What is BFS Algorithm? Breadth First Search Algorithm Explained

The Breadth First Search (BFS) algorithm is a fundamental graph traversal technique used to explore nodes in a graph or tree. It has widespread applications in networking, AI, and shortest path algorithms, making it highly relevant in today’s world of connected systems. 

For instance, BFS is used in social media platforms to find the shortest path between two users or to recommend connections. Its ability to explore all possible paths layer by layer ensures optimal solutions for problems requiring efficiency, such as route planning and web crawling.

In this blog, you will explore the Breadth First Search Algorithm, its working principles, key applications, and practical examples to help you understand its relevance and implementation.

What is Breadth First Search Algorithm?

BFS algorithm starts from a given source vertex and explores the graph layer by layer, examining all the vertices at the same level before descending further. It uses a queue data structure to maintain the order of exploration, ensuring that vertices are visited in a breadth first manner.

Its practical impact is evident in a range of real-world systems. For example, web crawlers for major search engines also rely on Breadth First Search Algorithm to systematically index billions of web pages, ensuring comprehensive coverage by visiting all links at each level before moving deeper. 

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Here are some important rules to remember when implementing the breadth first search algorithm for graph traversal:

• Queue: Use a queue data structure to keep track of the vertices to be visited in the breadth first traversal.
• Visited Marking: Maintain a visited array or set to keep track of the vertices that have been visited during the traversal.
• Enqueue and Mark: Enqueue the starting vertex into the queue and mark it as visited.
• Dequeue and Visit Neighbors: While the queue is not empty, dequeue a vertex, visit it, and enqueue its unvisited neighbouring vertices.
• Order of Visit: Visit the vertices in the order they were enqueued, ensuring a breadth-first exploration.
• Avoid Revisiting: Check if a vertex has already been visited before enqueueing it to avoid revisiting vertices.
• Termination: Terminate the algorithm when the queue becomes empty, indicating that all reachable vertices have been visited.
• Shortest Path: If finding the shortest path, track the parent of each vertex to reconstruct the path once the destination is reached.

Also Read: A Guide to the Types of AI Algorithms and Their Applications

What is the Need for Breadth First Search Algorithm?

The Breadth First Search (BFS) algorithm is essential for efficiently exploring all nodes in a graph or tree, especially when the shortest path or minimum traversal is required. It’s ideal for problems like finding the shortest route in navigation systems, solving puzzles, or network broadcasting where all possible connections need to be explored evenly. 

BFS ensures that the first time a node is encountered, it’s through the shortest possible path, making it a crucial tool in applications like web crawling, social network analysis, and shortest path algorithms in AI and computer science.

There are several reasons why using the BFS algorithm is essential:

1. Shortest Path Finding: BFS guarantees the shortest path between two vertices in an unweighted graph, making it an ideal choice for route planning or navigation systems.
2. Completeness: BFS is complete for finite graphs, ensuring it explores the entire graph and visits all reachable vertices.
3. Breadth-First Traversal: BFS explores vertices at the same level before moving to deeper levels, providing a breadth-first exploration of the graph.
4. Minimal Memory Usage: BFS uses minimal memory compared to other graph traversal algorithms like DFS, as it only needs to store vertices in the queue.
5. Optimal Solution and Accuracy: In unweighted graphs, BFS ensures that the first occurrence of a target vertex will yield the shortest path, making it efficient for searching tasks.

Programmers often use breadth first search Python for various applications in graph theory and data structures. 

Also Read: Top 9 Data Science Algorithms Every Data Scientist Should Know

Next, let’s look at how Breadth First Search Algorithm works.

How Does Breadth First Search Algorithm Work?

The architecture of the BFS algorithm centers around a queue data structure, which ensures nodes are explored in the order they are discovered, following the First-In, First-Out (FIFO) principle. Starting from a source node, BFS visits all immediate neighbors (same level) before moving deeper, marking nodes as visited to avoid repetition. 

This systematic, layer-by-layer approach guarantees that each node is processed at the shallowest possible depth, making BFS ideal for finding shortest paths and traversing graphs or trees efficiently.

The Breadth First Search (BFS) algorithm operates with a clear, structured architecture designed to efficiently explore a graph or tree. The components of this architecture are as follows:

1. Queue: The BFS algorithm uses a queue data structure to manage the order in which vertices are processed. The queue follows the First-In, First-Out (FIFO) principle, ensuring vertices are processed in the exact order they are discovered.

2. Visited Array or Set: A visited array or set keeps track of the vertices that have already been explored. This prevents revisiting vertices and ensures each vertex is processed only once during the traversal, enhancing efficiency and accuracy.

3. BFS Tree: As BFS explores the graph, it constructs a BFS tree. This tree represents the traversal path and illustrates the hierarchical relationships between vertices. Each vertex in the tree points to its parent vertex, which is the vertex that discovered it during the traversal.

4. Enqueue and Mark: The algorithm starts by enqueueing the start vertex into the queue and marking it as visited. This ensures the traversal begins from the correct starting point and that the start vertex is processed first.

5. Dequeue and Visit Neighbours: The core of the BFS process is the continuous dequeueing of vertices from the queue. After processing the current vertex, the algorithm explores its neighbours. Any unvisited neighbour is then enqueued and marked as visited.

6. Termination: BFS terminates when the queue is empty, indicating that all reachable vertices from the start vertex have been visited and processed.

BFS Algorithm (Pseudocode):

BFS(graph, start_vertex):
    queue = create an empty queue
    visited = create an empty set or array to track visited vertices
    enqueue start_vertex into the queue
    add start_vertex to visited

    while queue is not empty:
        current_vertex = dequeue from the queue
        process(current_vertex)  # e.g., print or perform operations on current_vertex
        for each neighbour in graph[current_vertex]:
            if neighbour is not in visited:
                enqueue neighbour into the queue
                add neighbour to visited

Explanation of the Architecture:

• Queue Initialization: The algorithm initializes an empty queue and an empty visited set or array.
• Enqueue Start Vertex: The start vertex is enqueued and marked as visited.
• While Loop: The algorithm processes vertices from the queue, visiting neighbours of each vertex.
• Neighbour Processing: Each unvisited neighbour is enqueued and marked as visited.
• Termination: The algorithm stops when the queue is empty, ensuring all reachable vertices have been processed.

The output of the BFS algorithm pseudocode depends on the structure of the input graph and the start vertex provided. Here's a step-by-step breakdown of what happens during execution:

1. Graph Structure: The graph is assumed to be represented as an adjacency list, where each vertex points to a list of its neighbours. For example:

 graph = {
    'A': ['B', 'C'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F'],
    'D': ['B'],
    'E': ['B', 'F'],
    'F': ['C', 'E']
}

2. Start Vertex: If we start the BFS from vertex 'A', the algorithm would explore all the vertices reachable from 'A' in breadth-first order.

3. Traversal Process:

• The queue starts with ['A'], and the algorithm processes the vertices layer by layer.
• The first node dequeued is 'A'. The neighbours ['B', 'C'] are added to the queue and marked as visited.
• Then, 'B' is dequeued, and its neighbours ['A', 'D', 'E'] are processed (but 'A' is already visited, so 'D' and 'E' are enqueued).
• 'C' is dequeued next, and its neighbour ['A', 'F'] is processed (but 'A' is already visited, so 'F' is enqueued).
• The algorithm continues to visit vertices 'D', 'E', and 'F'.

Output: The vertices are processed in the following order, and they are printed or processed during each iteration of the loop.

• A
• B
• C
• D
• E
• F

Final Output:

A
B
C
D
E
F

This output represents the order in which the vertices are visited using the Breadth First Search (BFS) algorithm, starting from vertex 'A'. Each vertex is printed once during the traversal.

Also Read: A Guide to the Types of AI Algorithms and Their Applications

Now that you know how it works, let’s look at some challenges of using Breadth First Search Algorithm.

Complexities Associated With Breadth First Search Algorithm 

BFS runs in O(V + E) time, efficiently handling even massive graphs, like Facebook’s social graph, which has billions of nodes and edges. However, its space complexity is O(V), meaning memory usage can spike for wide graphs, especially when many nodes are at the same level. 

This balance of speed and memory demands makes understanding BFS’s complexities crucial for real-world applications such as network analysis and web crawling.

The complexity of the breadth first search algorithm can be analysed in terms of time and space complexity.

1.Time Complexity

BFS has an O(V + E) time complexity, where V represents the number of nodes (vertices) in the graph, and E represents its edges. When dequeuing from its queue or exploring its adjacent vertices, BFS attempts to visit all nodes and edges once. Thus its time complexity increases linearly as more nodes and edges enter or exit it.

2. Space Complexity

Space complexity for BFS grows linearly with the number of vertices in a graph (V), represented as an integer value. This is because even under extreme conditions, the BFS queue can simultaneously contain all vertices in its maximum level traversal. Furthermore, its visited array or set requires O(V) space to store visited vertices visited during traversal; hence BFS grows linearly in space complexity with each increase in graph vertex count.

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Also Read: Time and Space Complexity in Machine Learning Explained

Applications of Breadth First Search Algorithm

The Breadth First Search (BFS) algorithm is one of the most fundamental and versatile algorithms in computer science. Its ability to explore graphs level by level makes it highly effective in solving a variety of problems, especially in situations where the shortest path, network connectivity, or optimal traversal is crucial.

BFS is widely used across different industries and applications, from navigating through networks to analyzing complex systems. Below are some insightful applications of BFS, showcasing its powerful capabilities in real-world scenarios:

1. Shortest Path

BFS is often used to determine the shortest path between two vertices in an unweighted graph.

Example: In GPS navigation, BFS can help find the fastest route between two locations on a map. This is done by treating each road as equal in length or time and ensuring the algorithm explores all possible routes efficiently until the destination is reached.

2. Connectivity

BFS can quickly check if a graph is connected, meaning all vertices are reachable from any starting point.

Example: In social media platforms like Facebook, BFS helps assess whether two users are connected, either directly or indirectly, through mutual friends. By traversing through the network, BFS determines if all users within a group are reachable from a given starting user.

3. Web Crawling

BFS is integral to web crawling, where it methodically explores websites by following links, discovering new pages level by level.

Example: Search engines like Google use BFS to index the web. The crawler starts at a homepage, follows all the links, then moves on to the links found on those pages, continuously expanding its search breadth to discover new pages across the internet.

4. Social Network Analysis

BFS is used to analyze social networks, revealing clusters, degrees of separation, and the shortest paths between users. 

Example: Platforms like LinkedIn use BFS to calculate the degree of separation between two users, helping identify the shortest connection path through mutual connections, and uncovering influencers and communities within the network.

5. Bipartite Graphs

BFS is useful for checking if a graph is bipartite, which means it can be divided into two distinct sets such that no two adjacent vertices belong to the same set.
Example: In online matchmaking systems, BFS helps determine if people can be grouped into two categories, such as matching users based on preferences or filtering users based on characteristics that should not overlap in a specific group.

6. Minimum Spanning Tree (MST)

BFS can assist in finding a Minimum Spanning Tree (MST) in a graph, especially when edge weights are equal.

Example: In infrastructure planning, such as laying out water pipes or electrical cables, BFS helps design the most cost-effective route that connects all nodes (e.g., homes or stations) while minimizing resource usage.

7. Puzzle Solving

BFS is a go-to solution for puzzles where the objective is to find the shortest path to a goal state, like in the sliding tile puzzle or maze problems.

Example: In AI-based games, BFS is used to solve challenges such as the 8-puzzle, where the algorithm systematically explores all possible moves, guaranteeing the shortest path to the goal configuration.

8. Network Routing

BFS is widely applied in network routing algorithms to determine the shortest route between network nodes or optimize data packet paths.

Example: In telecom networks or the Internet, BFS can find the quickest route for data transmission between two routers, minimizing latency and ensuring efficient data flow across the network.
These applications demonstrate the profound impact of BFS in both theoretical and practical contexts.

Also Read: What Are the Characteristics of an Algorithm? Definition, Features, and Examples

Next, let’s look at how upGrad can help you learn key AI algorithms.

How Can upGrad Help You Learn Algorithms?

The BFS algorithm helps you solve problems by exploring all possible paths level by level, which is perfect for tasks like finding the shortest path in unweighted graphs or analyzing networks. Employers are looking for professionals who can leverage such algorithms to optimize solutions, making BFS knowledge an important asset for securing tech-focused roles.

upGrad offers courses that teach essential algorithms, including BFS, through practical projects and expert-led mentorship. These programs prepare you for in-demand roles in AI, software development, and data science.

In addition to the courses above, let’s look at some free courses:

• Data Structures & Algorithms
• Introduction to Generative AI
• Advanced Prompt Engineering Course with ChatGPT
• Fundamentals of Deep Learning and Neural Networks

If you're unsure where to begin or which area to focus on, upGrad’s expert career counselors can guide you based on your goals. You can also visit a nearby upGrad offline center to explore course options, get hands-on experience, and speak directly with mentors! 

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References:
https://www.iquanta.in/blog/applications-of-bfs-or-breadth-first-search/
https://aistratagems.com/fuzzy-logic-statistics/
https://www.finalroundai.com/blog/what-is-breadth-first-search-a-clear-overview-of-the-algorithm