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# CXXGraph

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## Introduction

CXXGraph is a small library, header only, that manages the Graph and it's algorithms in C++. In other words a "Comprehensive C++ Graph Library".

## Algorithm Explanation

#### Dijkstra

Graph Dijkstras Shortest Path Algorithm(Dijkstra's Shortest Path) Dijkstra's Algorithm is used to find the shortest path from a source node to all other reachable nodes in the graph. The algorithm initially assumes all the…

## Introduction

CXXGraph is a small library, header only, that manages the Graph and it's algorithms in C++. In other words a "Comprehensive C++ Graph Library".

## Algorithm Explanation

### Dijkstra

Graph Dijkstras Shortest Path Algorithm(Dijkstra's Shortest Path)
Dijkstra's Algorithm is used to find the shortest path from a source node to all other reachable nodes in the graph. The algorithm initially assumes all the nodes are unreachable from the given source node so we mark the distances of all nodes as infinity.
(infinity) from source node (INF / infinity denotes unable to reach).

### Dial

Dial specialization of dijkstra’s algorithm.

When edge weights are small integers (bounded by a parameter C), specialized queues which take advantage of this fact can be used to speed up Dijkstra's algorithm. The first algorithm of this type was Dial's algorithm (Dial 1969) for graphs with positive integer edge weights, which uses a bucket queue to obtain a running time
O(|E|+|V|C).(source wikipedia)

Below is complete algorithm:

1. Maintains some buckets, numbered 0, 1, 2,…,wV.
2. Bucket k contains all temporarily labeled nodes with distance equal to k.
3. Nodes in each bucket are represented by list of vertices.
4. Buckets 0, 1, 2,..wV are checked sequentially until the first non-empty bucket is found. Each node contained in the first non-empty bucket has the minimum distance label by definition.
5. One by one, these nodes with minimum distance label are permanently labeled and deleted from the bucket during the scanning process.
6. Thus operations involving vertex include:
• Checking if a bucket is empty
• Adding a vertex to a bucket
• Deleting a vertex from a bucket.
7. The position of a temporarily labeled vertex in the buckets is updated accordingly when the distance label of a vertex changes.
8. Process repeated until all vertices are permanently labeled (or distances of all vertices are finalized).

At this link you can find a step-by-step illustrations.

### BFS

Breadth First Search, also quoted as BFS, is a Graph Traversal Algorithm. Time Complexity O(|V| + |E|) where V are the number of vertices and E are the number of edges in the graph.
Applications of Breadth First Search are :

1. Finding shortest path between two vertices say u and v, with path length measured by number of edges (an advantage over depth first search algorithm)
2. Ford-Fulkerson Method for computing the maximum flow in a flow network.
3. Testing bipartiteness of a graph.
4. Cheney's Algorithm, Copying garbage collection.

And there are many more...

### DFS

(Depth First Search)
Depth First Search Algorithm (Depth First Search)
Depth First Search, also quoted as DFS, is a Graph Traversal Algorithm. Time Complexity O(|V| + |E|) where V is number of vertices and E is number of edges in graph.
Application of Depth First Search are:

1. Finding connected components
2. Finding 2-(edge or vertex)-connected components.
3. Finding 3-(edge or vertex)-connected components.
4. Finding the bridges of a graph.
5. Generating words in order to plot the limit set of a group.
6. Finding strongly connected components.

And there are many more...

### Cycle Detection

Cycle (graph theory)

The existence of a cycle in directed and undirected graphs can be determined by whether depth-first search (DFS) finds an edge that points to an ancestor of the current vertex (it contains a back edge). All the back edges which DFS skips over are part of cycles. In an undirected graph, the edge to the parent of a node should not be counted as a back edge, but finding any other already visited vertex will indicate a back edge. In the case of undirected graphs, only O(n) time is required to find a cycle in an n-vertex graph, since at most n − 1 edges can be tree edges.

Many topological sorting algorithms will detect cycles too, since those are obstacles for topological order to exist. Also, if a directed graph has been divided into strongly connected components, cycles only exist within the components and not between them, since cycles are strongly connected.

For directed graphs, distributed message based algorithms can be used. These algorithms rely on the idea that a message sent by a vertex in a cycle will come back to itself. Distributed cycle detection algorithms are useful for processing large-scale graphs using a distributed graph processing system on a computer cluster (or supercomputer).

Applications of cycle detection include the use of wait-for graphs to detect deadlocks in concurrent systems.

WORK IN PROGRESS

## Partition Algorithm Explanation

### Vertex-Cut

A vertex-cut partitioning divides edges of a graph into equal size partitions. The vertices that hold the endpoints of an edge are also placed in the same partition as the edge itself. However, the vertices are not unique across partitions and might have to be replicated (cut), due to the distribution of their edge across different partitions.

Replication factor quantifies how many vertexes are replicated over computers compared with the the number of vertexes of the original input graph.

#### Greedy Vertex-Cut

This Algorithm is a simple vertex-cut in Round-Robin fashion.
It takes the original graph edges and assign them to the partitions, dividing it in equal(or similar) size. This algorithm does not take care of optimization in vertex replication ( Replication Factor) but only balance the edge in the partitions.

## Classes Explanation

The Classes Explanation can be found in the Doxygen Documentation, in the Classes Section

## Requirements

The minimun C++ standard required is C++17 and a G++ compiler version greater than 7.3.0.

## How to use

The use of the library is very simple, just put the header file where you need!

## Unit-Test Execution

The Unit-Test required the CMake version greater than 3.9 and the google test library.

## How to Compile

• If not exist create a directory "build" under the base directory.
• Enter the directory
• execute command `cmake ..`
• if all is succesfull execute the command `make`

## How to Run

After the compilation, you can run the executable that is under the "build" directory with the name "test_exe", with the simple command `./test_exe`.

Work in Progess

## How to contribute

If you want give your support you can create a pull request or report an issue .
If you want to change the code, or fix issue, or implement a new feature please read our CONTRIBUTING Guide

CXXGraph Site

## Contact

E-Mail : zigrazor@gmail.com

## Support

To get updated watch the project

## References

We are referenced by:

## Credits

Thanks to the community of TheAlgorithms for some algorithms ispiration.

Thanks to GeeksForGeeks for some algorithms inspiration.

## We are Looking for...

We are looking for developers and committer, also at first experience, we will guide you step by step to the open-source world!