# 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.

## A code example
```cpp
#include "roditty_zwick.h"

int main() {
    // Initialize directed graph G
    graph::Digraph<int> G(
        {1, {2}}, {2, {3, 4}}, {3, {1, 5, 9}},
        {4, {5, 6}},
        {5, {6, 7}}, {6, {8}}, {7, {8, 9}}, {8, {9}}, {9, {5}}
    );
    
    // Initialize dynamic reachability algorithm for general directed graphs
    auto hk = new algo::HenzingerKing(G);
    hk->init();

    // Query the dynamic reachability algorithm
    std::cout << "Path from 4 to 8 exists: " << hk.query(4, 8) << '\n';

    // Remove edges
    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
    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);

    return 0;    
}
```

## Run Locally
Clone the repository with submodules (doctest/nanobench):

```bash
git clone --recurse-submodules https://github.com/stefiosif/dynamic-reachability-algorithms
```

## References
* [Improved Dynamic Reachability Algorithms for Directed Graphs](www.google.com)