MatchingBlossomV.h

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#pragma once
 
#include <ogdf/basic/EdgeArray.h>
#include <ogdf/basic/EpsilonTest.h>
#include <ogdf/basic/Graph.h>
#include <ogdf/basic/GraphCopy.h>
#include <ogdf/basic/Logger.h>
#include <ogdf/graphalg/MatchingModule.h>
#include <ogdf/graphalg/matching_blossom/AlternatingTree.h>
#include <ogdf/graphalg/matching_blossom/AuxGraph.h>
#include <ogdf/graphalg/matching_blossom/BlossomVHelper.h>
#include <ogdf/graphalg/matching_blossom/Cycle.h>
#include <ogdf/graphalg/matching_blossom/Pseudonode.h>
#include <ogdf/graphalg/matching_blossom/utils.h>
 
#include <algorithm>
#include <chrono>
#include <iostream>
#include <limits>
#include <unordered_map>
#include <unordered_set>
#include <vector>
 
// Uncomment to print statistics
#define OGDF_BLOSSOMV_PRINT_STATS
 
// Helper macros for statistics
#ifdef OGDF_BLOSSOMV_PRINT_STATS
#   define OGDF_BLOSSOMV_START_TIMER() OGDF_BLOSSOMV_START_NAMED_TIMER(__timestamp)
#   define OGDF_BLOSSOMV_START_NAMED_TIMER(timer) auto timer = now()
#   define OGDF_BLOSSOMV_END_TIMER(stat) OGDF_BLOSSOMV_END_NAMED_TIMER(__timestamp, stat)
#   define OGDF_BLOSSOMV_END_NAMED_TIMER(timer, stat) m_stats[stat].add(end(timer))
#   define OGDF_BLOSSOMV_ADD_STAT(stat) m_stats[stat].add(0)
#else
#   define OGDF_BLOSSOMV_START_TIMER()
#   define OGDF_BLOSSOMV_START_NAMED_TIMER(timer)
#   define OGDF_BLOSSOMV_END_TIMER(name)
#   define OGDF_BLOSSOMV_END_NAMED_TIMER(timer, stat)
#   define OGDF_BLOSSOMV_ADD_STAT(stat)
#endif
 
namespace ogdf {
 
template<typename TWeight>
class MatchingBlossomV : public MatchingModule<TWeight> {
    BlossomVHelper<TWeight> m_helper;
    AuxGraph<TWeight> m_auxGraph;
 
    AuxNode<TWeight>* m_currentAuxNode = nullptr;
 
    EpsilonTest m_eps;
 
#ifdef OGDF_BLOSSOMV_PRINT_STATS
    struct stats {
        int count = 0;
        long long time = 0;
 
        void add(long long t) {
            count++;
            time += t;
        }
 
        long long ms() { return time / 1000000; }
    };
 
    std::unordered_map<std::string, stats> m_stats;
 
    std::chrono::high_resolution_clock::time_point now() {
        return std::chrono::high_resolution_clock::now();
    }
 
    long long end(std::chrono::high_resolution_clock::time_point start) {
        auto end = std::chrono::high_resolution_clock::now();
        return std::chrono::duration_cast<std::chrono::nanoseconds>(end - start).count();
    }
#endif
 
    using Logger::lout;
 
    std::ostream& louth() { return lout(Logger::Level::High); }
 
    void advanceCurrentAuxNode() {
        auto succ = m_currentAuxNode->graphNode()->succ();
        if (!succ) {
            succ = m_auxGraph.graph().firstNode();
        }
        m_currentAuxNode = m_auxGraph.auxNode(succ);
    }
 
#ifdef OGDF_HEAVY_DEBUG
    void assertConsistency() {
        // aux graph & trees
        for (auto auxNode : m_auxGraph.nodes()) {
            OGDF_ASSERT(m_auxGraph.auxNode(auxNode->graphNode()) == auxNode);
            auto tree = auxNode->tree();
            for (node v : tree.evenNodes) {
                OGDF_ASSERT(m_auxGraph.treeAuxNode(v) == auxNode);
                OGDF_ASSERT(!tree.isOdd(v));
            }
            for (node v : tree.oddNodes) {
                OGDF_ASSERT(m_auxGraph.treeAuxNode(v) == auxNode);
                OGDF_ASSERT(!tree.isEven(v));
            }
            // tree structure
            for (node v : tree.evenNodes) {
                // all even nodes except the root have a corresponding matching edge
                if (v != tree.root()) {
                    OGDF_ASSERT(m_helper.matching(v) == tree.evenBackEdge(v));
                }
            }
            for (node v : tree.oddNodes) {
                // all odd nodes have both a back edge in the tree and a forward matching
                // edge, since the matching edges are always defined for both ends
                node w = m_helper.matching(v)->opposite(v);
                OGDF_ASSERT(tree.isEven(w));
            }
            for (auto adj : auxNode->graphNode()->adjEntries) {
                OGDF_ASSERT(m_auxGraph.auxEdge(adj->theEdge()) != nullptr);
            }
        }
        // assert that all matching edges are correctly defined on both ends
        int matchedNodes = 0;
        for (node v : m_helper.graph().nodes) {
            if (edge matchingEdge = m_helper.matching(v)) {
                matchedNodes++;
                OGDF_ASSERT(matchingEdge->isIncident(v));
                OGDF_ASSERT(m_helper.matching(matchingEdge->opposite(v)) == matchingEdge);
            }
        }
        // matching
        std::unordered_set<edge> hiddenEdges;
        for (auto entry : m_helper.pseudonodes()) {
            auto pseudonode = entry.second;
            for (edge e : pseudonode->cycle->edgeOrder()) {
                hiddenEdges.insert(e);
            }
        }
        OGDF_ASSERT(matchedNodes + m_auxGraph.graph().numberOfNodes() + hiddenEdges.size()
                == (size_t)m_helper.graph().numberOfNodes());
        // priority queues
        auto checkAllPQs = [&](edge e, BlossomPQ<edge, TWeight>* shouldContain = nullptr) {
            for (auto auxNode : m_auxGraph.nodes()) {
                for (auto* pq : {&auxNode->evenFreeEdges(), &auxNode->evenEvenEdges()}) {
                    OGDF_ASSERT(pq->contains(e) == (pq == shouldContain));
                }
            }
            for (auto auxEdge : m_auxGraph.edges()) {
                for (auto* pq : {&auxEdge->evenEvenEdges(), &auxEdge->evenOddEdges(),
                             &auxEdge->oddEvenEdges()}) {
                    OGDF_ASSERT(pq->contains(e) == (pq == shouldContain));
                }
            }
            if (shouldContain != nullptr) {
                OGDF_ASSERT(shouldContain->priority(e) == m_helper.getReducedWeight(e));
            }
        };
        for (edge e : m_helper.graph().edges) {
            bool sourceInGraph = m_helper.repr(e->source()) == e->source();
            bool targetInGraph = m_helper.repr(e->target()) == e->target();
            OGDF_ASSERT(sourceInGraph == targetInGraph);
            if (!sourceInGraph) {
                checkAllPQs(e);
                continue;
            }
            OGDF_ASSERT(m_helper.getRealReducedWeight(e) >= 0);
            auto sourceNode = m_auxGraph.treeAuxNode(e->source());
            auto targetNode = m_auxGraph.treeAuxNode(e->target());
            bool sourceIsEven = sourceNode && sourceNode->tree().isEven(e->source());
            bool targetIsEven = targetNode && targetNode->tree().isEven(e->target());
            if (hiddenEdges.find(e) != hiddenEdges.end()) {
                OGDF_ASSERT(sourceNode == nullptr && targetNode == nullptr);
            }
            if (sourceNode == nullptr && targetNode == nullptr) {
                checkAllPQs(e);
                OGDF_ASSERT(m_helper.getRealReducedWeight(e) == m_helper.getReducedWeight(e));
            } else if (sourceNode == nullptr) {
                if (targetIsEven) {
                    checkAllPQs(e, &targetNode->evenFreeEdges());
                }
            } else if (targetNode == nullptr) {
                if (sourceIsEven) {
                    checkAllPQs(e, &sourceNode->evenFreeEdges());
                }
            } else if (sourceNode == targetNode) {
                if (sourceIsEven && targetIsEven) {
                    checkAllPQs(e, &sourceNode->evenEvenEdges());
                } else {
                    checkAllPQs(e);
                }
            } else {
                if (!sourceIsEven && !targetIsEven) {
                    checkAllPQs(e);
                } else {
                    edge graphAuxEdge = sourceNode->graphNode()->graphOf()->searchEdge(
                            sourceNode->graphNode(), targetNode->graphNode());
                    OGDF_ASSERT(graphAuxEdge != nullptr);
                    auto auxEdge = m_auxGraph.auxEdge(graphAuxEdge);
                    if (sourceIsEven && targetIsEven) {
                        checkAllPQs(e, &auxEdge->evenEvenEdges());
                    } else if (sourceIsEven) {
                        checkAllPQs(e, &auxEdge->evenOddEdgesFromPerspective(sourceNode));
                    } else {
                        checkAllPQs(e, &auxEdge->evenOddEdgesFromPerspective(targetNode));
                    }
                }
            }
        }
        for (auto entry : m_helper.pseudonodes()) {
            if (m_helper.repr(entry.first) == entry.first) {
                OGDF_ASSERT(m_helper.realY(entry.first) >= 0);
                auto auxNode = m_auxGraph.treeAuxNode(entry.first);
                for (auto other : m_auxGraph.nodes()) {
                    OGDF_ASSERT(other->oddPseudonodes().contains(entry.first)
                            == (other == auxNode && auxNode->tree().isOdd(entry.first)));
                }
            }
        }
    }
#endif
 
public:
    MatchingBlossomV(bool greedyInit = true) : m_helper(greedyInit), m_auxGraph(m_helper) { }
 
private:
    bool doCall(const Graph& G, const EdgeArray<TWeight>& weights,
            std::unordered_set<edge>& matching) {
        return _doCall(G, weights, matching);
    }
 
    bool doCall(const GraphAttributes& GA, std::unordered_set<edge>& matching) {
        return _doCall(GA.constGraph(), GA, matching);
    }
 
    template<class WeightContainer>
    bool _doCall(const Graph& G, const WeightContainer& weights, std::unordered_set<edge>& matching) {
        // init
        lout() << "start init" << std::endl;
#ifdef OGDF_BLOSSOMV_PRINT_STATS
        m_stats.clear();
#endif
        OGDF_BLOSSOMV_START_TIMER();
        if (!m_helper.init(G, weights, &m_auxGraph)) {
            return false;
        };
        OGDF_BLOSSOMV_END_TIMER("initialize");
        lout() << "finish init" << std::endl;
#ifdef OGDF_BLOSSOMV_PRINT_STATS
        louth() << "Trees: " << m_auxGraph.graph().numberOfNodes() << std::endl;
#endif
        return findMatching(matching);
    }
 
    bool findMatching(std::unordered_set<edge>& matching) {
#ifdef OGDF_BLOSSOMV_PRINT_STATS
        std::chrono::high_resolution_clock::time_point last_path, last_four_paths;
        // Calculate the next power of two for the number of aux nodes for logging purposes
        int p = 1;
        while (p < m_auxGraph.graph().numberOfNodes()) {
            p <<= 1;
        }
#endif
        // main loop
        while (m_auxGraph.graph().numberOfNodes() > 0) {
#ifdef OGDF_HEAVY_DEBUG
            assertConsistency();
#endif
#ifdef OGDF_BLOSSOMV_PRINT_STATS
            if (m_auxGraph.graph().numberOfNodes() == p / 2) {
                p /= 2;
                lout() << "." << p << std::flush;
                if (p == 2) {
                    last_path = now();
                } else if (p == 8) {
                    last_four_paths = now();
                }
            }
#endif
            if (!primalChange() && !dualChange()) {
                return false;
            }
        }
        lout() << "found matching" << std::endl;
#ifdef OGDF_BLOSSOMV_PRINT_STATS
        printParallelEdgesStats();
#endif
        OGDF_BLOSSOMV_START_TIMER();
        m_helper.getOriginalMatching(matching);
        OGDF_BLOSSOMV_END_TIMER("getOriginalMatching");
#ifdef OGDF_BLOSSOMV_PRINT_STATS
        m_stats["extraLastPathTime"].add(end(last_path));
        m_stats["extraLastFourPathsTime"].add(end(last_four_paths));
        printStatistics();
#endif
        return true;
    }
 
    bool primalChange() {
#ifdef OGDF_HEAVY_DEBUG
        std::unordered_map<edge, TWeight> edgeWeights;
        m_helper.getReducedEdgeWeights(edgeWeights);
#endif
        if (!m_currentAuxNode) {
            m_currentAuxNode = m_auxGraph.auxNode(m_auxGraph.graph().firstNode());
        }
        auto start = m_currentAuxNode;
        AuxNode<TWeight>* auxNode;
        // iterate all aux nodes in cyclic order
        do {
            auxNode = m_currentAuxNode;
            advanceCurrentAuxNode();
            // invalidate currentEdges of all aux nodes
            m_helper.currentIteration++;
            if (findMatchingAugmentation(auxNode) || findTreeAugmentation(auxNode)
                    || findShrinkableCycle(auxNode) || findExpandablePseudonode(auxNode)) {
#ifdef OGDF_HEAVY_DEBUG
                m_helper.assertConsistentEdgeWeights(edgeWeights);
#endif
                return true;
            }
        } while (m_currentAuxNode != start);
        m_currentAuxNode = nullptr;
        return false;
    }
 
    bool findMatchingAugmentation(AuxNode<TWeight>* auxNode) {
        OGDF_BLOSSOMV_START_TIMER();
        AuxEdge<TWeight>* auxEdge;
        AuxNode<TWeight>* other;
        edge minEdge;
        for (auto adj : auxNode->graphNode()->adjEntries) {
            auxEdge = m_auxGraph.auxEdge(adj->theEdge());
            other = m_auxGraph.auxNode(adj->twinNode());
 
            // set the currentEdge for all future operations in this iteration
            other->setCurrentEdge(auxEdge);
            // check if augmentation is possible
            minEdge = m_helper.getTopEligibleElement(auxEdge->evenEvenEdges());
            if (minEdge != nullptr) {
                OGDF_BLOSSOMV_END_TIMER("findAugment");
                augment(minEdge);
                return true;
            }
        }
        OGDF_BLOSSOMV_END_TIMER("findAugment");
        return false;
    }
 
    bool findTreeAugmentation(AuxNode<TWeight>* auxNode) {
        OGDF_BLOSSOMV_START_TIMER();
        edge minEdge = m_helper.getTopEligibleElement(auxNode->evenFreeEdges());
        if (minEdge != nullptr) {
            OGDF_BLOSSOMV_END_TIMER("findGrow");
            grow(minEdge);
            return true;
        }
        OGDF_BLOSSOMV_END_TIMER("findGrow");
        return false;
    }
 
    bool findShrinkableCycle(AuxNode<TWeight>* auxNode) {
        OGDF_BLOSSOMV_START_TIMER();
        edge minEdge = m_helper.getTopEligibleElement(auxNode->evenEvenEdges());
        if (minEdge != nullptr) {
            OGDF_BLOSSOMV_END_TIMER("findShrink");
            shrink(minEdge);
            return true;
        }
        OGDF_BLOSSOMV_END_TIMER("findShrink");
        return false;
    }
 
    bool findExpandablePseudonode(AuxNode<TWeight>* auxNode) {
        OGDF_BLOSSOMV_START_TIMER();
        node minNode = m_helper.getTopEligibleElement(auxNode->oddPseudonodes());
        if (minNode != nullptr) {
            auxNode->oddPseudonodes().pop();
            Pseudonode* pseudonode = m_helper.pseudonode(minNode);
            OGDF_BLOSSOMV_END_TIMER("findExpand");
            expand(pseudonode);
            return true;
        }
        OGDF_BLOSSOMV_END_TIMER("findExpand");
        return false;
    }
 
    bool dualChange() {
        OGDF_BLOSSOMV_START_TIMER();
        NodeArray<TWeight> deltas(m_auxGraph.graph(), 0);
        TWeight delta, otherDelta;
        AuxEdge<TWeight>* auxEdge;
        node w;
 
        // Calculates the connected components of the aux graph and sets the same delta for nodes in
        // the same component.
        std::vector<std::unordered_set<node>> components;
        m_auxGraph.connectedComponents(components);
        for (auto& component : components) {
            delta = infinity<TWeight>();
            AuxNode<TWeight>* auxNode;
            for (node v : component) {
                auxNode = m_auxGraph.auxNode(v);
                if (!auxNode->evenEvenEdges().empty()) {
                    delta = std::min(delta,
                            m_helper.getRealTopPriority(auxNode->evenEvenEdges()) / 2);
                }
                delta = std::min({delta, m_helper.getRealTopPriority(auxNode->evenFreeEdges()),
                        m_helper.getRealTopPriority(auxNode->oddPseudonodes())});
                for (auto& adj : v->adjEntries) {
                    w = adj->twinNode();
                    auxEdge = m_auxGraph.auxEdge(adj->theEdge());
                    if (component.find(w) != component.end()) {
                        // same component = same delta
                        if (!auxEdge->evenEvenEdges().empty()) {
                            delta = std::min(delta,
                                    m_helper.getRealTopPriority(auxEdge->evenEvenEdges()) / 2);
                        }
                    } else {
                        otherDelta = deltas[w];
                        if (!auxEdge->evenEvenEdges().empty()) {
                            delta = std::min(delta,
                                    m_helper.getRealTopPriority(auxEdge->evenEvenEdges())
                                            - otherDelta);
                        }
                        auto& evenOddPQ = auxEdge->evenOddEdgesFromPerspective(auxNode);
                        if (!evenOddPQ.empty()) {
                            delta = std::min(delta,
                                    m_helper.getRealTopPriority(evenOddPQ) + otherDelta);
                        }
                    }
                    // if already at zero, no dual change can be made in this tree
                    if (m_helper.isZero(delta)) {
                        break;
                    }
                }
            }
            // apply delta to all nodes of the component
            if (delta > 0 && delta < infinity<TWeight>()) {
                for (auto& v : component) {
                    deltas[v] = delta;
                }
            }
        }
 
        bool dualChange = false;
        for (auto& auxNode : m_auxGraph.nodes()) {
            delta = deltas[auxNode->graphNode()];
            if (delta > 0) {
                dualChange = true;
                auxNode->addDelta(delta);
            }
            lout() << "Delta for " << auxNode->tree().root() << ": " << delta << std::endl;
        }
        OGDF_BLOSSOMV_END_TIMER("dualChange");
        return dualChange;
    }
 
    void augment(edge augmentationEdge) {
        OGDF_BLOSSOMV_START_TIMER();
        OGDF_ASSERT(augmentationEdge->graphOf() == &m_helper.graph());
        for (auto augmentationEdgeNode : augmentationEdge->nodes()) {
            auto auxNode = m_auxGraph.treeAuxNode(augmentationEdgeNode);
            auto oppositeAuxNode =
                    m_auxGraph.treeAuxNode(augmentationEdge->opposite(augmentationEdgeNode));
            // merge PQs
            std::vector<edge> edgesToUpdate;
            for (auto adj : auxNode->graphNode()->adjEntries) {
                auto other = m_auxGraph.auxNode(adj->twinNode());
                if (other != auxNode && other != oppositeAuxNode) {
                    auto otherEdge = m_auxGraph.auxEdge(adj->theEdge());
                    for (auto pq : {&otherEdge->evenEvenEdges(),
                                 &otherEdge->evenOddEdgesFromPerspective(other)}) {
                        for (edge e : *pq) {
                            // delay insertion into PQs until the weights have been updated
                            edgesToUpdate.push_back(e);
                        }
                    }
                }
            }
            auxNode->tree().augmentMatching(augmentationEdge);
            if (m_currentAuxNode == auxNode) {
                advanceCurrentAuxNode();
            }
            m_auxGraph.deleteNode(auxNode);
            for (edge e : edgesToUpdate) {
                auto an = m_auxGraph.auxNodeForEdge(e);
                an->addEvenFreeEdge(e);
            }
        }
        OGDF_BLOSSOMV_END_TIMER("augment");
        lout() << "Matching augmented with " << augmentationEdge << std::endl;
    }
 
    void grow(edge newEdge) {
        OGDF_BLOSSOMV_START_TIMER();
        auto auxNode = m_auxGraph.auxNodeForEdge(newEdge);
        auto& tree = auxNode->tree();
        // (tree - u) - v -- w, where v -- w is the matching edge
        node u = tree.commonNode(newEdge);
        node v = newEdge->opposite(u);
        edge matchingEdge = m_helper.matching(v);
        node w = matchingEdge->opposite(v);
        tree.grow(u, newEdge, matchingEdge);
 
        // adjust y values
        for (node x : matchingEdge->nodes()) {
            m_auxGraph.setAuxNode(x, auxNode);
            m_helper.y(x) -= auxNode->delta(x);
        }
 
        // update data priority queues
        if (m_helper.isPseudonode(v)) {
            auxNode->addOddPseudonode(v);
        }
        for (auto adj : v->adjEntries) {
            node x = adj->twinNode();
            edge e = adj->theEdge();
            auto xAuxNode = m_auxGraph.treeAuxNode(x);
            if (xAuxNode != nullptr && xAuxNode->tree().isEven(x)) {
                if (x != w) {
                    xAuxNode->evenFreeEdges().remove(e);
                }
                if (xAuxNode != auxNode) {
                    m_auxGraph.assertCurrentEdge(xAuxNode, auxNode)
                            ->addEvenOddEdgeFromPerspective(e, xAuxNode);
                }
            }
        }
        edge augmentationEdge = nullptr;
        for (auto adj : w->adjEntries) {
            node x = adj->twinNode();
            edge e = adj->theEdge();
            auto xAuxNode = m_auxGraph.treeAuxNode(x);
            if (xAuxNode == nullptr) {
                // x is free
                auxNode->addEvenFreeEdge(e);
            } else if (xAuxNode == auxNode) {
                // x belongs to the same tree
                if (tree.isEven(x)) {
                    auxNode->evenFreeEdges().remove(e);
                    auxNode->addEvenEvenEdge(e);
                }
            } else {
                auto auxEdge = m_auxGraph.assertCurrentEdge(xAuxNode, auxNode);
                auto xTree = xAuxNode->tree();
                if (xTree.isOdd(x)) {
                    auxEdge->addEvenOddEdgeFromPerspective(e, auxNode);
                } else {
                    xAuxNode->evenFreeEdges().remove(e);
                    auxEdge->addEvenEvenEdge(e);
                    if (augmentationEdge == nullptr && m_helper.isEqualityEdge(e)) {
                        augmentationEdge = e;
                    }
                }
            }
        }
        OGDF_BLOSSOMV_END_TIMER("grow");
        lout() << "Tree augmented with " << newEdge << std::endl;
        if (augmentationEdge != nullptr) {
            OGDF_BLOSSOMV_ADD_STAT("extraAugmentShortcut");
            augment(augmentationEdge);
        }
    }
 
    void shrink(edge cycleEdge) {
        OGDF_BLOSSOMV_START_TIMER();
        auto auxNode = m_auxGraph.auxNodeForEdge(cycleEdge);
        auto& tree = auxNode->tree();
        Cycle* cycle = tree.getCycle(cycleEdge);
        OGDF_BLOSSOMV_END_TIMER("extraGetCycle");
        OGDF_BLOSSOMV_START_NAMED_TIMER(beforeShrinkTimer);
        // update priority queues
        std::vector<edge> oddEdges;
        std::unordered_map<node, edge> bestEdges;
        edge augmentationEdge = nullptr;
        for (node u : cycle->nodes()) {
            bool isOdd = tree.isOdd(u);
            for (auto adj : u->adjEntries) {
                edge e = adj->theEdge();
                node v = adj->twinNode();
                if (isOdd) {
                    if (!cycle->contains(v)) {
                        oddEdges.push_back(e);
                        OGDF_BLOSSOMV_ADD_STAT("extraShrinkFoundOddEdge");
                    }
                } else if (e->source() == v && tree.isEven(v) && cycle->contains(v)) {
                    // only remove if v is the source of the edge to prevent duplicate removal
                    auxNode->evenEvenEdges().remove(e);
                    OGDF_BLOSSOMV_ADD_STAT("extraShrinkRemoveEvenEvenEdge");
                }
            }
            if (isOdd && m_helper.isPseudonode(u)) {
                auxNode->oddPseudonodes().remove(u);
                OGDF_BLOSSOMV_ADD_STAT("extraShrinkOddPseudonodeChild");
            }
        }
 
        // update y values and tree associations
        for (node u : cycle->nodes()) {
            m_helper.y(u) = m_helper.realY(u);
            m_auxGraph.setAuxNode(u, nullptr);
        }
        OGDF_BLOSSOMV_END_NAMED_TIMER(beforeShrinkTimer, "extraShrinkUpdatePQsBefore");
 
        // do the actual shrinking
        std::vector<std::tuple<edge, bool>> selfLoops;
        OGDF_BLOSSOMV_START_NAMED_TIMER(actualShrinkTimer);
        Pseudonode* pseudonode = tree.shrink(cycle, selfLoops);
        OGDF_BLOSSOMV_END_NAMED_TIMER(actualShrinkTimer, "extraActualShrink");
        OGDF_BLOSSOMV_START_NAMED_TIMER(afterShrinkTimer);
        node newNode = pseudonode->graphNode;
        m_auxGraph.setAuxNode(newNode, auxNode);
        // set y to -delta so that realY is 0 (newNode is always even)
        m_helper.y(newNode) = -auxNode->delta();
 
        // remove self loops from pqs
        std::unordered_set<edge> hiddenEdges;
        for (auto& entry : selfLoops) {
            edge e = std::get<0>(entry);
            bool isEven = std::get<1>(entry);
            node vInner = m_helper.getOppositeBaseNode(e, newNode);
            node v = m_helper.repr(vInner);
            hiddenEdges.insert(e);
            auto other = m_auxGraph.treeAuxNode(v);
            if (other == nullptr) {
                if (isEven) {
                    auxNode->evenFreeEdges().remove(e);
                }
            } else if (other == auxNode) {
                if (isEven && tree.isEven(v)) {
                    auxNode->evenEvenEdges().remove(e);
                }
            } else {
                if (isEven && other->tree().isEven(v)) {
                    other->currentEdge()->evenEvenEdges().remove(e);
                }
                if (isEven && other->tree().isOdd(v)) {
                    other->currentEdge()->evenOddEdgesFromPerspective(auxNode).remove(e);
                }
                if (!isEven && other->tree().isEven(v)) {
                    other->currentEdge()->evenOddEdgesFromPerspective(other).remove(e);
                }
            }
        }
 
        // add edges back to correct priority queues after the costs have been updated
        for (edge e : oddEdges) {
            if (hiddenEdges.find(e) != hiddenEdges.end()) {
                continue;
            }
            node v = e->opposite(newNode);
            auto other = m_auxGraph.treeAuxNode(v);
            if (other == nullptr) {
                // v is free -> add edge to evenFreeEdges
                auxNode->addEvenFreeEdge(e);
            } else if (other->tree().isEven(v)) {
                if (other == auxNode) {
                    auxNode->addEvenEvenEdge(e);
                } else {
                    // u-v is in the evenOddEdges/oddEvenEdges of other->currentEdge and has to
                    // be switched to the evenEvenEdges, since the new pseudonode is even
                    auto auxEdge = m_auxGraph.assertCurrentEdge(other, auxNode);
                    auxEdge->evenOddEdgesFromPerspective(other).remove(e);
                    auxEdge->addEvenEvenEdge(e);
                    if (augmentationEdge == nullptr && m_helper.isEqualityEdge(e)) {
                        augmentationEdge = e;
                    }
                }
            } else if (other != auxNode) {
                m_auxGraph.assertCurrentEdge(other, auxNode)->addEvenOddEdgeFromPerspective(e, auxNode);
            }
        }
        OGDF_BLOSSOMV_END_NAMED_TIMER(afterShrinkTimer, "extraShrinkUpdatePQsAfter");
        OGDF_BLOSSOMV_END_TIMER("shrink");
        OGDF_BLOSSOMV_ADD_STAT("extraShrinkSize" + std::to_string(cycle->nodes().size()));
        lout() << std::endl << "Shrank at " << cycleEdge << " into " << newNode << std::endl;
        if (augmentationEdge != nullptr) {
            OGDF_BLOSSOMV_ADD_STAT("extraAugmentShortcut");
            augment(augmentationEdge);
        }
    }
 
    void expand(Pseudonode* pseudonode) {
        OGDF_BLOSSOMV_START_TIMER();
        auto auxNode = m_auxGraph.treeAuxNode(pseudonode->graphNode);
        auto& tree = auxNode->tree();
        auto cycle = pseudonode->cycle;
        int nodeIndex = pseudonode->graphNode->index();
        tree.expand(pseudonode);
 
        // update y values and tree associations
        for (node u : cycle->nodes()) {
            if (tree.contains(u)) {
                m_auxGraph.setAuxNode(u, auxNode);
                m_helper.y(u) -= auxNode->delta(u);
            }
        }
 
        // update priority queues
        edge augmentationEdge = nullptr;
        for (node u : cycle->nodes()) {
            if (tree.isEven(u)) {
                for (auto adj : u->adjEntries) {
                    edge e = adj->theEdge();
                    node v = adj->twinNode();
                    auto other = m_auxGraph.treeAuxNode(v);
                    if (other == nullptr) {
                        // v is free
                        auxNode->addEvenFreeEdge(e);
                    } else if (other == auxNode) {
                        // v belongs to the same tree
                        // prevent double adding for cycle edges by only adding if either v is not
                        // part of the cycle or v is the source of the edge
                        if (tree.isEven(v) && (!cycle->contains(v) || e->source() == v)) {
                            auxNode->addEvenEvenEdge(e);
                        }
                    } else {
                        auto auxEdge = m_auxGraph.assertCurrentEdge(other, auxNode);
                        if (other->tree().isEven(v)) {
                            if (auxEdge->evenOddEdgesFromPerspective(other).contains(e)) {
                                auxEdge->evenOddEdgesFromPerspective(other).remove(e);
                            }
                            auxEdge->addEvenEvenEdge(e);
                            if (augmentationEdge == nullptr && m_helper.isEqualityEdge(e)) {
                                augmentationEdge = e;
                            }
                        } else {
                            auxEdge->addEvenOddEdgeFromPerspective(e, auxNode);
                        }
                    }
                }
            } else if (tree.isOdd(u)) {
                if (m_helper.isPseudonode(u)) {
                    auxNode->addOddPseudonode(u);
                }
                for (auto adj : u->adjEntries) {
                    edge e = adj->theEdge();
                    node v = adj->twinNode();
                    auto other = m_auxGraph.treeAuxNode(v);
                    if (other && other != auxNode && other->tree().isEven(v)) {
                        auto auxEdge = m_auxGraph.assertCurrentEdge(other, auxNode);
                        if (!auxEdge->evenOddEdgesFromPerspective(other).contains(e)) {
                            auxEdge->addEvenOddEdgeFromPerspective(e, other);
                        }
                    }
                }
            } else {
                // u is free
                for (auto adj : u->adjEntries) {
                    edge e = adj->theEdge();
                    node v = adj->twinNode();
                    auto other = m_auxGraph.treeAuxNode(v);
                    if (other && other->tree().isEven(v)) {
                        if (other != auxNode) {
                            if (other->currentEdge()->evenOddEdgesFromPerspective(other).contains(e)) {
                                other->currentEdge()->evenOddEdgesFromPerspective(other).remove(e);
                            }
                        }
                        // only add if v is not part of the cycle, otherwise it is already added in
                        // the if-clause above
                        if (!cycle->contains(v)) {
                            other->addEvenFreeEdge(e);
                        }
                    }
                }
            }
        }
        delete pseudonode;
        OGDF_BLOSSOMV_END_TIMER("expand");
        lout() << std::endl << "Expanded " << nodeIndex << std::endl;
        if (augmentationEdge != nullptr) {
            OGDF_BLOSSOMV_ADD_STAT("extraAugmentShortcut");
            augment(augmentationEdge);
        }
    }
 
#ifdef OGDF_BLOSSOMV_PRINT_STATS
    void printStatistics() {
        long long total = 0;
        for (std::string key : {"initialize", "augment", "grow", "shrink", "expand", "dualChange",
                     "findAugment", "findGrow", "findShrink", "findExpand"}) {
            total += processStatisticEntry(key);
        }
 
        std::vector<std::string> extraKeys;
        std::vector<std::string> otherKeys;
        for (auto entry : m_stats) {
            if (entry.first.substr(0, 5) == "extra") {
                extraKeys.push_back(entry.first);
            } else {
                otherKeys.push_back(entry.first);
            }
        }
        std::sort(extraKeys.begin(), extraKeys.end());
        std::sort(otherKeys.begin(), otherKeys.end());
 
        for (auto key : otherKeys) {
            total += processStatisticEntry(key);
        }
        louth() << "Total tracked time: " << total << " ms" << std::endl;
        for (auto key : extraKeys) {
            processStatisticEntry(key);
        }
    }
 
    void printParallelEdgesStats() {
        int max = 0, sum = 0, total = 0;
        std::unordered_map<int, std::unordered_map<int, int>> edgeCount;
        for (edge e : m_helper.graph().edges) {
            if (m_helper.repr(e->source()) == e->source()
                    && m_helper.repr(e->target()) == e->target()) {
                OGDF_ASSERT(!e->isSelfLoop());
                total++;
                int i = std::min(e->source()->index(), e->target()->index());
                int j = std::max(e->source()->index(), e->target()->index());
                edgeCount[i][j]++;
            }
        }
        for (auto iEntry : edgeCount) {
            for (auto jEntry : iEntry.second) {
                int count = jEntry.second;
                if (count > max) {
                    max = count;
                }
                sum += count - 1;
            }
        }
        louth() << "Max number of parallel edges: " << max << std::endl;
        louth() << "Total number of parallel edges: " << sum << " (" << ((double)sum / total * 100)
                << "%)" << std::endl;
    }
 
    long long processStatisticEntry(const std::string& key) {
        louth() << key << ": " << m_stats[key].count << " (" << m_stats[key].ms() << " ms)"
                << std::endl;
        auto time = m_stats[key].ms();
        m_stats.erase(key);
        return time;
    }
#endif
};
 
}