MinimumCutStoerWagner.h

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#pragma once
 
#include <ogdf/basic/GraphCopy.h>
#include <ogdf/basic/Math.h>
#include <ogdf/basic/PriorityQueue.h>
#include <ogdf/graphalg/MinimumCutModule.h>
 
namespace ogdf {
 
template<typename T = double>
struct MinimumCutStoerWagner : public MinimumCutModule<T> {
    virtual T call(const Graph& G) override {
        EdgeArray<T> weights(G, 1);
        return call(G, weights);
    }
 
    virtual T call(const Graph& G, const EdgeArray<T>& weights) override {
        m_minCut = std::numeric_limits<T>::max();
        m_GC.init(G);
        m_w.init(m_GC);
        m_contractedNodes.init(m_GC);
 
        for (edge e : m_GC.edges) {
            m_w[e] = weights[m_GC.original(e)];
            OGDF_ASSERT(m_w[e] >= T {});
        }
        for (node v : m_GC.nodes) {
            m_contractedNodes[v].pushBack(m_GC.original(v));
        }
 
        mainLoop();
 
        return value();
    }
 
    virtual const ArrayBuffer<edge>& edges() override {
        if (!m_cutEdges.empty()) {
            return m_cutEdges;
        }
 
        NodeArray<bool> inPartition(m_GC.original(), false);
 
        for (node v : m_partition) {
            inPartition[v] = true;
        }
 
        for (node v : m_partition) {
            for (adjEntry adj : v->adjEntries) {
                if (!inPartition[adj->twinNode()]) {
                    m_cutEdges.push(adj->theEdge());
                }
            }
        }
        return m_cutEdges;
    }
 
    virtual const ArrayBuffer<node>& nodes() override { return m_partition; }
 
    virtual T value() const override { return m_minCut; }
 
protected:
    T m_minCut;
 
    GraphCopy m_GC;
 
    EdgeArray<T> m_w;
 
    ArrayBuffer<node> m_partition;
 
    ArrayBuffer<edge> m_cutEdges;
 
    NodeArray<List<node>> m_contractedNodes;
 
    void mainLoop() {
        m_partition.clear();
        m_cutEdges.clear();
        while (m_GC.numberOfNodes() > 1) {
            Math::updateMin(m_minCut, minimumCutPhase());
            if (m_minCut == T {}) { // cannot get better so return early
                return;
            }
        }
    }
 
    T minimumCutPhase();
 
    void contraction(node t, node s);
};
 
template<typename T>
void MinimumCutStoerWagner<T>::contraction(node t, node s) {
    OGDF_ASSERT(t != s);
 
    // Since nodes in #m_GC correspond to sets of nodes (due to the node contraction),
    // the NodeArray #m_contractedNodes has to be updated.
    // Hence append the list of contracted nodes of s to the list of t.
    m_contractedNodes[t].conc(m_contractedNodes(s));
 
    // Redirect edges and delete node s
    safeForEach(s->adjEntries, [&](adjEntry adj) {
        edge e = adj->theEdge();
        if (e->source() == t || e->target() == t) {
            m_GC.delEdge(e);
        } else if (e->source() == s) {
            m_GC.moveSource(e, t);
        } else {
            m_GC.moveTarget(e, t);
        }
    });
    m_GC.delNode(s);
 
    // NodeArray containing the first edge of parallel edges
    NodeArray<edge> incident {m_GC, nullptr};
 
    // Delete parallel edges and add their weights
    safeForEach(t->adjEntries, [&](adjEntry adj) {
        node v {adj->twinNode()};
        if (v != t) {
            edge e {adj->theEdge()};
            edge& f {incident[v]};
            if (f == nullptr) {
                f = e;
            } else {
                m_w[f] += m_w[e];
                m_GC.delEdge(e);
            }
        }
    });
}
 
template<typename T>
T MinimumCutStoerWagner<T>::minimumCutPhase() {
    /*
     * This function computes the mincut of the current phase.
     * First, nodes are explored successively in descending order of the sum of
     * their incident edge weights; \a s and \a t are always the two last added nodes.
     * Afterwards, the current mincut value \a cutOfThePhase is computed, which corresponds to the
     * sum of the weights of those edges incident to node \a t.
     * At the end, \a s and \a t are contracted and the \a cutOfThePhase is returned.
     */
 
    // A priority queue containing the unexplored nodes.
    // Priorities are the (negative) sum of edge weights incident to the explored nodes.
    PrioritizedMapQueue<node, T> pq(m_GC);
    for (node v : m_GC.nodes) {
        pq.push(v, T {});
    }
    std::function<void(node)> updatePQ {[&](node currentNode) {
        OGDF_ASSERT(!pq.contains(currentNode));
        for (adjEntry adj : currentNode->adjEntries) {
            node v {adj->twinNode()};
            // The code below is at it is due to numerical issues with T=double.
            if (pq.contains(v)) {
                T newPriority {pq.priority(v) - m_w[adj->theEdge()]};
                if (newPriority < pq.priority(v)) {
                    pq.decrease(adj->twinNode(), newPriority);
                }
            }
        }
    }};
 
    // The start node can be chosen arbitrarily. It has no effect on the correctness of the algorithm.
    node s {nullptr};
    node t {pq.topElement()};
    pq.pop();
 
    updatePQ(t);
 
    // Successively adding the most tightly connected node.
    while (!pq.empty()) {
        // Find the most tightly connected node and remove it from the priority queue
        node currentNode {pq.topElement()};
        pq.pop();
 
        // Push the current node to the 2-element list consisting of s and t
        s = currentNode;
        std::swap(s, t);
 
        // Update the priorities
        updatePQ(currentNode);
    }
 
    // Contains the mincut value according to the current phase.
    T phaseCut {};
    for (adjEntry adj : t->adjEntries) {
        edge e {adj->theEdge()};
        if (!e->isSelfLoop()) {
            phaseCut += m_w[adj->theEdge()];
        }
    }
 
    // If the current \a phaseCut is strictly smaller than the global mincut value,
    // the partition defining the mincut has to be updated.
    if (phaseCut < m_minCut) {
        m_partition.clear();
        for (node v : m_contractedNodes[t]) {
            m_partition.push(v);
        }
    }
 
    // Performing the node contraction of nodes \a s and \a t.
    contraction(t, s);
 
    return phaseCut;
}
 
}