diff --git a/cpp/switchchain_exponent.cpp b/cpp/switchchain_exponent.cpp new file mode 100644 index 0000000000000000000000000000000000000000..3691b4160f717fec9bbb4e5eb43df71cafdddd5a --- /dev/null +++ b/cpp/switchchain_exponent.cpp @@ -0,0 +1,170 @@ +#include "exports.hpp" +#include "graph.hpp" +#include "powerlaw.hpp" +#include +#include +#include +#include +#include +#include + +// Its assumed that u,v are distinct. +// Check if all four vertices are distinct +bool edgeConflicts(const Edge& e1, const Edge& e2) { + return (e1.u == e2.u || e1.u == e2.v || e1.v == e2.u || e1.v == e2.v); +} + +class SwitchChain { + public: + SwitchChain() + : mt(std::random_device{}()), permutationDistribution(0.5) + // permutationDistribution(0, 2) + { + // random_device uses hardware entropy if available + // std::random_device rd; + // mt.seed(rd()); + } + ~SwitchChain() {} + + bool initialize(const Graph& gstart) { + if (gstart.edgeCount() == 0) + return false; + g = gstart; + edgeDistribution.param( + std::uniform_int_distribution<>::param_type(0, g.edgeCount() - 1)); + return true; + } + + bool doMove() { + int e1index, e2index; + int timeout = 0; + // Keep regenerating while conflicting edges + do { + e1index = edgeDistribution(mt); + e2index = edgeDistribution(mt); + if (++timeout % 100 == 0) { + std::cerr << "Warning: sampled " << timeout + << " random edges but they keep conflicting.\n"; + } + } while (edgeConflicts(g.getEdge(e1index), g.getEdge(e2index))); + + // Consider one of the three possible permutations + // 1) e1.u - e1.v and e2.u - e2.v (original) + // 2) e1.u - e2.u and e1.v - e2.v + // 3) e1.u - e2.v and e1.v - e2.u + bool switchType = permutationDistribution(mt); + return g.exchangeEdges(e1index, e2index, switchType); + } + + Graph g; + std::mt19937 mt; + std::uniform_int_distribution<> edgeDistribution; + //std::uniform_int_distribution<> permutationDistribution; + std::bernoulli_distribution permutationDistribution; +}; + +int main() { + // Generate a random degree sequence + std::mt19937 rng(std::random_device{}()); + + // Goal: + // Degrees follow a power-law distribution with some parameter tau + // Expect: #tri = const * n^{ something } + // The goal is to find the 'something' by finding the number of triangles + // for different values of n and tau + float tauValues[] = {2.1f, 2.2f, 2.3f, 2.4f, 2.5f, 2.6f, 2.7f, 2.8f, 2.9f}; + + Graph g; + Graph g1; + Graph g2; + + std::ofstream outfile("graphdata_exponent.m"); + outfile << '{'; + bool outputComma = false; + + for (int numVertices = 200; numVertices <= 2000; numVertices += 200) { + for (float tau : tauValues) { + + DegreeSequence ds(numVertices); + powerlaw_distribution degDist(tau, 1, numVertices); + //std::poisson_distribution<> degDist(12); + + // For a single n,tau take samples over several instances of + // the degree distribution. + // 500 samples seems to give reasonable results + for (int degreeSample = 0; degreeSample < 1000; ++degreeSample) { + // Generate a graph + // might require multiple tries + for (int i = 1; ; ++i) { + std::generate(ds.begin(), ds.end(), + [°Dist, &rng] { return degDist(rng); }); + // First make the sum even + unsigned int sum = std::accumulate(ds.begin(), ds.end(), 0); + if (sum % 2) { + continue; + // Can we do this: ?? + ds.back()++; + } + + if (g.createFromDegreeSequence(ds)) + break; + + // When 10 tries have not worked, output a warning + if (i % 10 == 0) { + std::cerr << "Warning: could not create graph from " + "degree sequence. Trying again...\n"; + } + } + + SwitchChain chain; + if (!chain.initialize(g)) { + std::cerr << "Could not initialize Markov chain.\n"; + return 1; + } + + std::cout << "Running n = " << numVertices << ", tau = " << tau + << ". \t" << std::flush; + + int mixingTime = (32.0f - 26.0f*(tau - 2.0f)) * numVertices; //40000; + constexpr int measurements = 50; + constexpr int measureSkip = + 200; // Take a sample every ... steps + + int movesDone = 0; + + long long trianglesTotal = 0; + + for (int i = 0; i < mixingTime; ++i) { + if (chain.doMove()) + ++movesDone; + } + for (int i = 0; i < measurements; ++i) { + for (int j = 0; j < measureSkip; ++j) + if (chain.doMove()) + ++movesDone; + trianglesTotal += chain.g.countTriangles(); + } + + std::cout << movesDone << '/' << mixingTime + measurements * measureSkip + << " moves succeeded (" + << 100.0f * float(movesDone) / + float(mixingTime + measurements * measureSkip) + << "%)."; + //std::cout << std::endl; + + if (outputComma) + outfile << ',' << '\n'; + outputComma = true; + + float avgTriangles = + float(trianglesTotal) / float(measurements); + outfile << '{' << '{' << numVertices << ',' << tau << '}'; + outfile << ',' << avgTriangles << '}' << std::flush; + + std::cout << std::endl; + } + } + } + outfile << '}'; + return 0; +}