Graphs are all around us. A graph can be thought of as an interconnected network of nodes and edges. Your friends on Facebook, your connections on LinkedIn, or your Twitter/Instagram followers constitute your social graph. Similarly, if you want to go from point A to point B, you can do so via multiple routes, which can be visualized on Google Maps.
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All these multiple route options from point A to point B also constitutes a graph. Graphs are among the most common data structures that we encounter in academia and the real world alike because they are so ubiquitous. And one of the most frequent operations that can be performed on a graph is graph traversal.
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What is Graph Traversal?
Graph Traversal is a method of visiting every node in a graph exactly once with speed and precision. It is an advanced graph search algorithm that enables you to print the sequence of visited nodes without getting caught in an infinite loop. There are many graph traversal algorithms like Depth-First Search, Breadth-First Search, Djikstra’s Algorithm, A-Star Algorithm, and more.
This article will take a deep dive into the Breadth First Search Algorithm or BFS.
Graph Structure
Before we take a detailed look under the BFS hood, let us get familiar with some graph terminologies with the help of the graph above:
Root Node – The node where you start the traversal process. For simplicity, we can consider A to be the root node.
Levels – A level is a collection of all nodes that are equidistant from the root node. So if we consider node A to be at Level 0, nodes B and C are at Level 1, while nodes D, E, and F are at level 2. A simple heuristic for determining the level number of a node is to count the number of edges between said node and the root node. Note that this only works if you define the root node to be at Level 0.
Parent Node – A node’s parent node is the one that is one level above it and adjacent to it. It can be thought of as the node from which said node originates. A is the parent node of B and C.
Child / Children Nodes – Node(s) that branch off and are adjacent to a parent node. B and C are child nodes of A
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BFS is a graph traversal algorithm to explore a tree or a graph efficiently. The algorithm starts with an initial node (root node) and then proceeds to explore all the nodes adjacent to it, in a breadth-first fashion, as opposed to depth-first, which goes down a particular branch till all the nodes in that branch are visited. Put simply, it traverses the graph level-wise, not moving down a level till all the nodes in that level are visited and marked.
It operates on the first-in-first-out (FIFO) principle, and is implemented using a queue data structure. Once a node is visited, it is inserted into a queue. Then it is recorded and all its children nodes are inserted into the queue. This process goes on till all the nodes in the graph are visited and recorded.
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Let us look at the detailed queue operations for the BFS algorithm for the graph given above:
() – denotes queue
[] – denotes printed output
- Insert A into the queue (a)
- Print A, insert B and C into the queue (cb)[a]
- Print B, insert its child nodes D and E into the queue (edc)[ba]
- Print C, insert its child node F into queue (fed)[cba]
- Print D, insert its child node into the queue. There are none. (fe)[dcba]
- Print E, whose child node F has already been inserted into the queue. (f)[edcba]
- Print F. [fedcba]
What Makes The BFS Algorithm Important
There are myriad reasons to deploy BFS as a method to search through vast datasets quickly. Some of the salient features that make it the preferred choice for developers and data engineers are:
- BFS can effectively explore all the nodes in the graph and find out the shortest possible path to explore all of them.
- The number of iterations required to traverse the whole graph is lesser than other search algorithms.
- Since it is implemented using a queue, its architecture is robust, reliable, and elegant.
- Compared to other algorithms, the output of BFS is exact and error-free.
- BFS iterations go smoothly, without running the risk of getting caught in an infinite loop.
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Applications of BFS Algorithm
Because of its simplicity and ease of setup, the BFS algorithm has found widespread use in various key real-world situations. Let us look at a few prominent applications:
Search Engine Crawlers – Try imagining a world without Google or Bing. You can’t. Search engines are the backbones of the internet. And the BFS algorithm is the backbone of search engines. It is the primary algorithm used to index web pages. The algorithm starts its journey from the source page (root node) and then follows all the links on that source page in a breadth-wise manner. Each web page can be thought of as an independent node in the graph.
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Unweighted Graph Traversals – BFS can identify the shortest path and minimum spanning tree in an unweighted graph. Finding the shortest route is merely about finding a path with the least number of edges, for which BFS is ideally suited. It can get work done by visiting the least number of nodes.
GPS Navigation – BFS leverages the GPS systems to surface all the possible neighbouring locations from your starting point, helping you navigate from point A to B seamlessly.
Broadcasting – Broadcast networking uses packets as units to carry signals and data. The BFS algorithm steers these packets to make their way to all the nodes in the network they are supposed to reach.
P2P Networks – Torrents or other file-sharing networks rely on P2P communication. BFS works excellent to find the nearest nodes so that the data transfer can happen faster.
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Conclusion
Ergo, the Breadth First Search Algorithm is one of the most important algorithms of the modern internet. Hopefully, this blog will serve as a handy starting point in your search algorithm explorations.
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