + + std::cout << "Total arc length (tree) : " << totalLen() << std::endl; + + std::cout << "Make it Euler..." << std::endl; + + { + std::vector leafs; + for(NodeIt n(g);n!=INVALID;++n) + if(countIncEdges(g,n)%2==1) leafs.push_back(n); + +// for(unsigned int i=0;i pedges; + for(unsigned int i=0;i enext(g); + { + EulerIt e(g); + Arc eo=e; + Arc ef=e; +// std::cout << "Tour arc: " << g.id(Edge(e)) << std::endl; + for(++e;e!=INVALID;++e) + { +// std::cout << "Tour arc: " << g.id(Edge(e)) << std::endl; + enext[eo]=e; + eo=e; + } + enext[eo]=ef; + } + + std::cout << "Creating a tour from that..." << std::endl; + + int nnum = countNodes(g); + int ednum = countEdges(g); + + for(Arc p=enext[EdgeIt(g)];ednum>nnum;p=enext[p]) + { +// std::cout << "Checking arc " << g.id(p) << std::endl; + Arc e=enext[p]; + Arc f=enext[e]; + Node n2=g.source(f); + Node n1=g.oppositeNode(n2,e); + Node n3=g.oppositeNode(n2,f); + if(countIncEdges(g,n2)>2) + { +// std::cout << "Remove an Arc" << std::endl; + Arc ff=enext[f]; + g.erase(e); + g.erase(f); + if(n1!=n3) + { + Arc ne=g.direct(g.addEdge(n1,n3),n1); + enext[p]=ne; + enext[ne]=ff; + ednum--; + } + else { + enext[p]=ff; + ednum-=2; + } + } + } + + std::cout << "Total arc length (tour) : " << totalLen() << std::endl; + + std::cout << "2-opt the tour..." << std::endl; + + tsp_improve(); + + std::cout << "Total arc length (2-opt tour) : " << totalLen() << std::endl; +} + + +int main(int argc,const char **argv) +{ + ArgParser ap(argc,argv); + +// bool eps; + bool disc_d, square_d, gauss_d; +// bool tsp_a,two_a,tree_a; + int num_of_cities=1; + double area=1; + N=100; +// girth=10; + std::string ndist("disc"); + ap.refOption("n", "Number of nodes (default is 100)", N) + .intOption("g", "Girth parameter (default is 10)", 10) + .refOption("cities", "Number of cities (default is 1)", num_of_cities) + .refOption("area", "Full relative area of the cities (default is 1)", area) + .refOption("disc", "Nodes are evenly distributed on a unit disc (default)", + disc_d) + .optionGroup("dist", "disc") + .refOption("square", "Nodes are evenly distributed on a unit square", + square_d) + .optionGroup("dist", "square") + .refOption("gauss", "Nodes are located according to a two-dim Gauss " + "distribution", gauss_d) + .optionGroup("dist", "gauss") + .onlyOneGroup("dist") + .boolOption("eps", "Also generate .eps output (.eps)") + .boolOption("nonodes", "Draw only the edges in the generated .eps output") + .boolOption("dir", "Directed graph is generated (each edge is replaced by " + "two directed arcs)") + .boolOption("2con", "Create a two connected planar graph") + .optionGroup("alg","2con") + .boolOption("tree", "Create a min. cost spanning tree") + .optionGroup("alg","tree") + .boolOption("tsp", "Create a TSP tour") + .optionGroup("alg","tsp") + .boolOption("tsp2", "Create a TSP tour (tree based)") + .optionGroup("alg","tsp2") + .boolOption("dela", "Delaunay triangulation graph") + .optionGroup("alg","dela") + .onlyOneGroup("alg") + .boolOption("rand", "Use time seed for random number generator") + .optionGroup("rand", "rand") + .intOption("seed", "Random seed", -1) + .optionGroup("rand", "seed") + .onlyOneGroup("rand") + .other("[prefix]","Prefix of the output files. Default is 'lgf-gen-out'") + .run(); + + if (ap["rand"]) { + int seed = int(time(0)); + std::cout << "Random number seed: " << seed << std::endl; + rnd = Random(seed); + } + if (ap.given("seed")) { + int seed = ap["seed"]; + std::cout << "Random number seed: " << seed << std::endl; + rnd = Random(seed); + } + + std::string prefix; + switch(ap.files().size()) + { + case 0: + prefix="lgf-gen-out"; + break; + case 1: + prefix=ap.files()[0]; + break; + default: + std::cerr << "\nAt most one prefix can be given\n\n"; + exit(1); + } + + double sum_sizes=0; + std::vector sizes; + std::vector cum_sizes; + for(int s=0;s(g,prefix+".lgf"). + nodeMap("coordinates_x",scaleMap(xMap(coords),600)). + nodeMap("coordinates_y",scaleMap(yMap(coords),600)). + run(); + else GraphWriter(g,prefix+".lgf"). + nodeMap("coordinates_x",scaleMap(xMap(coords),600)). + nodeMap("coordinates_y",scaleMap(yMap(coords),600)). + run(); +} +