reachability-algorithms/include/algorithm/frigioni.h

#ifndef FRIGIONI_H_
#define FRIGIONI_H_

#include "algorithm/decremental_reachability.h"
#include "algorithm/roditty_zwick.h"

#include <utility>

namespace algo {

template <typename T> class Frigioni : public DecrementalReachability<T> {
public:
  Frigioni() = default;

  explicit Frigioni(graph::Digraph<T> G) { this->G = G; }

  // Initialize the decremental maintenance data structure for general graphs
  void init() override;

  // Execute reachability query q(u, v) from vertex u to vertex v
  // in O(1) using the transitive closure matrix
  bool query(const T &u, const T &v) override;

  // Delete set of edges and explicitely maintain the transitive closure
  void remove(const std::vector<std::pair<T, T>> &edges) override;

private:
  // Transitive closure matrix, used to answer reachability queries in O(1)
  std::unordered_map<T, std::unordered_map<T, bool>> TC;

  // For each SCC, store a reachability tree created as a BFS tree
  std::unordered_map<SCC<T>, BreadthFirstTree<T>, HashSCC<T>> RT;

  // For each SCC, store collections of incoming, outgoing and internal edges
  struct Edges {
    std::set<std::pair<T, T>> in;
    std::set<std::pair<T, T>> inc;
    std::set<std::pair<T, T>> out;
  };
  std::unordered_map<SCC<T>, Edges, HashSCC<T>> E;

  // Structure that keeps candidate components to use as a hook
  std::unordered_map<SCC<T>, std::stack<T>, HashSCC<T>> H;

  // Decremental maintenance of strongly connected components
  RodittyZwick<T> rodittyZwick;

  // Delete internal edge e(u, v)
  void removeInternal(const T &u, const T &v);

  // Delete external edge e(u, v)
  void removeExternal(const T &u, const T &v);

  // Repair reachability trees
  void repairTrees();

  //
  void splitEdges(std::unordered_map<T, SCC<T>> &L,
                  std::unordered_map<T, SCC<T>> C, const T &w);
};

template <typename T> void Frigioni<T>::init() {
  rodittyZwick = RodittyZwick<T>(this->G);
  rodittyZwick.init();
  auto C = rodittyZwick.getComponentMap();

  for (const auto &w : std::views::keys(C)) {
    RT[C[w]] = BreadthFirstTree<T>(this->G, w);
    for (const auto &u : this->G.vertices()) {
      for (const auto &v : this->G.adjList[u]) {
        if (!C[w].contains(u) && C[w].contains(v))
          E[C[w]].inc.insert({u, v});
        else if (C[w].contains(u) && !C[w].contains(v))
          E[C[w]].out.insert({u, v});
        else
          E[C[w]].in.insert({u, v});
        TC[u][v] = false;
      }
    }
  }
  for (const auto &w : std::views::keys(C)) {
    for (const auto &u : C[w].vertices()) {
      for (const auto &v : RT[C[w]].vertices()) {
        TC[u][v] = true;
      }
    }
  }
}

template <typename T> bool Frigioni<T>::query(const T &u, const T &v) {
  return TC[u][v];
}

template <typename T>
void Frigioni<T>::remove(const std::vector<std::pair<T, T>> &edges) {
  std::vector<std::pair<T, T>> Eint;
  std::vector<std::pair<T, T>> Eext;

  for (const auto &[u, v] : edges) {
    if (!this->G.adjList[u].contains(v))
      continue;

    if (rodittyZwick.query(u, v))
      Eint.push_back({u, v});
    else
      Eext.push_back({u, v});
  }
  for (const auto &[u, v] : Eint)
    removeInternal(u, v);
  for (const auto &[u, v] : Eext)
    removeExternal(u, v);

  repairTrees();
}

template <typename T> void Frigioni<T>::removeInternal(const T &u, const T &v) {
  this->G.remove(u, v);
  auto L = rodittyZwick.getComponentMap();
  rodittyZwick.remove(u, v);
  auto C = rodittyZwick.getComponentMap();

  if (rodittyZwick.query(u, v)) {
    E[C[u]].in.erase({u, v});
    return;
  }

  if (L[u] == C[u]) {
    E[L[u]].out.erase({u, v});
    E.erase(L[v]);
    splitEdges(L, C, v);
  } else {
    E[L[v]].inc.erase({u, v});
    E.erase(L[u]);
    splitEdges(L, C, u);
  }

  for (const auto &w : std::views::keys(C)) {
    if (!RT[C[w]].contains(v))
      continue;

    RT[C[w]].removeEdgeTo(v);
    if (E[C[v]].inc.size() > 0) {
      H[C[w]].push(v); /*h mipos C[v].id?*/
      continue;
    }
    for (const auto &x : C[w].vertices()) {
      for (const auto &y : C[v].vertices()) {
        TC[x][y] = false;
      }
    }
    for (const auto &[a, b] : E[C[v]].out)
      H[C[w]].push(b);
  }
}

template <typename T> void Frigioni<T>::removeExternal(const T &u, const T &v) {
  this->G.remove(u, v);
  auto C = rodittyZwick.getComponentMap();
  E[C[v]].inc.erase({u, v});
  E[C[u]].out.erase({u, v});

  for (const auto &w : std::views::keys(C)) {
    if (!RT[C[w]].contains(v))
      continue;

    RT[C[w]].removeEdgeTo(v);
    if (E[C[v]].inc.size() > 0) {
      H[C[w]].push(v);
      continue;
    }
    for (const auto &x : C[w].vertices()) {
      for (const auto &y : C[v].vertices()) {
        TC[x][y] = false;
      }
    }
    for (const auto &[a, b] : E[C[v]].out)
      H[C[w]].push(b);
  }
}

template <typename T> void Frigioni<T>::repairTrees() {
  auto C = rodittyZwick.getComponentMap();
  for (const auto &w : std::views::keys(C)) {
    while (H[C[w]].size() > 0) {
      const auto &h = H[C[w]].top();
      H[C[w]].pop();
      bool foundHook = false;

      for (const auto &[a, b] : E[C[h]].inc) {
        if (RT[C[w]].adjList[w].contains(a)) {
          RT[C[w]].insert(a, h);
          foundHook = true;
          break;
        }
      }
      if (foundHook)
        continue;

      for (const auto &x : C[w].vertices()) {
        for (const auto &y : C[h].vertices()) {
          TC[x][y] = false;
        }
      }
      for (const auto &[a, b] : E[C[h]].out) {
        if (RT[C[w]].adjList[h].contains(a)) {
          H[C[w]].push(b);
        }
      }
    }
  }
}

template <typename T>
void Frigioni<T>::splitEdges(std::unordered_map<T, SCC<T>> &L,
                             std::unordered_map<T, SCC<T>> C, const T &w) {
  for (const auto &[a, b] : E[L[w]].inc)
    E[C[b]].inc.insert({a, b});

  for (const auto &[a, b] : E[L[w]].out)
    E[C[a]].out.insert({a, b});

  for (const auto &[a, b] : E[L[w]].in) {
    if (C[a] == C[b]) {
      E[C[a]].in.insert({a, b});
    } else {
      E[C[a]].out.insert({a, b});
      E[C[b]].in.insert({a, b});
    }
  }
}

} // namespace algo

#endif