MinSteinerTreeRZLoss.h

Go to the documentation of this file.

 
#pragma once
 
#include <ogdf/graphalg/MinSteinerTreeMehlhorn.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/FullComponentStore.h>
#include <ogdf/graphalg/steiner_tree/SaveStatic.h>
 
#include <memory>
#include <set>
 
#define OGDF_STEINERTREE_RZLOSS_REDUCE_ON
 
namespace ogdf {
 
template<typename T>
class MinSteinerTreeRZLoss : public MinSteinerTreeModule<T> {
    int m_restricted;
 
    class Main;
    std::unique_ptr<Main> m_alg;
 
public:
    MinSteinerTreeRZLoss() { setMaxComponentSize(3); }
 
    MinSteinerTreeRZLoss(int v) { setMaxComponentSize(v); }
 
    virtual ~MinSteinerTreeRZLoss() { }
 
    void setMaxComponentSize(int k) { m_restricted = k; }
 
    long numberOfGeneratedComponents() {
        if (m_alg == nullptr) {
            return 0;
        }
        return m_alg->numberOfGeneratedComponents();
    }
 
    long numberOfContractedComponents() {
        if (m_alg == nullptr) {
            return 0;
        }
        return m_alg->numberOfContractedComponents();
    }
 
    long numberOfComponentLookUps() {
        if (m_alg == nullptr) {
            return 0;
        }
        return m_alg->numberOfComponentLookUps();
    }
 
protected:
    virtual T computeSteinerTree(const EdgeWeightedGraph<T>& G, const List<node>& terminals,
            const NodeArray<bool>& isTerminal, EdgeWeightedGraphCopy<T>*& finalSteinerTree) override {
        m_alg.reset(new Main(G, terminals, isTerminal, m_restricted));
        return m_alg->getApproximation(finalSteinerTree);
    }
};
 
template<typename T>
class MinSteinerTreeRZLoss<T>::Main {
    template<typename TYPE>
    using SaveStatic = steiner_tree::SaveStatic<TYPE>;
 
 
    void findFullComponentsDW(const EdgeWeightedGraphCopy<T>& tree,
            const NodeArray<NodeArray<T>>& distance, const NodeArray<NodeArray<edge>>& pred);
    void findFullComponentsEMV(const EdgeWeightedGraphCopy<T>& tree);
    void findFull3Components(const EdgeWeightedGraphCopy<T>& tree,
            const NodeArray<NodeArray<T>>& distance, const NodeArray<NodeArray<edge>>& pred);
    template<typename FCG>
    void retrieveComponents(const FCG& fcg, const EdgeWeightedGraphCopy<T>& tree);
 
 
    void generateInitialTerminalSpanningTree(EdgeWeightedGraphCopy<T>& steinerTree,
            const NodeArray<NodeArray<T>>& distance, const NodeArray<NodeArray<edge>>& pred);
 
    void setup(EdgeWeightedGraphCopy<T>& tree) {
        tree.createEmpty(m_G);
 
        if (m_restricted >= 4
                && steiner_tree::FullComponentDecisions::shouldUseErickson(m_G.numberOfNodes(),
                        m_G.numberOfEdges())) {
            steiner_tree::constructTerminalSpanningTreeUsingVoronoiRegions(tree, m_G, m_terminals);
            m_save.reset(new steiner_tree::SaveStatic<T>(tree));
            findFullComponentsEMV(tree);
        } else {
            NodeArray<NodeArray<T>> distance;
            NodeArray<NodeArray<edge>> pred;
 
            steiner_tree::FullComponentGeneratorCaller<T>::computeDistanceMatrix(distance, pred,
                    m_G, m_terminals, m_isTerminal, m_restricted);
 
            generateInitialTerminalSpanningTree(tree, distance, pred);
            m_save.reset(new steiner_tree::SaveStatic<T>(tree));
 
            if (m_restricted >= 4) { // use Dreyfus-Wagner based full component generation
                findFullComponentsDW(tree, distance, pred);
            } else {
                findFull3Components(tree, distance, pred);
            }
        }
 
        m_fullCompStore.computeAllLosses();
        m_componentsGenerated = m_fullCompStore.size();
    }
 
    void multiPass(EdgeWeightedGraphCopy<T>& steinerTree);
 
    double extractMaxComponent(const EdgeWeightedGraphCopy<T>& steinerTree, int& maxCompId);
 
    template<typename TERMINAL_CONTAINER>
    T gain(const TERMINAL_CONTAINER& terminals, const EdgeWeightedGraphCopy<T>& steinerTree);
 
    void contractLoss(EdgeWeightedGraphCopy<T>& steinerTree, int compId);
 
    const EdgeWeightedGraph<T>& m_G; 
    const NodeArray<bool>& m_isTerminal; 
    List<node> m_terminals; 
    int m_restricted; 
    std::unique_ptr<steiner_tree::SaveStatic<T>> m_save; 
    steiner_tree::FullComponentWithLossStore<T> m_fullCompStore; 
    NodeArray<bool> m_isNewTerminal; 
 
    long m_componentsGenerated; 
    long m_componentsContracted; 
    long m_componentsLookUps; 
 
public:
    Main(const EdgeWeightedGraph<T>& G, const List<node>& terminals,
            const NodeArray<bool>& isTerminal, int restricted);
 
    T getApproximation(EdgeWeightedGraphCopy<T>*& finalSteinerTree) const {
        // obtain final Steiner Tree using (MST-based) Steiner tree approximation algorithm
        return steiner_tree::obtainFinalSteinerTree(m_G, m_isNewTerminal, m_isTerminal,
                finalSteinerTree);
    }
 
    long numberOfGeneratedComponents() { return m_componentsGenerated; }
 
    long numberOfContractedComponents() { return m_componentsContracted; }
 
    long numberOfComponentLookUps() { return m_componentsLookUps; }
};
 
template<typename T>
MinSteinerTreeRZLoss<T>::Main::Main(const EdgeWeightedGraph<T>& G, const List<node>& terminals,
        const NodeArray<bool>& isTerminal, int restricted)
    : m_G(G)
    , m_isTerminal(isTerminal)
    , m_terminals(terminals)
    , // copy
    m_restricted(min(restricted, terminals.size()))
    , m_fullCompStore(m_G, m_terminals, m_isTerminal)
    , m_isNewTerminal(m_G, false)
    , m_componentsGenerated(0)
    , m_componentsContracted(0)
    , m_componentsLookUps(0) {
    MinSteinerTreeModule<T>::sortTerminals(m_terminals);
 
    for (node v : terminals) {
        m_isNewTerminal[v] = true;
    }
 
    // init terminal-spanning tree and its save-edge data structure
    EdgeWeightedGraphCopy<T> steinerTree; // the terminal-spanning tree to be modified
 
    setup(steinerTree);
 
    // contraction phase
    multiPass(steinerTree);
 
    m_save.reset();
}
 
template<typename T>
void MinSteinerTreeRZLoss<T>::Main::generateInitialTerminalSpanningTree(
        EdgeWeightedGraphCopy<T>& steinerTree, const NodeArray<NodeArray<T>>& distance,
        const NodeArray<NodeArray<edge>>& pred) {
    // generate complete graph
    for (node v : m_terminals) {
        steinerTree.newNode(v);
    }
    for (node u : steinerTree.nodes) {
        const node uO = steinerTree.original(u);
        const NodeArray<T>& dist = distance[uO];
        const NodeArray<edge>& p = pred[uO];
        for (node v = u->succ(); v; v = v->succ()) {
            const node vO = steinerTree.original(v);
            if (p[vO] != nullptr) {
                steinerTree.newEdge(u, v, dist[vO]);
            }
        }
    }
    // compute MST
    makeMinimumSpanningTree(steinerTree, steinerTree.edgeWeights());
    OGDF_ASSERT(steinerTree.numberOfNodes() == steinerTree.numberOfEdges() + 1);
}
 
template<typename T>
void MinSteinerTreeRZLoss<T>::Main::findFull3Components(const EdgeWeightedGraphCopy<T>& tree,
        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.createEmpty(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]);
                OGDF_ASSERT(isTree(minComp));
#ifdef OGDF_STEINERTREE_RZLOSS_REDUCE_ON
                if (gain(std::vector<node> {t0, t1, t2}, tree) > minCost) { // reduction
                    m_fullCompStore.insert(minComp);
                }
#else
        m_fullCompStore.insert(minComp);
#endif
            });
}
 
template<typename T>
template<typename FCG>
void MinSteinerTreeRZLoss<T>::Main::retrieveComponents(const FCG& fcg,
        const EdgeWeightedGraphCopy<T>& tree) {
    SubsetEnumerator<node> terminalSubset(m_terminals);
    for (terminalSubset.begin(3, m_restricted); terminalSubset.valid(); terminalSubset.next()) {
        EdgeWeightedGraphCopy<T> component;
        List<node> terminals;
        terminalSubset.list(terminals);
#ifdef OGDF_STEINERTREE_RZLOSS_REDUCE_ON
        T cost =
#endif
                fcg.getSteinerTreeFor(terminals, component);
        if (
#ifdef OGDF_STEINERTREE_RZLOSS_REDUCE_ON
                gain(terminals, tree) > cost &&
#endif
                fcg.isValidComponent(component)) {
            m_fullCompStore.insert(component);
        }
    }
}
 
template<typename T>
void MinSteinerTreeRZLoss<T>::Main::findFullComponentsDW(const EdgeWeightedGraphCopy<T>& tree,
        const NodeArray<NodeArray<T>>& distance, const NodeArray<NodeArray<edge>>& pred) {
    steiner_tree::FullComponentGeneratorDreyfusWagner<T> fcg(m_G, m_terminals, m_isTerminal,
            distance, pred);
    fcg.call(m_restricted);
    retrieveComponents(fcg, tree);
}
 
template<typename T>
void MinSteinerTreeRZLoss<T>::Main::findFullComponentsEMV(const EdgeWeightedGraphCopy<T>& tree) {
    steiner_tree::FullComponentGeneratorDreyfusWagnerWithoutMatrix<T> fcg(m_G, m_terminals,
            m_isTerminal);
    fcg.call(m_restricted);
    retrieveComponents(fcg, tree);
}
 
template<typename T>
void MinSteinerTreeRZLoss<T>::Main::multiPass(EdgeWeightedGraphCopy<T>& steinerTree) {
    while (!m_fullCompStore.isEmpty()) {
        int maxCompId;
        double r = extractMaxComponent(steinerTree, maxCompId);
        if (r > 1e-9) {
            ++m_componentsContracted;
 
            // convert nodes of component to terminals
            m_fullCompStore.foreachNode(maxCompId, [&](node v) { m_isNewTerminal[v] = true; });
 
            contractLoss(steinerTree, maxCompId);
            m_fullCompStore.remove(maxCompId);
 
            if (!m_fullCompStore.isEmpty()) {
                m_save->rebuild();
            }
        } else {
            return;
        }
    }
}
 
template<typename T>
double MinSteinerTreeRZLoss<T>::Main::extractMaxComponent(
        const EdgeWeightedGraphCopy<T>& steinerTree, int& maxCompId) {
    maxCompId = -1;
    double max(0);
    for (int i = 0; i < m_fullCompStore.size();) {
        ++m_componentsLookUps;
        const double winAbs =
                gain(m_fullCompStore.terminals(i), steinerTree) - m_fullCompStore.cost(i);
        if (winAbs > 1e-9) {
            const double r = winAbs / m_fullCompStore.loss(i);
            if (r > max) {
                max = r;
                maxCompId = i;
            }
            ++i;
        }
#ifdef OGDF_STEINERTREE_RZLOSS_REDUCE_ON
        else {
            // reduction
            m_fullCompStore.remove(i);
        }
#endif
    }
    return max;
}
 
template<typename T>
template<typename TERMINAL_CONTAINER>
T MinSteinerTreeRZLoss<T>::Main::gain(const TERMINAL_CONTAINER& terminals,
        const EdgeWeightedGraphCopy<T>& steinerTree) {
    std::set<edge> saveEdges;
    T result(0);
 
    // extract edges and compute their sum (result value)
    for (auto it1 = terminals.begin(); it1 != terminals.end(); ++it1) {
        auto next = it1;
        ++next;
        for (auto it2 = next; it2 != terminals.end(); ++it2) {
            const edge e = m_save->saveEdge(*it1, *it2);
            saveEdges.insert(e);
        }
    }
 
    for (edge e : saveEdges) {
        result += steinerTree.weight(e);
    }
    return result;
}
 
template<typename T>
void MinSteinerTreeRZLoss<T>::Main::contractLoss(EdgeWeightedGraphCopy<T>& steinerTree, int compId) {
    // for every non-loss edge {st} in the component,
    // where s belongs to the loss component of terminal u
    //   and t belongs to the loss component of terminal v,
    // we insert edges from u to v in the terminal-spanning tree
    for (edge e : m_fullCompStore.lossBridges(compId)) {
        const node u = m_fullCompStore.lossTerminal(e->source());
        OGDF_ASSERT(u);
        const node v = m_fullCompStore.lossTerminal(e->target());
        OGDF_ASSERT(v);
        steinerTree.newEdge(steinerTree.copy(u), steinerTree.copy(v),
                m_fullCompStore.graph().weight(e));
        // parallel edges are ok, will be removed by MST
    }
    if (steinerTree.numberOfNodes() != steinerTree.numberOfEdges() + 1) {
        makeMinimumSpanningTree(steinerTree, steinerTree.edgeWeights());
    }
}
 
}