LeftistOrdering.h

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#pragma once
 
#include <ogdf/basic/AdjEntryArray.h>
#include <ogdf/planarlayout/ShellingOrderModule.h>
 
namespace ogdf {
 
// context class for the leftist canonical ordering algorithm
class LeftistOrdering {
protected:
    // struct for a candidate aka belt item
    struct Candidate {
        Candidate() : stopper(nullptr) {};
 
        // the edges in the belt item
        List<adjEntry> chain;
 
        // a possible stopper of the candidate
        node stopper;
    };
 
public:
    // computes the leftist canonical order. Requires that G is simple, triconnected and embedded.
    // adj_v1n is the adjEntry at v_1 looking towards v_n, the outerface is choosen such that v_2 is the cyclic pred
    // of v_n. the result is saved in result, a list of list of nodes, first set is v_1, v_2, last one is v_n.
    bool call(const Graph& G, adjEntry adj_v1n, List<List<node>>& result);
 
private:
    // the leftmost feasible candidate function from the paper
    bool leftmostFeasibleCandidate(List<node>& result);
 
    // this is used to check a candidate for a singleton copy
    bool isSingletonWith(const Candidate& c, node v) const;
 
    // update belt function from the paper
    void updateBelt();
 
    // belt extension function from the paper
    void beltExtension(List<Candidate>& extension);
 
    // returns true if v is forbidde
    bool forbidden(node v) const {
        // too many cut faces?
        return m_cutFaces[v] > m_cutEdges[v] + 1;
    }
 
    // returns true if v is singular
    bool singular(node v) const {
        // not more cutfaces then cut edges plus one ?
        return m_cutFaces[v] > 2 && m_cutFaces[v] == m_cutEdges[v] + 1;
    }
 
    // the belt
    List<Candidate> m_belt;
 
    // the curr candidate in the belt
    List<Candidate>::iterator m_currCandidateIt;
 
    // number of cutfaces incident to a vertex
    NodeArray<int> m_cutFaces;
 
    // number of cutedges incident to a vertex
    NodeArray<int> m_cutEdges;
 
    // flag for marking directed edges
    AdjEntryArray<bool> m_marked;
 
public:
    // this is a custom class to have a more convienent way to access a canonical ordering
    // used somewhere
    class Partitioning {
    public:
        Partitioning() { }
 
        Partitioning(const Graph& G, const List<List<node>>& lco) { buildFromResult(G, lco); }
 
        void buildFromResult(const Graph& G, const List<List<node>>& lco);
 
        // returns the adjEntry to the left node in G_k-1
        adjEntry left(int k) const {
            if (m_ears[k][0]) {
                return m_ears[k][0]->twin();
            } else {
                return nullptr;
            }
        }
 
        // returns the adjEntry to the left node in G_k-1
        adjEntry right(int k) const { return m_ears[k][m_ears[k].size() - 1]; }
 
        // returns the edge from v_i to v_i+1 in the k-th partition
        adjEntry getChainAdj(int k, int i) const { return m_ears[k][i + 1]; }
 
        adjEntry getPathAdj(int k, int i) const { return m_ears[k][i]; }
 
        node getNode(int k, int i) const { return m_ears[k][i + 1]->theNode(); }
 
        // returns the number of all partitions
        int numPartitions() const { return m_ears.size(); }
 
        // returns the number of nodes in partition k
        int numNodes(int k) const { return m_ears[k].size() - 1; }
 
        int pathLength(int k) const { return m_ears[k].size(); }
 
        bool isSingleton(int k) const { return numNodes(k) == 1; }
 
    private:
        // keeps for every partition the path from left, v_1, ... v_k, right
        Array<Array<adjEntry>> m_ears;
    };
 
    bool call(const Graph& G, adjEntry adj_v1n, Partitioning& partition) {
        // the simple result
        List<List<node>> result;
        // compute it
        if (!call(G, adj_v1n, result)) {
            return false;
        }
 
        // generate the comfortable partitioning
        partition.buildFromResult(G, result);
 
        // success hopefully..
        return true;
    }
};
 
}