MinSteinerTreeGoemans139.h

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#pragma once
 
#include <ogdf/graphalg/steiner_tree/Full2ComponentGenerator.h>
#include <ogdf/graphalg/steiner_tree/Full3ComponentGeneratorVoronoi.h>
#include <ogdf/graphalg/steiner_tree/FullComponentGeneratorCaller.h>
#include <ogdf/graphalg/steiner_tree/FullComponentGeneratorDreyfusWagner.h>
#include <ogdf/graphalg/steiner_tree/FullComponentGeneratorDreyfusWagnerWithoutMatrix.h>
#include <ogdf/graphalg/steiner_tree/LPRelaxationSER.h>
#include <ogdf/graphalg/steiner_tree/common_algorithms.h>
#include <ogdf/graphalg/steiner_tree/goemans/Approximation.h>
 
namespace ogdf {
 
template<typename T>
class MinSteinerTreeGoemans139 : public MinSteinerTreeModule<T> {
private:
    class Main;
 
protected:
    int m_restricted;
    bool m_preprocess;
    bool m_use2approx;
    bool m_separateCycles;
    int m_seed;
 
public:
    MinSteinerTreeGoemans139()
        : m_restricted(3)
        , m_preprocess(true)
        , m_use2approx(false)
        , m_separateCycles(false)
        , m_seed(1337) { }
 
    virtual ~MinSteinerTreeGoemans139() { }
 
    void setMaxComponentSize(int k) { m_restricted = k; }
 
    void setSeed(int seed) { m_seed = seed; }
 
    void use2Approximation(bool use2approx = true) { m_use2approx = use2approx; }
 
    void disablePreprocessing(bool preprocess = true) { m_preprocess = !preprocess; }
 
    void separateCycles(bool separateCycles = true) { m_separateCycles = separateCycles; }
 
protected:
    virtual T computeSteinerTree(const EdgeWeightedGraph<T>& G, const List<node>& terminals,
            const NodeArray<bool>& isTerminal, EdgeWeightedGraphCopy<T>*& finalSteinerTree) override;
};
 
template<typename T>
T MinSteinerTreeGoemans139<T>::computeSteinerTree(const EdgeWeightedGraph<T>& G,
        const List<node>& terminals, const NodeArray<bool>& isTerminal,
        EdgeWeightedGraphCopy<T>*& finalSteinerTree) {
    std::minstd_rand rng(m_seed);
    List<node> sortedTerminals(terminals);
    MinSteinerTreeModule<T>::sortTerminals(sortedTerminals);
    Main main(G, sortedTerminals, isTerminal, m_restricted, m_use2approx, m_separateCycles);
    return main.getApproximation(finalSteinerTree, rng, m_preprocess);
}
 
template<typename T>
class MinSteinerTreeGoemans139<T>::Main {
    const EdgeWeightedGraph<T>& m_G;
    const NodeArray<bool>& m_isTerminal;
    const List<node>& m_terminals; 
    steiner_tree::FullComponentWithExtraStore<T, double>
            m_fullCompStore; 
 
    int m_restricted;
    enum class Approx2State {
        Off,
        On,
        JustUseIt,
    };
    Approx2State m_use2approx;
 
    const double m_eps; 
 
    EdgeWeightedGraphCopy<T>* m_approx2SteinerTree;
    T m_approx2Weight;
 
 
    void findFull2Components(const NodeArray<NodeArray<T>>& distance,
            const NodeArray<NodeArray<edge>>& pred);
    void findFull3Components(const NodeArray<NodeArray<T>>& distance,
            const NodeArray<NodeArray<edge>>& pred);
    void find3RestrictedComponents();
    void findFullComponentsDW();
    void findFullComponentsEMV();
    template<typename FCG>
    void retrieveComponents(const FCG& fcg);
    void findFullComponents();
 
 
    void removeInactiveComponents() {
        for (int k = m_fullCompStore.size() - 1; k >= 0; --k) {
            OGDF_ASSERT(k < m_fullCompStore.size());
            if (m_fullCompStore.extra(k) <= m_eps) {
                m_fullCompStore.remove(k);
            }
        }
    }
 
    void removeComponents(ArrayBuffer<int>& ids) {
        ids.quicksort();
        for (int i = ids.size() - 1; i >= 0; --i) {
            m_fullCompStore.remove(ids[i]);
        }
    }
 
    void addComponent(NodeArray<bool>& isNewTerminal, int id) {
        m_fullCompStore.foreachNode(id, [&](node v) { isNewTerminal[v] = true; });
    }
 
    void preprocess(NodeArray<bool>& isNewTerminal) {
        Graph H; // a graph where each component is a star
        NodeArray<int> id(H); // ids each center of the star to the component id
        NodeArray<node> copy(m_G, nullptr); // ids orig in m_G -> copy in H
 
        List<node> centers; // all centers
        for (int i = 0; i < m_fullCompStore.size(); ++i) {
            const node center = H.newNode();
            centers.pushBack(center);
            id[center] = i;
 
            for (node vG : m_fullCompStore.terminals(i)) {
                node vH = copy[vG];
                if (!vH) {
                    vH = H.newNode();
                    copy[vG] = vH;
                }
                H.newEdge(vH, center); // target is always center
            }
        }
 
        // find components to be inserted into the steinerTree and insert them
        ArrayBuffer<int> inactive; // ids of components we insert; we have to remove them from the set of active components afterwards
        bool changed;
        do {
            changed = false;
            ListIterator<node> it2;
            for (ListIterator<node> it = centers.begin(); it.valid(); it = it2) {
                it2 = it.succ();
                node c = *it;
                int innerNodes = 0; // count inner nodes
                for (adjEntry adj : c->adjEntries) {
                    innerNodes += (adj->twinNode()->degree() != 1);
                }
                if (innerNodes <= 1) { // this center represents a component to add to steinerTree
                    // insert component into steinerTree
                    addComponent(isNewTerminal, id[c]);
 
                    // remove center from H (adjacent leaves can remain being isolated nodes)
                    inactive.push(id[c]);
                    H.delNode(c);
                    centers.del(it);
 
                    changed = true;
                }
            }
        } while (changed);
 
        removeComponents(inactive);
    }
 
 
public:
    Main(const EdgeWeightedGraph<T>& G, const List<node>& terminals,
            const NodeArray<bool>& isTerminal, int restricted, bool use2approx, bool separateCycles,
            double eps = 1e-8)
        : m_G(G)
        , m_isTerminal(isTerminal)
        , m_terminals(terminals)
        , m_fullCompStore(G, m_terminals, isTerminal)
        , m_restricted(restricted)
        , m_use2approx(use2approx ? Approx2State::On : Approx2State::Off)
        , m_eps(eps)
        , m_approx2SteinerTree(nullptr)
        , m_approx2Weight(0) {
        if (m_use2approx == Approx2State::On) { // add upper bound by 2-approximation
            MinSteinerTreeTakahashi<T> mstT;
            m_approx2Weight = mstT.call(m_G, m_terminals, m_isTerminal, m_approx2SteinerTree);
        }
 
        if (m_restricted > m_terminals.size()) {
            m_restricted = m_terminals.size();
        }
 
        findFullComponents();
 
        steiner_tree::LPRelaxationSER<T> lp(m_G, m_terminals, m_isTerminal, m_fullCompStore,
                m_approx2Weight, separateCycles ? m_restricted + 1 : 0, m_eps);
        if (!lp.solve()) {
            OGDF_ASSERT(m_use2approx == Approx2State::On);
            m_use2approx = Approx2State::JustUseIt;
        }
    }
 
    ~Main() { }
 
    T getApproximation(EdgeWeightedGraphCopy<T>*& finalSteinerTree, const std::minstd_rand& rng,
            const bool doPreprocessing = true);
};
 
template<typename T>
void MinSteinerTreeGoemans139<T>::Main::findFull2Components(const NodeArray<NodeArray<T>>& distance,
        const NodeArray<NodeArray<edge>>& pred) {
    steiner_tree::Full2ComponentGenerator<T> fcg;
    fcg.call(m_G, m_terminals, distance, pred, [&](node s, node t, T cost) {
        EdgeWeightedGraphCopy<T> minComp;
        minComp.setOriginalGraph(m_G);
        minComp.newEdge(minComp.newNode(s), minComp.newNode(t), distance[s][t]);
        m_fullCompStore.insert(minComp);
    });
}
 
template<typename T>
void MinSteinerTreeGoemans139<T>::Main::findFull3Components(const NodeArray<NodeArray<T>>& distance,
        const NodeArray<NodeArray<edge>>& pred) {
    steiner_tree::Full3ComponentGeneratorVoronoi<T> fcg;
    fcg.call(m_G, m_terminals, m_isTerminal, distance, pred,
            [&](node t0, node t1, node t2, node minCenter, T minCost) {
                // create a full 3-component
                EdgeWeightedGraphCopy<T> minComp;
                minComp.setOriginalGraph(m_G);
                node minCenterC = minComp.newNode(minCenter);
                minComp.newEdge(minComp.newNode(t0), minCenterC, distance[t0][minCenter]);
                minComp.newEdge(minComp.newNode(t1), minCenterC, distance[t1][minCenter]);
                minComp.newEdge(minComp.newNode(t2), minCenterC, distance[t2][minCenter]);
                m_fullCompStore.insert(minComp);
            });
}
 
template<typename T>
void MinSteinerTreeGoemans139<T>::Main::find3RestrictedComponents() {
    NodeArray<NodeArray<T>> distance;
    NodeArray<NodeArray<edge>> pred;
 
    steiner_tree::FullComponentGeneratorCaller<T>::computeDistanceMatrix(distance, pred, m_G,
            m_terminals, m_isTerminal, m_restricted);
 
    findFull2Components(distance, pred);
    if (m_restricted == 3) {
        findFull3Components(distance, pred);
    }
}
 
template<typename T>
template<typename FCG>
void MinSteinerTreeGoemans139<T>::Main::retrieveComponents(const FCG& fcg) {
    SubsetEnumerator<node> terminalSubset(m_terminals);
    for (terminalSubset.begin(2, m_restricted); terminalSubset.valid(); terminalSubset.next()) {
        EdgeWeightedGraphCopy<T> component;
        List<node> terminals;
        terminalSubset.list(terminals);
        fcg.getSteinerTreeFor(terminals, component);
        if (fcg.isValidComponent(component)) {
            m_fullCompStore.insert(component);
        }
    }
}
 
template<typename T>
void MinSteinerTreeGoemans139<T>::Main::findFullComponentsDW() {
    NodeArray<NodeArray<T>> distance;
    NodeArray<NodeArray<edge>> pred;
    steiner_tree::FullComponentGeneratorCaller<T>::computeDistanceMatrix(distance, pred, m_G,
            m_terminals, m_isTerminal, m_restricted);
 
    steiner_tree::FullComponentGeneratorDreyfusWagner<T> fcg(m_G, m_terminals, m_isTerminal,
            distance, pred);
    fcg.call(m_restricted);
    retrieveComponents(fcg);
}
 
template<typename T>
void MinSteinerTreeGoemans139<T>::Main::findFullComponentsEMV() {
    steiner_tree::FullComponentGeneratorDreyfusWagnerWithoutMatrix<T> fcg(m_G, m_terminals,
            m_isTerminal);
    fcg.call(m_restricted);
    retrieveComponents(fcg);
}
 
template<typename T>
void MinSteinerTreeGoemans139<T>::Main::findFullComponents() {
    if (m_restricted >= 4) { // use Dreyfus-Wagner based full component generation
        if (steiner_tree::FullComponentDecisions::shouldUseErickson(m_G.numberOfNodes(),
                    m_G.numberOfEdges())) {
            findFullComponentsEMV();
        } else {
            findFullComponentsDW();
        }
    } else {
        find3RestrictedComponents();
    }
}
 
template<typename T>
T MinSteinerTreeGoemans139<T>::Main::getApproximation(EdgeWeightedGraphCopy<T>*& finalSteinerTree,
        const std::minstd_rand& rng, const bool doPreprocessing) {
    if (m_use2approx == Approx2State::JustUseIt) {
        // no remaining components
        finalSteinerTree = m_approx2SteinerTree;
        return m_approx2Weight;
    }
 
    removeInactiveComponents();
 
    NodeArray<bool> isNewTerminal(m_G, false);
    for (node v : m_terminals) {
        isNewTerminal[v] = true;
    }
 
    if (doPreprocessing) {
        preprocess(isNewTerminal);
    }
 
    if (!m_fullCompStore.isEmpty()) {
        steiner_tree::goemans::Approximation<T> approx(m_G, m_terminals, m_isTerminal,
                m_fullCompStore, rng, m_eps);
        approx.solve(isNewTerminal);
    }
 
    T cost = steiner_tree::obtainFinalSteinerTree(m_G, isNewTerminal, m_isTerminal, finalSteinerTree);
 
    if (m_use2approx != Approx2State::Off) {
        if (m_approx2Weight < cost) {
            delete finalSteinerTree;
            finalSteinerTree = m_approx2SteinerTree;
            cost = m_approx2Weight;
        } else {
            delete m_approx2SteinerTree;
        }
    }
 
    return cost;
}
 
}