FullComponentGeneratorDreyfusWagnerWithoutMatrix.h

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#pragma once
 
#include <ogdf/basic/Hashing.h>
#include <ogdf/basic/Math.h>
#include <ogdf/basic/SubsetEnumerator.h>
#include <ogdf/graphalg/MinSteinerTreeModule.h>
#include <ogdf/graphalg/steiner_tree/EdgeWeightedGraphCopy.h>
 
namespace ogdf {
namespace steiner_tree {
 
template<typename T>
class FullComponentGeneratorDreyfusWagnerWithoutMatrix {
    const EdgeWeightedGraph<T>& m_G; 
    const List<node>& m_terminals; 
    const NodeArray<bool>& m_isTerminal; 
 
    class AuxiliaryGraph {
        const EdgeWeightedGraph<T>& m_original; 
        EdgeWeightedGraph<T> m_copy; 
        NodeArray<node> m_copyOfNode; 
        NodeArray<node> m_origOfNode; 
        EdgeArray<edge> m_origOfEdge; 
        NodeArray<bool> m_isTerminal; 
 
        node m_source; 
 
    public:
        AuxiliaryGraph(const EdgeWeightedGraph<T>& orig, const List<node>& terminals)
            : m_original(orig)
            , m_copyOfNode(m_original)
            , m_origOfNode(m_copy, nullptr)
            , m_origOfEdge(m_copy, nullptr)
            , m_isTerminal(m_copy, false) {
            // copy nodes and edges
            for (node v : m_original.nodes) {
                node vCopy = m_copy.newNode();
                m_copyOfNode[v] = vCopy;
                m_origOfNode[vCopy] = v;
            }
            for (edge e : m_original.edges) {
                edge eCopy =
                        m_copy.newEdge(copy(e->source()), copy(e->target()), m_original.weight(e));
                m_origOfEdge[eCopy] = e;
            }
 
            // set terminals
            for (node v : terminals) {
                m_isTerminal[copy(v)] = true;
            }
 
            // initialize source node and its edges to every other node
            m_source = m_copy.newNode();
            for (node w : m_original.nodes) {
                m_copy.newEdge(m_source, copy(w), std::numeric_limits<T>::max());
            }
        }
 
        node copy(node v) const {
            OGDF_ASSERT(v->graphOf() == &m_original);
            return m_copyOfNode[v];
        }
 
        node original(node v) const {
            OGDF_ASSERT(v->graphOf() == &m_copy);
            return m_origOfNode[v];
        }
 
        edge original(edge e) const {
            OGDF_ASSERT(e->graphOf() == &m_copy);
            return m_origOfEdge[e];
        }
 
        node source() const { return m_source; }
 
        const EdgeWeightedGraph<T>& graph() const { return m_copy; }
 
        const NodeArray<bool>& terminalArray() const { return m_isTerminal; }
 
        T weight(edge e) const {
            OGDF_ASSERT(e->graphOf() == &m_copy);
            return m_copy.weight(e);
        }
 
        void setWeight(edge e, T value) {
            OGDF_ASSERT(e->graphOf() == &m_copy);
            m_copy.setWeight(e, value);
        }
    };
 
    AuxiliaryGraph m_auxG; 
    SubsetEnumerator<node> m_terminalSubset; 
 
    struct DWMData {
        T cost;
        ArrayBuffer<edge> edges;
        ArrayBuffer<const DWMData*> subgraphs;
 
        DWMData(T _cost, ArrayBuffer<edge> _edges) : cost(_cost), edges(_edges) { }
 
        explicit DWMData(T _cost = std::numeric_limits<T>::max()) : cost(_cost) { }
 
        void invalidate() {
            edges.clear();
            subgraphs.clear();
        }
 
        bool valid() const { return cost == 0 || !(edges.empty() && subgraphs.empty()); }
 
        void add(const DWMData* other) {
            if (valid()) {
                if (other->valid()) {
                    subgraphs.push(other);
                } else {
                    invalidate();
                }
            }
            cost += other->cost;
        }
 
        void clear() {
            invalidate();
            cost = 0; // make it valid again
        }
 
        void add(edge e, T c) {
            if (valid()) {
                edges.push(e);
            }
            cost += c;
        }
    };
 
    struct DWMSplit {
        T cost = std::numeric_limits<T>::max();
        const DWMData* subgraph1 = nullptr;
        const DWMData* subgraph2 = nullptr;
 
        void set(const DWMData* s1, const DWMData* s2) {
            subgraph1 = s1;
            subgraph2 = s2;
            cost = s1->cost + s2->cost;
        }
    };
 
    class SortedNodeListHashFunc;
 
    Hashing<List<node>, DWMData, SortedNodeListHashFunc> m_map;
 
    const DWMData* dataOf(const List<node>& key) const {
        OGDF_ASSERT(key.size() > 1);
        OGDF_ASSERT(m_map.member(key));
        return &m_map.lookup(key)->info();
    }
 
    T costOf(const List<node>& key) const {
        OGDF_ASSERT(key.size() > 1);
        return dataOf(key)->cost;
    }
 
    bool safeIfSumSmaller(const T summand1, const T summand2, const T compareValue) const {
#ifdef OGDF_FULL_COMPONENT_GENERATION_ALWAYS_SAFE
        return summand1 + summand2 < compareValue;
#else
        return summand1 < std::numeric_limits<T>::max() && summand2 < std::numeric_limits<T>::max()
                && summand1 + summand2 < compareValue;
#endif
    }
 
    static void sortedInserter(node w, List<node>& list, bool& inserted, node newNode) {
        if (!inserted && w->index() > newNode->index()) {
            list.pushBack(newNode);
            inserted = true;
        }
        list.pushBack(w);
    }
 
    void makeKey(List<node>& newSubset, node v) const {
        bool inserted = false;
        m_terminalSubset.forEachMember([&](node w) { sortedInserter(w, newSubset, inserted, v); });
        if (!inserted) {
            newSubset.pushBack(v);
        }
    }
 
    void makeKey(List<node>& newSubset, List<node>& newComplement,
            const SubsetEnumerator<node>& subset, node v) const {
        bool insertedIntoSubset = false;
        bool insertedIntoComplement = false;
        // Interestingly std::bind is much slower than using lambdas (at least on g++ 6.3)
        subset.forEachMemberAndNonmember(
                [&](node w) { sortedInserter(w, newSubset, insertedIntoSubset, v); },
                [&](node w) { sortedInserter(w, newComplement, insertedIntoComplement, v); });
        if (!insertedIntoSubset) {
            newSubset.pushBack(v);
        }
        if (!insertedIntoComplement) {
            newComplement.pushBack(v);
        }
    }
 
    void computeSplit(NodeArray<DWMSplit>& split, node v, SubsetEnumerator<node>& subset) const {
        OGDF_ASSERT(v->graphOf() == &m_G);
        OGDF_ASSERT(split[v].subgraph1 == nullptr);
        OGDF_ASSERT(split[v].subgraph2 == nullptr);
 
        DWMSplit& best = split[v];
        for (subset.begin(1, subset.numberOfMembersAndNonmembers() / 2); subset.valid();
                subset.next()) {
            List<node> newSubset, newComplement;
            makeKey(newSubset, newComplement, subset, v);
 
            if (safeIfSumSmaller(costOf(newSubset), costOf(newComplement), best.cost)) {
                best.set(dataOf(newSubset), dataOf(newComplement));
            }
        }
    }
 
    template<typename CONTAINER>
    void computePartialSolutions(const CONTAINER& targets) {
        OGDF_ASSERT(m_terminalSubset.size() >= 2);
 
        List<node> terminals;
        m_terminalSubset.list(terminals);
        SubsetEnumerator<node> subset(terminals); // done here because of linear running time
        NodeArray<DWMSplit> split(m_G);
 
        // update auxiliary graph
        updateAuxGraph(split, subset, costOf(terminals));
 
        // compute shortest-paths tree on graph
        NodeArray<T> distance;
        NodeArray<edge> pred;
        MinSteinerTreeModule<T>::singleSourceShortestPaths(m_auxG.graph(), m_auxG.source(),
                m_auxG.terminalArray(), distance, pred);
 
        // insert best subtrees
        insertBestSubtrees(targets, split, pred, distance, terminals);
    }
 
    void initializeMap() {
        for (node t : m_terminals) {
            NodeArray<T> distance;
            NodeArray<edge> pred;
            MinSteinerTreeModule<T>::singleSourceShortestPaths(m_G, t, m_isTerminal, distance, pred);
 
            for (node v : m_G.nodes) {
                // make key
                List<node> key;
                key.pushBack(t);
                if (v->index() < t->index()) {
                    key.pushFront(v);
                } else {
                    key.pushBack(v);
                }
 
                // insert if not already defined
                if (!m_map.member(key)) {
                    T dist = distance[v];
                    ArrayBuffer<edge> edges;
                    for (node curr = v; pred[curr] != nullptr; curr = pred[curr]->opposite(curr)) {
                        edges.push(pred[curr]);
                    }
                    m_map.fastInsert(key, DWMData(dist, edges));
                }
            }
        }
    }
 
    void updateAuxGraph(NodeArray<DWMSplit>& split, SubsetEnumerator<node>& subset, T oldCost) {
        for (adjEntry adj : m_auxG.source()->adjEntries) {
            node w = m_auxG.original(adj->twinNode());
            T cost = oldCost;
            if (!m_terminalSubset.hasMember(w)) {
                computeSplit(split, w, subset);
                cost = split[w].cost;
            }
            m_auxG.setWeight(adj->theEdge(), cost);
        }
    }
 
    edge addNewPath(DWMData& result, node curr, const NodeArray<edge>& pred) const {
        edge e = nullptr;
        while (curr != m_auxG.source()) {
            e = pred[curr];
            OGDF_ASSERT(e != nullptr);
            node prev = e->opposite(curr);
            OGDF_ASSERT(prev != curr);
            if (prev != m_auxG.source()) {
                edge eO = m_auxG.original(e);
                OGDF_ASSERT(eO != nullptr);
                result.add(eO, m_auxG.weight(e));
            }
            curr = prev;
        }
        OGDF_ASSERT(e != nullptr);
        OGDF_ASSERT(e->source() == curr);
        OGDF_ASSERT(curr == m_auxG.source());
 
        return e;
    }
 
    void insertInvalidBestSubtree(node v, const NodeArray<T>& distance, const List<node>& newSubset) {
        OGDF_ASSERT(v->graphOf() == &m_auxG.graph());
        OGDF_ASSERT(v != m_auxG.source());
        DWMData best(distance[v]);
        best.invalidate();
        m_map.fastInsert(newSubset, best);
    }
 
    void insertValidBestSubtree(node v, const NodeArray<DWMSplit>& split,
            const NodeArray<edge>& pred, const List<node>& newSubset, const List<node>& terminals) {
        OGDF_ASSERT(v->graphOf() == &m_auxG.graph());
        OGDF_ASSERT(v != m_auxG.source());
        DWMData best(0);
 
        edge e = addNewPath(best, v, pred);
        // add best solution so far
        node tO = m_auxG.original(e->target());
        if (m_terminalSubset.hasMember(tO)) {
            best.add(dataOf(terminals));
        } else {
            best.add(split[tO].subgraph1);
            best.add(split[tO].subgraph2);
        }
 
        m_map.fastInsert(newSubset, best);
    }
 
    template<typename CONTAINER>
    void insertBestSubtrees(const CONTAINER& targets, const NodeArray<DWMSplit>& split,
            const NodeArray<edge>& pred, const NodeArray<T>& distance, const List<node>& terminals) {
        for (node v : targets) {
            if (!m_terminalSubset.hasMember(v)) {
                List<node> newSubset;
                makeKey(newSubset, v);
 
                if (!m_map.member(newSubset)) { // not already defined
                    node vCopy = m_auxG.copy(v);
                    if (pred[m_auxG.copy(v)] == nullptr) { // path over terminal
                        insertInvalidBestSubtree(vCopy, distance, newSubset);
                    } else {
                        insertValidBestSubtree(vCopy, split, pred, newSubset, terminals);
                    }
                }
            }
        }
    }
 
    T getSteinerTreeFor(const DWMData& data, EdgeWeightedGraphCopy<T>& tree) const {
        T cost(0);
 
        if (data.valid()) {
            // add edges
            for (edge e : data.edges) {
                node uO = e->source();
                node vO = e->target();
                OGDF_ASSERT(uO != nullptr);
                OGDF_ASSERT(vO != nullptr);
                node uC = tree.copy(uO);
                node vC = tree.copy(vO);
                if (uC == nullptr) {
                    uC = tree.newNode(uO);
                }
                if (vC == nullptr) {
                    vC = tree.newNode(vO);
                }
                T dist = m_G.weight(e);
                tree.newEdge(e, dist);
                cost += dist;
            }
 
            // recurse
            for (const DWMData* subgraph : data.subgraphs) {
                cost += getSteinerTreeFor(*subgraph, tree);
            }
 
            OGDF_ASSERT(isAcyclicUndirected(tree));
        }
 
        return cost;
    }
 
public:
    FullComponentGeneratorDreyfusWagnerWithoutMatrix(const EdgeWeightedGraph<T>& G,
            const List<node>& terminals, const NodeArray<bool>& isTerminal)
        : m_G(G)
        , m_terminals(terminals)
        , m_isTerminal(isTerminal)
        , m_auxG(m_G, m_terminals)
        , m_terminalSubset(m_terminals)
        , m_map(1 << 22) { // we initially allocate 4MB*sizeof(DWMData) for hashing
    }
 
    void call(int restricted) {
        OGDF_ASSERT(restricted >= 2);
        Math::updateMin(restricted, m_terminals.size());
        initializeMap();
        for (m_terminalSubset.begin(2, restricted - 2); m_terminalSubset.valid();
                m_terminalSubset.next()) {
            computePartialSolutions(m_G.nodes);
        }
        // save time by only adding terminals instead of all nodes
        for (m_terminalSubset.begin(restricted - 1); m_terminalSubset.valid();
                m_terminalSubset.next()) {
            computePartialSolutions(m_terminals);
        }
    }
 
    T getSteinerTreeFor(const List<node>& terminals, EdgeWeightedGraphCopy<T>& tree) const {
        tree.setOriginalGraph(m_G);
        T cost(getSteinerTreeFor(*dataOf(terminals), tree));
        OGDF_ASSERT(isTree(tree));
        return cost;
    }
 
    bool isValidComponent(const EdgeWeightedGraphCopy<T>& tree) const {
        if (tree.empty()) {
            return false;
        }
        for (node v : tree.nodes) {
            OGDF_ASSERT(v->degree() > 1 || m_isTerminal[tree.original(v)]);
            if (m_isTerminal[tree.original(v)] // is a terminal
                    && v->degree() > 1) { // but not a leaf
                return false;
            }
        }
        return true;
    }
};
 
template<typename T>
class FullComponentGeneratorDreyfusWagnerWithoutMatrix<T>::SortedNodeListHashFunc {
    static const unsigned int c_prime = 0x7fffffff; // mersenne prime 2**31 - 1
    // would be nicer: 0x1fffffffffffffff; // mersenne prime 2**61 - 1
    const int m_random;
 
public:
    SortedNodeListHashFunc() : m_random(randomNumber(2, c_prime - 1)) { }
 
    unsigned int hash(const List<node>& key) const {
        unsigned int hash = 0;
        for (node v : key) {
            hash = (hash * m_random + v->index()) % c_prime;
        }
        return hash;
    }
};
 
}
}