59 lines
2.0 KiB
Markdown
59 lines
2.0 KiB
Markdown
# Dynamic Reachability Algorithms [DRA]
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The goal of this project is to implement a collection of dynamic reachability
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algorithms covered in "Improved Dynamic Reachability Algorithms for Directed Graphs"
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by Liam Roditty and Uri Zwick.
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In more detail, the algorithms implemented, include a decremental reachability
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algorithm for the transitive closure of a directed acyclic graph, a decremental
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reachability algorithm for the transitive closure of a general directed graph, a
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dynamic reachability algorithm of a directed acyclic graph and a dynami reachability
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algorithm of a general directed graph.
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The core algorithm of Roditty and Zwick is a decremental reachability algorithm for
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the strongly connected components of the general directed graph, on which all
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reachability algorithms for general directed graphs are based.
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## A code example
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```cpp
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#include "roditty_zwick.h"
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int main() {
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// Initialize directed graph G
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graph::Digraph<int> G(
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{1, {2}}, {2, {3, 4}}, {3, {1, 5, 9}},
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{4, {5, 6}},
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{5, {6, 7}}, {6, {8}}, {7, {8, 9}}, {8, {9}}, {9, {5}}
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);
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// Initialize dynamic reachability algorithm for general directed graphs
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auto hk = new algo::HenzingerKing(G);
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hk->init();
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// Query the dynamic reachability algorithm
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std::cout << "Path from 4 to 8 exists: " << hk.query(4, 8) << '\n';
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// Remove edges
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std::vector<std::pair<int, int>> delEdges( {4, 6}, {5, 6}, {3, 1} );
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for (const auto& [u, v] : delEdges)
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hk.remove(u, v);
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std::cout << "Path from 4 to 8 exists: " << dr.query(4, 8);
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// Insert edges
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std::pair<int, std::vector<int>> addEdges( { 1 , {2, 3, 4, 5} } );
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hk.insert(u, { v });
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std::cout << "Path from 4 to 8 exists: " << dr.query(4, 8);
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return 0;
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}
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```
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## Run Locally
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Clone the repository with submodules (doctest/nanobench):
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```bash
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git clone --recurse-submodules https://github.com/stefiosif/dynamic-reachability-algorithms
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```
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## References
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* [Improved Dynamic Reachability Algorithms for Directed Graphs](www.google.com)
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