Update decremental maintenance of SCC algorithm

algorithm/decremental_maintenance.h

@@ -20,40 +20,71 @@ public:
   void init();
 
   //
-  void query();
+  bool query(const T& u, const T& v);
 
   //
-  void remove();
+  void remove(const T& u, const T& v);
 private:
   Digraph<T> G;
+
+  // Array used to answer strong connectivity queries in O(1) time
+  std::map<T, T> A;
+
+  // Connect SCC/SCC representative with 2 SPTs
+  // pair.first: Shortest-paths out-tree
+  // pair.second: Shortest-paths in-tree
+  std::map<T, std::pair<Digraph<T>, Digraph<T>>> SPT;
+
+  // Connect each representative with its SCC
+  std::map<T, SCC<T>> SCCs;
 };
 
 template<typename T>
 void DecrementalMaintenance<T>::init() {
-  std::map<T, T> A;
-  Tarjan<T> tarjan(G);
+  auto tarjan = Tarjan<T>(G).run();
 
-  auto sccs = tarjan.run();
+  for (auto& C : tarjan) {
+    const auto& w = C.representative();
 
-  for (auto& scc : sccs) {
-    const auto& root = scc.representative();
-    BFS<T> bfs(scc);
-    auto spt = bfs.run(root);
-    for (const auto& vertex : scc.vertices) {
-      A[vertex] = root;
-    }
+    // Create shortest-paths out-tree/in-tree
+    auto outTree = BFS<T>(C).run(w);
+    SPT[w] = std::make_pair(outTree, outTree.reverse());
 
+    // Update A with current SCCs vertices
+    for (const auto& v : C.vertices)
+      A[v] = w;
+
+    // Link SCC with its representative w
+    SCCs[w] = C;
   }
 }
 
 template<typename T>
-inline void DecrementalMaintenance<T>::query()
-{
+bool DecrementalMaintenance<T>::query(const T& u, const T& v) {
+  return A[u] == A[v];
 }
 
 template<typename T>
-inline void DecrementalMaintenance<T>::remove()
-{
+void DecrementalMaintenance<T>::remove(const T& u, const T& v) {
+  // If u and v are not in the same SCC, do nothing
+  if (A[u] != A[v]) return;
+
+  const auto& w = A[u];
+
+  // If edge e(u, v) is not contained in In(w) and Out(w), do nothing
+  if (!SPT[w].first.vertices.contains(w) &&
+      !SPT[w].second.vertices.contains(w))
+    return;
+
+  // Update In(w) and Out(w)
+  auto inTree = BFS<T>(SCCs[w]).run(w);
+  SPT[w] = std::make_pair(inTree, inTree.reverse());
+
+  if (!SPT[w].second.vertices.contains(u) ||
+      !SPT[w].first.vertices.contains(v)) {
+    // TODO: Decompose C into C1, C2, ... Ck
+  }
+
 }
 
 }; // namespace algo

algorithm/roditty_zwick.h

@@ -14,10 +14,10 @@ public:
   virtual void init() =0;
 
   //
-  virtual void query() =0;
+  virtual bool query(const T& u, const T& v) =0;
 
   //
-  virtual void remove() =0;
+  virtual void remove(const T& u, const T& v) =0;
 };
 
 template<typename T>

graph/scc.h

@@ -10,6 +10,8 @@ namespace graph {
 template<typename T>
 class SCC : public Graph<T> {
 public:
+  SCC() = default;
+
   SCC(std::map<T, std::set<T>> scc);
 
   //

test/algorithm_test.cc

@@ -4,7 +4,6 @@
 #include "graph/scc.h"
 #include "algorithm/tarjan.h"
 #include "algorithm/bfs.h"
-#include "algorithm/roditty_zwick.h"
 #include "algorithm/decremental_maintenance.h"
 
 using namespace graph;
@@ -133,5 +132,7 @@ TEST_SUITE("Algorithm") {
 
     algo::DecrementalMaintenance<std::uint16_t> rz(G);
     rz.init();
+
+    //CHECK_EQ(rz.query(1, 2), true);
   }
 }