MinSteinerTreeShore.h

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#pragma once
 
// enable this to print messages
// for all branches (edge inclusion or exclusion)
// additionally a SVG image is generated for each
// recursion depth
//#define OGDF_MINSTEINERTREE_SHORE_LOGGING
 
#include <ogdf/basic/EdgeArray.h>
#include <ogdf/basic/List.h>
#include <ogdf/basic/NodeArray.h>
#include <ogdf/basic/NodeSet.h>
#include <ogdf/graphalg/MinSteinerTreeModule.h>
#include <ogdf/graphalg/steiner_tree/EdgeWeightedGraphCopy.h>
 
#include <memory>
 
namespace ogdf {
 
template<typename T>
class MinSteinerTreeShore : public MinSteinerTreeModule<T> {
public:
    MinSteinerTreeShore() : MAX_WEIGHT(std::numeric_limits<T>::max()) {};
    virtual ~MinSteinerTreeShore() {};
 
protected:
    virtual T computeSteinerTree(const EdgeWeightedGraph<T>& G, const List<node>& terminals,
            const NodeArray<bool>& isTerminal, EdgeWeightedGraphCopy<T>*& finalSteinerTree) override;
 
    const T MAX_WEIGHT;
 
private:
    const EdgeWeightedGraph<T>* m_originalGraph;
    const List<node>* m_originalTerminals;
 
    Graph m_graph;
    std::unique_ptr<NodeSet<>> m_terminals;
    EdgeArray<edge> m_mapping;
    T m_upperBound;
    Array2D<edge> m_edges;
    List<edge> m_chosenEdges;
    int m_recursionDepth;
 
    bool validateMapping() const;
 
    T weightOf(edge e) const;
 
    T bnbInternal(T prevCost, List<edge>& currentEdges);
 
    edge deleteEdge(edge e);
 
    edge newEdge(node source, node target, const edge originalEdge);
 
    void moveSource(edge e, node v);
 
    void moveTarget(edge e, node v);
 
    void setTerminal(const node v, bool makeTerminal);
 
    bool isTerminal(const node v) const;
 
    void setEdgeLookup(const node u, const node v, const edge e);
 
    edge lookupEdge(const node u, const node v) const;
 
    edge determineBranchingEdge(T prevCost) const;
 
    T solve(List<edge>& chosenEdges);
 
    void printSVG();
};
 
template<typename T>
T MinSteinerTreeShore<T>::computeSteinerTree(const EdgeWeightedGraph<T>& G,
        const List<node>& terminals, const NodeArray<bool>& isTerminal,
        EdgeWeightedGraphCopy<T>*& finalSteinerTree) {
    m_originalGraph = &G;
    m_originalTerminals = &terminals;
 
    m_upperBound = MAX_WEIGHT;
    m_graph.clear();
    m_mapping.init(m_graph);
    m_terminals.reset(new NodeSet<>(m_graph));
    int nodeCount = m_originalGraph->numberOfNodes();
    m_edges = Array2D<edge>(0, nodeCount, 0, nodeCount, nullptr);
 
    NodeArray<node> copiedNodes(*m_originalGraph);
 
    for (node v : m_originalGraph->nodes) {
        node copiedNode = m_graph.newNode();
        copiedNodes[v] = copiedNode;
    }
 
    for (edge e : m_originalGraph->edges) {
        node source = copiedNodes[e->source()], target = copiedNodes[e->target()];
 
        newEdge(source, target, e);
    }
 
    for (node v : *m_originalTerminals) {
        setTerminal(copiedNodes[v], true);
    }
 
    List<edge> chosenEdges;
    T result = solve(chosenEdges);
 
    finalSteinerTree = new EdgeWeightedGraphCopy<T>();
    finalSteinerTree->setOriginalGraph(*m_originalGraph);
 
    for (edge e : chosenEdges) {
        node v = e->source();
        node w = e->target();
 
        OGDF_ASSERT(v != nullptr);
        OGDF_ASSERT(w != nullptr);
        OGDF_ASSERT(e->graphOf() == m_originalGraph);
        OGDF_ASSERT(v->graphOf() == m_originalGraph);
        OGDF_ASSERT(w->graphOf() == m_originalGraph);
 
        if (finalSteinerTree->copy(v) == nullptr) {
            finalSteinerTree->newNode(v);
        }
        if (finalSteinerTree->copy(w) == nullptr) {
            finalSteinerTree->newNode(w);
        }
        finalSteinerTree->newEdge(e, m_originalGraph->weight(e));
    }
 
    return result;
}
 
template<typename T>
T MinSteinerTreeShore<T>::weightOf(const edge e) const {
    T result = MAX_WEIGHT;
 
    if (e != nullptr) {
        OGDF_ASSERT(e->graphOf() == &m_graph);
        OGDF_ASSERT(m_mapping[e] != nullptr);
        OGDF_ASSERT(m_mapping[e]->graphOf() == m_originalGraph);
        result = m_originalGraph->weight(m_mapping[e]);
    }
 
    return result;
}
 
template<typename T>
bool MinSteinerTreeShore<T>::validateMapping() const {
    for (edge e : m_graph.edges) {
        OGDF_ASSERT(m_mapping[e] != nullptr);
        OGDF_ASSERT(m_mapping[e]->graphOf() == m_originalGraph);
    }
    return true;
}
 
template<typename T>
edge MinSteinerTreeShore<T>::lookupEdge(const node u, const node v) const {
    return m_edges(u->index(), v->index());
}
 
template<typename T>
void MinSteinerTreeShore<T>::setEdgeLookup(const node u, const node v, const edge e) {
    m_edges(u->index(), v->index()) = m_edges(v->index(), u->index()) = e;
}
 
template<typename T>
edge MinSteinerTreeShore<T>::deleteEdge(edge e) {
    edge result = m_mapping[e];
    setEdgeLookup(e->source(), e->target(), nullptr);
    m_graph.delEdge(e);
    e->~EdgeElement();
 
    return result;
}
 
template<typename T>
edge MinSteinerTreeShore<T>::newEdge(node source, node target, edge e) {
    edge result = m_graph.newEdge(source, target);
    m_mapping[result] = e;
    setEdgeLookup(source, target, result);
 
    return result;
}
 
template<typename T>
void MinSteinerTreeShore<T>::moveSource(edge e, node v) {
    OGDF_ASSERT(e != nullptr);
    setEdgeLookup(e->source(), e->target(), nullptr);
    setEdgeLookup(v, e->target(), e);
    m_graph.moveSource(e, v);
}
 
template<typename T>
void MinSteinerTreeShore<T>::moveTarget(edge e, node v) {
    OGDF_ASSERT(e != nullptr);
    setEdgeLookup(e->source(), e->target(), nullptr);
    setEdgeLookup(e->source(), v, e);
    m_graph.moveTarget(e, v);
}
 
template<typename T>
bool MinSteinerTreeShore<T>::isTerminal(const node v) const {
    return m_terminals->isMember(v);
}
 
template<typename T>
void MinSteinerTreeShore<T>::setTerminal(const node v, bool makeTerminal) {
    if (makeTerminal) {
        m_terminals->insert(v);
    } else {
        m_terminals->remove(v);
    }
}
 
template<typename T>
T MinSteinerTreeShore<T>::solve(List<edge>& chosenEdges) {
    m_chosenEdges.clear();
 
    m_recursionDepth = 0;
    List<edge> tmp;
    T result = bnbInternal(0, tmp);
 
    for (edge e : m_chosenEdges) {
        chosenEdges.pushFront(e);
    }
 
    return result;
}
 
template<typename T>
edge MinSteinerTreeShore<T>::determineBranchingEdge(T prevCost) const {
    edge result = nullptr;
    T maxPenalty = -1;
 
    // calculate penalties for nodes
    T sumOfMinWeights = 0; // b
    T sumOfMinTermWeights = 0; // c
    T absoluteMinTermWeight = MAX_WEIGHT;
    for (ListConstIterator<node> it = m_terminals->nodes().begin();
            sumOfMinWeights < MAX_WEIGHT && it.valid(); ++it) {
        const node t = *it;
        T minTermWeight = MAX_WEIGHT, minWeight = MAX_WEIGHT, secondMinWeight = MAX_WEIGHT;
        edge minEdge = nullptr;
 
        // investigate all edges of each terminal
        // calculate lower boundary and find branching edge
        for (adjEntry adj = t->firstAdj(); adj; adj = adj->succ()) {
            edge e = adj->theEdge();
            if (weightOf(e) < minWeight) {
                secondMinWeight = minWeight;
                minWeight = weightOf(e);
                minEdge = e;
            } else {
                if (weightOf(e) < secondMinWeight) {
                    secondMinWeight = weightOf(e);
                }
            }
 
            if (isTerminal(adj->twinNode()) && weightOf(e) < minTermWeight) {
                minTermWeight = weightOf(e);
                if (minTermWeight < absoluteMinTermWeight) {
                    absoluteMinTermWeight = minTermWeight;
                }
            }
        }
 
        if (sumOfMinTermWeights < MAX_WEIGHT && minTermWeight < MAX_WEIGHT) {
            sumOfMinTermWeights += minTermWeight;
        } else {
            sumOfMinTermWeights = MAX_WEIGHT;
        }
        OGDF_ASSERT(absoluteMinTermWeight <= sumOfMinTermWeights);
 
        // is terminal isolated or has only one edge?
        // if so we can break here
        if (minWeight == MAX_WEIGHT || secondMinWeight == MAX_WEIGHT) {
            result = minEdge;
            if (minWeight == MAX_WEIGHT) {
                sumOfMinWeights = MAX_WEIGHT;
            }
        } else {
            sumOfMinWeights += minWeight;
            // update branching edge if need be
            T penalty = secondMinWeight - minWeight;
            if (penalty > maxPenalty) {
                maxPenalty = penalty;
                result = minEdge;
            }
        }
    }
 
    // compare bounds for this graph
    if (result != nullptr) {
        T maxCost = m_upperBound - prevCost;
        if (sumOfMinTermWeights < MAX_WEIGHT) {
            sumOfMinTermWeights -= absoluteMinTermWeight;
        }
        if (maxCost <= sumOfMinWeights && maxCost <= sumOfMinTermWeights) {
            result = nullptr;
        }
    }
 
    return result;
}
 
template<typename T>
T MinSteinerTreeShore<T>::bnbInternal(T prevCost, List<edge>& currentEdges) {
    T result = MAX_WEIGHT;
    m_recursionDepth++;
 
#ifdef OGDF_MINSTEINERTREE_SHORE_LOGGING
    printSVG();
#endif
 
    if (prevCost <= m_upperBound) {
        if (m_terminals->size() < 2) {
            // update currently chosen edges
            if (prevCost != m_upperBound || m_chosenEdges.empty()) {
                m_chosenEdges = List<edge>(currentEdges);
            }
            // all terminals are connected
            m_upperBound = prevCost;
            result = prevCost;
        } else {
            edge branchingEdge = determineBranchingEdge(prevCost);
            T branchingEdgeWeight = weightOf(branchingEdge);
 
#ifdef OGDF_MINSTEINERTREE_SHORE_LOGGING
            for (int i = 0; i < m_recursionDepth; i++) {
                std::cout << " ";
            }
            std::cout << "branching on edge: " << branchingEdge << std::endl;
#endif
            // branching edge has been found or there is no feasible solution
            if (branchingEdgeWeight < MAX_WEIGHT) {
                // chose node to remove
                node nodeToRemove = branchingEdge->source();
                node targetNode = branchingEdge->target();
 
                // This seems to speed up things.
                if (nodeToRemove->degree() < targetNode->degree()) {
                    nodeToRemove = branchingEdge->target();
                    targetNode = branchingEdge->source();
                }
 
                // remove branching edge
                edge origBranchingEdge = deleteEdge(branchingEdge);
 
                List<node> delEdges, movedEdges;
                List<edge> origDelEdges;
 
                // first branch: Inclusion of the edge
                // remove source node of edge and calculate new edge weights
                OGDF_ASSERT(targetNode != nullptr);
                OGDF_ASSERT(nodeToRemove != nullptr);
 
                // remove edges in case of multigraph
                while (m_graph.searchEdge(targetNode, nodeToRemove) != nullptr) {
                    edge e = m_graph.searchEdge(targetNode, nodeToRemove);
                    delEdges.pushFront(e->target());
                    delEdges.pushFront(e->source());
                    origDelEdges.pushFront(m_mapping[e]);
                    deleteEdge(e);
                }
                while (m_graph.searchEdge(nodeToRemove, targetNode) != nullptr) {
                    edge e = m_graph.searchEdge(targetNode, nodeToRemove);
                    delEdges.pushFront(e->target());
                    delEdges.pushFront(e->source());
                    origDelEdges.pushFront(m_mapping[e]);
                    deleteEdge(e);
                }
 
                OGDF_ASSERT(m_graph.searchEdge(targetNode, nodeToRemove) == nullptr);
                OGDF_ASSERT(m_graph.searchEdge(nodeToRemove, targetNode) == nullptr);
 
                adjEntry adjNext;
                for (adjEntry adj = nodeToRemove->firstAdj(); adj; adj = adjNext) {
                    adjNext = adj->succ();
                    edge e = adj->theEdge();
 
                    OGDF_ASSERT(e != branchingEdge);
                    OGDF_ASSERT(e->target() == nodeToRemove || e->source() == nodeToRemove);
                    OGDF_ASSERT(adj->twinNode() != targetNode);
 
                    edge f = lookupEdge(targetNode, adj->twinNode());
                    bool deletedEdgeE = false;
                    if (f != nullptr) {
                        if (weightOf(f) < weightOf(e)) {
                            delEdges.pushFront(e->target());
                            delEdges.pushFront(e->source());
                            origDelEdges.pushFront(m_mapping[e]);
                            deleteEdge(e);
 
                            deletedEdgeE = true;
                        } else {
                            delEdges.pushFront(f->target());
                            delEdges.pushFront(f->source());
                            origDelEdges.pushFront(m_mapping[f]);
                            deleteEdge(f);
                        }
                    }
                    if (!deletedEdgeE) {
                        if (e->target() == nodeToRemove) {
                            OGDF_ASSERT(e->source() != targetNode);
                            movedEdges.pushFront(e->source());
                            moveTarget(e, targetNode);
                        } else {
                            OGDF_ASSERT(e->source() == nodeToRemove);
                            OGDF_ASSERT(e->target() != targetNode);
                            movedEdges.pushFront(e->target());
                            moveSource(e, targetNode);
                        }
                    }
                }
                // nodeToRemove is isolated at this point
                // thus no need to actually remove it
                // (easier to keep track of CopyGraph mapping)
 
                // remove node from terminals too
                bool targetNodeIsTerminal = isTerminal(targetNode),
                     nodeToRemoveIsTerminal = isTerminal(nodeToRemove);
 
                OGDF_ASSERT(targetNodeIsTerminal || nodeToRemoveIsTerminal);
                setTerminal(nodeToRemove, false);
                setTerminal(targetNode, true);
 
#ifdef OGDF_MINSTEINERTREE_SHORE_LOGGING
                for (int i = 0; i < m_recursionDepth; i++) {
                    std::cout << " ";
                }
                std::cout << "inclusion branch" << std::endl;
#endif
                // calculate result on modified graph
                currentEdges.pushFront(origBranchingEdge);
                result = bnbInternal(branchingEdgeWeight + prevCost, currentEdges);
                OGDF_ASSERT(currentEdges.front() == origBranchingEdge);
                currentEdges.popFront();
 
                // restore previous graph
 
                // restore terminals
                setTerminal(nodeToRemove, nodeToRemoveIsTerminal);
                setTerminal(targetNode, targetNodeIsTerminal);
 
                // restore moved edges
                while (!movedEdges.empty()) {
                    node v = movedEdges.popFrontRet();
 
                    edge e = lookupEdge(v, targetNode);
                    OGDF_ASSERT(e != nullptr);
                    OGDF_ASSERT(e->opposite(targetNode) != nodeToRemove);
 
                    if (e->source() == v) {
                        moveTarget(e, nodeToRemove);
                    } else {
                        moveSource(e, nodeToRemove);
                    }
                }
 
                // restore deleted edges
                while (!delEdges.empty()) {
                    OGDF_ASSERT(!origDelEdges.empty());
 
                    node source = delEdges.popFrontRet();
                    node target = delEdges.popFrontRet();
 
                    newEdge(source, target, origDelEdges.popFrontRet());
                }
                OGDF_ASSERT(origDelEdges.empty());
 
#ifdef OGDF_MINSTEINERTREE_SHORE_LOGGING
                for (int i = 0; i < m_recursionDepth; i++) {
                    std::cout << " ";
                }
                std::cout << "exclusion branch" << std::endl;
#endif
                // sencond branch: Exclusion of the edge
                T exEdgeResult = bnbInternal(prevCost, currentEdges);
 
                // decide which branch returned best result
                if (exEdgeResult < result) {
                    result = exEdgeResult;
                }
 
                // finally: restore the branching edge
                newEdge(nodeToRemove, targetNode, origBranchingEdge);
            }
        }
        OGDF_ASSERT(validateMapping());
    }
    m_recursionDepth--;
    return result;
}
 
template<typename T>
void MinSteinerTreeShore<T>::printSVG() {
    EdgeWeightedGraphCopy<T> copiedGraph;
    copiedGraph.setOriginalGraph(m_graph);
    List<node> nodes;
    m_graph.allNodes(nodes);
    NodeArray<bool> copiedIsTerminal(m_graph);
    for (node v : nodes) {
        copiedGraph.newNode(v);
        copiedIsTerminal[v] = isTerminal(v);
    }
    List<edge> edges;
    m_graph.allEdges(edges);
    for (edge e : edges) {
        copiedGraph.newEdge(e, weightOf(e));
    }
    std::stringstream filename;
    filename << "bnb_internal_" << m_recursionDepth << ".svg";
    this->drawSteinerTreeSVG(copiedGraph, copiedIsTerminal, filename.str().c_str());
}
 
}