Update README

README.md

@@ -1,47 +1,45 @@
-# Dynamic Reachability Algorithms
-The goal of this project is to implement a collection of dynamic
-reachability algorithms covered in "Improved Dynamic Reachability
-Algorithms for Directed Graphs" by Liam Roditty and Uri Zwick.
+# Dynamic Reachability Algorithms [DRA]
+The goal of this project is to implement a collection of dynamic reachability
+algorithms covered in "Improved Dynamic Reachability Algorithms for Directed Graphs"
+by Liam Roditty and Uri Zwick.
+In more detail, the algorithms implemented, include a decremental reachability
+algorithm for the transitive closure of a directed acyclic graph, a decremental
+reachability algorithm for the transitive closure of a general directed graph, a
+dynamic reachability algorithm of a directed acyclic graph and a dynami reachability
+algorithm of a general directed graph.
+The core algorithm of Roditty and Zwick is a decremental reachability algorithm for
+the strongly connected components of the general directed graph, on which all
+reachability algorithms for general directed graphs are based.
 
-## Usage/Examples
+## A code example
 ```cpp
 #include "roditty_zwick.h"
 
 int main() {
-    // Initialize a graph G
+    // Initialize directed graph G
     graph::Digraph<int> G(
-        {1, {2}},
-        {2, {3, 4}},
-        {3, {1, 5, 9}},
+        {1, {2}}, {2, {3, 4}}, {3, {1, 5, 9}},
         {4, {5, 6}},
-        {5, {6, 7}},
-        {6, {8}},
-        {7, {8, 9}},
-        {8, {9}},
-        {9, {5}}
+        {5, {6, 7}}, {6, {8}}, {7, {8, 9}}, {8, {9}}, {9, {5}}
     );
     
-    // Initialize dynamic reachability algorithm for general graphs
-    algo::HenzingerKing<int> hk(G);
-    hk.init();
+    // Initialize dynamic reachability algorithm for general directed graphs
+    auto hk = new algo::HenzingerKing(G);
+    hk->init();
 
-    // Query
-    std::cout << "Path from 4 to 8 exists: " << dr.query(4, 8);
-
-    std::vector<std::pair<int, int>> edges(
-        {4, 6}, {5, 6}, {3, 1}
-    );
+    // Query the dynamic reachability algorithm
+    std::cout << "Path from 4 to 8 exists: " << hk.query(4, 8) << '\n';
 
     // Remove edges
-    for (const auto& [u, v] : edges)
-        dk.remove(u, v);
+    std::vector<std::pair<int, int>> delEdges( {4, 6}, {5, 6}, {3, 1} );
+    for (const auto& [u, v] : delEdges)
+        hk.remove(u, v);
 
     std::cout << "Path from 4 to 8 exists: " << dr.query(4, 8);
 
-
     // Insert edges
-    for (const auto& [u, v] : edges)
-        dk.insert(u, v);
+    std::pair<int, std::vector<int>> addEdges( { 1 , {2, 3, 4, 5} } );
+    hk.insert(u, { v });
 
     std::cout << "Path from 4 to 8 exists: " << dr.query(4, 8);
 
@@ -50,21 +48,11 @@ int main() {
 ```
 
 ## Run Locally
-
 Clone the repository with submodules (doctest/nanobench):
 
 ```bash
 git clone --recurse-submodules https://github.com/stefiosif/dynamic-reachability-algorithms
 ```
 
-Run with CMake:
-
-``` bash
-> mkdir build && cd build
-> cmake ..
-> make
-> ./main
-```
-
 ## References
 * [Improved Dynamic Reachability Algorithms for Directed Graphs](www.google.com)