Common Graph Algorithms: Breadth-First Search (BFS)
Tags: apacheage, graphtheory
Published: 2023-06-15 00:16:24

## Introduction
Graph theory offers a wide array of algorithms to solve complex problems, and one of the fundamental ones is Breadth-First Search (BFS). BFS is a graph traversal algorithm that explores a graph by visiting all its neighboring vertices before moving on to the next level of vertices. In this blog post, we will dive into the inner workings of BFS, discuss its time complexity, and explore its real-world applications. Let's embark on a journey through the realm of graph exploration with BFS.

## Understanding BFS
Graph Representation:
Before we delve into the algorithm, let's briefly revisit how graphs are represented. A graph consists of vertices (also known as nodes) connected by edges. In BFS, we explore a graph starting from a given source vertex and visit its neighbors in a systematic manner.

## Key Concepts:
Queue: BFS utilizes a queue data structure to manage the order in which vertices are visited. The queue follows the First-In-First-Out (FIFO) principle, ensuring that vertices are explored in the order they were encountered.

Visited and Unvisited Vertices: To keep track of the vertices that have been visited and those that are yet to be explored, we maintain two sets: the set of visited vertices and the set of unvisited vertices.

Step-by-Step Execution:
Initialization: We start by selecting a source vertex and enqueue it in the queue. We also mark it as visited.
Main Loop: While the queue is not empty, we dequeue a vertex from the front of the queue and explore its neighbors.
Visiting Neighbors: For each unvisited neighbor of the current vertex, we enqueue it in the queue, mark it as visited, and proceed to the next neighbor.
Repeat: We repeat steps 2 and 3 until the queue is empty, indicating that all reachable vertices from the source have been visited.

## Time Complexity Analysis:
The time complexity of BFS is dependent on the size of the graph and the way it is represented. In an adjacency list representation, BFS runs in O(|V| + |E|) time, where |V| represents the number of vertices and |E| represents the number of edges. This is because BFS visits each vertex and edge once.

## Real-World Applications:
BFS finds applications in a wide range of fields:

Shortest Path and Distance Calculation: BFS can be used to find the shortest path between two vertices in an unweighted graph. By augmenting BFS to record the path during traversal, we can determine the shortest path and its length.

Web Crawling and Social Network Analysis: BFS is a fundamental component in web crawlers that explore the internet by following links. It is also utilized in analyzing social networks to identify connections, communities, or influencers.

Maze Solving: BFS can efficiently find the shortest path from a start position to an exit in a maze. By treating the maze as a graph, where each cell is a vertex connected to its adjacent cells, BFS can discover the optimal path.

Finding Connected Components: BFS helps identify connected components in a graph, which is useful in network analysis, image segmentation, and detecting clusters.

Memory Management: BFS can be applied in garbage collection algorithms to determine which objects are still reachable and mark others for deallocation.

Breadth-First Search (BFS) is a fundamental graph traversal algorithm that efficiently explores a graph and finds various applications in diverse fields. By systematically visiting vertices in a breadth-first manner, BFS allows us to analyze connectivity, find shortest paths, and uncover hidden patterns in graphs. However, it is essential to note that BFS is suitable for unweighted graphs. 

To use graph as databases you can use PostgreSQL's extension Apache AGE: -
More about apache age here: https://age.apache.org/
Github here: https://github.com/apache/age/
To implement BFS algorithm in Apache AGE, you can use drivers given here and use AGE with programming languages such as python.: https://github.com/apache/age/tree/master/drivers