From 371104a33712a4a71bbb3dfa3bfa6aa3c83e1835 Mon Sep 17 00:00:00 2001
From: stefiosif <stef8iosif@gmail.com>
Date: Thu, 29 Sep 2022 23:34:42 +0300
Subject: [PATCH] Complete RZ dynamic algorithm inspired by henzinger and king,
 TODO: finish frigioni

---
 algorithm/henzinger_king.h | 97 +++++++++++++++++++++++++-------------
 1 file changed, 65 insertions(+), 32 deletions(-)

diff --git a/algorithm/henzinger_king.h b/algorithm/henzinger_king.h
index f6d90a1..2b51d78 100644
--- a/algorithm/henzinger_king.h
+++ b/algorithm/henzinger_king.h
@@ -6,6 +6,8 @@
 
 using namespace graph;
 
+constexpr int max_set_size = 5;
+
 namespace algo {
 
 template<typename T>
@@ -15,63 +17,94 @@ public:
 
   HenzingerKing(Digraph<T> G) { this->G = G; }
 
-  // 1. Initialize a decremental reachability data structure.
-  // 2. Let S <- phi.
-
-  // In the beginning of each phase, a decremental reachability data structure
-  // is initialized. We let S be the set of vertices that were centers of
-  // insertions during this phase. Initially S = phi. When a set of edges Ev, all
-  // touching v, is inserted, we add v to S and construct reachability trees In(v)
-  // and Out(v) rooted at v. When the size of S, the set of insertion centers,
-  // reaches t, a parameter fixed in advance, the phase is declared over, and
-  // all the data structures are reinitialized.
+  // Initialize decremental maintenance data structure and the empty set S
   void init() override;
 
-  // 1. Query the decremental reachability data structure.
-  // 2. For each w in S check if u in In(w) and v in Out(w).
-
-  // First the decremental data structure is queried to see whether there is a
-  // directed path from u to v composed solely of edges that were present in the
-  // graph at the start of the current phase. If not, it is checked whether there
-  // exists w in S such that u in In(w) and v in Out(w). If such a vertex w exists,
-  // then the answer is YES.
+  // Execute query q(u, v) from vertex u to vertex v by querying the
+  // decremental reachability data structure at the start of the phase
+  // and then if necessary check the set S
   bool query(const T& u, const T& v) override;
 
-  // 1. Let E <- E - E'.
-  // 2. Delete E' from the decremental data structure.
-  // 3. For every w in S, rebuilt the trees In(w) and Out(w).
-
-  // First, the edges of E' are removed from the decremental data structure. Next,
-  // for every w in S, the shortest-paths trees In(w) and Out(w) are built from
-  // scratch.
+  // Delete edge e(u, v)
   void remove(const T& u, const T& v) override;
-  
-  // 1. Let E <- E union Ev.
-  // 2. Let S <- S union {v}.
-  // 3. If |S| > t, then call init.
-  // 4. Otherwise, construct the trees In(v) and Out(v).
+
+  // Remove collection of edges from the decremental maintenance data structure
+  // and for every vertex in set S, rebuilt reachability trees from scratch
+  void remove(const std::vector<std::pair<T,T>>& edges);
+
+  // Add edge e(u, v)
   void insert(const T& u, const T& v) override;
+
+  // Insert collection of edges in set S, if threshold is reached re-initialize
+  // algorithm, otherwise construct reachability trees for the vertex that is
+  // the center-of-insertions
+  void insert(const T& c, const std::vector<T>& vertices);
+private:
+  // Decremental maintenance data structure
+  Frigioni<T> frigioni;
+
+  // Collection of vertices that have been centers of insertions in this phase
+  std::set<T> S;
+
+  // Maintain in-out bfs trees
+  std::map<T, BreadthFirstTree<T>> In;
+  std::map<T, BreadthFirstTree<T>> Out;
 };
 
 template<typename T>
 void HenzingerKing<T>::init() {
-
+  S.clear();
+  frigioni = Frigioni<T>(this->G);
+  frigioni.init();
 }
 
 template<typename T>
 bool HenzingerKing<T>::query(const T& u, const T& v) {
+  if (frigioni.query(u, v))
+    return true;
 
-  return false;
+  return std::any_of(S.begin(), S.end(),
+                     [&](const T& w) {
+                       return In[w].contains(w, u) && Out[w].contains(w, v);
+                     });
 }
 
 template<typename T>
 void HenzingerKing<T>::remove(const T& u, const T& v) {
+  this->G.remove(u, v);
+}
 
+template<typename T>
+void HenzingerKing<T>::remove(const std::vector<std::pair<T, T>>& edges) {
+  for (const auto& [u, v]: edges) {
+    remove(u, v);
+  }
+  frigioni.remove(edges);
+
+  for (const auto& w : S) {
+    In[w] = BreadthFirstTree(this->G.reverse(), w);
+    Out[w] = BreadthFirstTree(this->G, w);
+  }
 }
 
 template<typename T>
 void HenzingerKing<T>::insert(const T& u, const T& v) {
+  this->G.insert(u, v);
+}
 
+template<typename T>
+void HenzingerKing<T>::insert(const T& c, const std::vector<T>& vertices) {
+  for (const auto& w : vertices)
+    insert(c, w);
+
+  S.insert(c);
+  if (S.size() > max_set_size) {
+    init();
+    return;
+  }
+
+  In[c] = BreadthFirstTree(this->G.reverse(), c);
+  Out[c] = BreadthFirstTree(this->G, c);
 }
 
 } // namespace algo