all: switchchain switchchain_exponent switchchain_initialtris

switchchain_exponent:

switchchain_initialtris:

    float tauValues[] = {2.1f, 2.2f, 2.3f, 2.4f, 2.5f, 2.6f, 2.7f, 2.8f, 2.9f};

                int mixingTime = 8*(32.0f - 26.0f*(tau - 2.0f)) * numVertices; //40000;

#include "exports.hpp"

#include "graph.hpp"

#include "powerlaw.hpp"

#include <algorithm>

#include <fstream>

#include <iostream>

#include <numeric>

#include <random>

#include <vector>

// 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;

};

//

// Assumes degree sequence does NOT contain any zeroes!

//

// method2 = true  -> take highest degree and finish its pairing completely

// method2 = false -> take new highest degree after every pairing

bool greedyConfigurationModel(DegreeSequence& ds, Graph& g, auto& rng, bool method2) {

    // Similar to Havel-Hakimi but instead of pairing up with the highest ones

    // that remain, simply pair up with random ones

    unsigned int n = ds.size();

    // degree, vertex index

    std::vector<std::pair<unsigned int, unsigned int>> degrees(n);

    for (unsigned int i = 0; i < n; ++i) {

        degrees[i].first = ds[i];

        degrees[i].second = i;

    }

    std::vector<decltype(degrees.begin())> available;

    available.reserve(n);

    // Clear the graph

    g.reset(n);

    while (!degrees.empty()) {

        std::shuffle(degrees.begin(), degrees.end(), rng);

        // Get the highest degree:

        // If there are multiple highest ones, we pick a random one,

        // ensured by the shuffle.

        // The shuffle is needed anyway for the remaining part

        unsigned int dmax = 0;

        auto uIter = degrees.begin();

        for (auto iter = degrees.begin(); iter != degrees.end(); ++iter) {

            if (iter->first >= dmax) {

                dmax = iter->first;

                uIter = iter;

            }

        }

        if (dmax > degrees.size() - 1)

            return false;

        if (dmax == 0) {

            std::cerr << "ERROR 1 in GCM.\n";

        }

        unsigned int u = uIter->second;

        if (method2) {

            // Take the highest degree out of the vector

            degrees.erase(uIter);

            // Now assign randomly to the remaining vertices

            // Since its shuffled, we can pick the first 'dmax' ones

            auto vIter = degrees.begin();

            while (dmax--) {

                if (vIter->first == 0)

                    std::cerr << "ERROR in GCM2.\n";

                if (!g.addEdge({u, vIter->second}))

                    std::cerr << "ERROR. Could not add edge in GCM2.\n";

                vIter->first--;

                if (vIter->first == 0)

                    vIter = degrees.erase(vIter);

                else

                    vIter++;

            }

        } else {

            // Pair with a random vertex that is not u itself and to which

            // u has not paired yet!

            available.clear();

            for (auto iter = degrees.begin(); iter != degrees.end(); ++iter) {

                if (iter->second != u && !g.hasEdge({u, iter->second}))

                    available.push_back(iter);

            }

            if (available.empty())

                return false;

            std::uniform_int_distribution<> distr(0, available.size() - 1);

            auto vIter = available[distr(rng)];

            // pair u to v

            if (vIter->first == 0)

                std::cerr << "ERROR 2 in GCM1.\n";

            if (!g.addEdge({u, vIter->second}))

                std::cerr << "ERROR. Could not add edge in GCM1.\n";

            // Purge anything with degree zero

            // Be careful with invalidating the other iterator!

            // Degree of u is always greater or equal to the degree of v

            if (dmax == 1) {

                // Remove both

                // Erasure invalidates all iterators AFTER the erased one

                if (vIter > uIter) {

                    degrees.erase(vIter);

                    degrees.erase(uIter);

                } else {

                    degrees.erase(uIter);

                    degrees.erase(vIter);

                }

            } else {

                // Remove only v if it reaches zero

                uIter->first--;

                vIter->first--;

                if (vIter->first == 0)

                    degrees.erase(vIter);

            }

            //degrees.erase(std::remove_if(degrees.begin(), degrees.end(),

            //                             [](auto x) { return x.first == 0; }));

        }

    }

    return true;

}

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;

    std::ofstream outfile("graphdata_initialtris.m");

    outfile << '{';

    bool outputComma = false;

    for (int numVertices = 200; numVertices <= 2000; numVertices += 400) {

        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 < 200; ++degreeSample) {

                // Generate a graph

                // might require multiple tries

                for (int i = 1; ; ++i) {

                    std::generate(ds.begin(), ds.end(),

                                  [&degDist, &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";

                    }

                }

                //

                // Test the GCM1 and GCM2 success rate

                //

                long long gcmTris1 = 0;

                long long gcmTris2 = 0;

                int successrate1 = 0;

                int successrate2 = 0;

                for (int i = 0; i < 100; ++i) {

                    Graph gtemp;

                    // Take new highest degree every time

                    if (greedyConfigurationModel(ds, gtemp, rng, false)) {

                        ++successrate1;

                        gcmTris1 += gtemp.countTriangles();

                    }

                    // Finish all pairings of highest degree first

                    if (greedyConfigurationModel(ds, gtemp, rng, true)) {

                        ++successrate2;

                        gcmTris2 += gtemp.countTriangles();

                    }

                }

                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 - 20.0f * (tau - 2.0f)) * numVertices;

                constexpr int measurements = 20;

                constexpr int measureSkip = 200;

                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 << '{';

                outfile << '{' << numVertices << ',' << tau << '}';

                outfile << ',' << avgTriangles;

                outfile << ',' << '{' << gcmTris1 << ',' << successrate1 << '}';

                outfile << ',' << '{' << gcmTris2 << ',' << successrate2 << '}';

                outfile << '}' << std::flush;

                std::cout << std::endl;

            }

        }

    }

    outfile << '}';

    return 0;

}

graphdata_exponent_mixN.m

    degreeSamples = 500 + 1000 for mix1 and 1000 for mix4,mix8

    mixingTime = N* (32.0f - 26.0f*(tau - 2.0f)) * n

    output: {{n,tau},triangleseq,ds, {...??...} }