Bandwidth reduction on graphs refers to techniques used to reduce the amount of data that needs to be transmitted or stored in order to represent a graph. Graphs are often used to represent data in a wide range of applications, including social networks, transportation networks, and biological networks. The size of a graph can be reduced by applying various techniques, such as graph summarization, graph compression, and graph simplification. Graph summarization techniques, such as graph clustering and graph sketching, can be used to extract a smaller, representative subgraph from a large graph that still captures the essential structural properties of the original graph.
Graph compression algorithms work to represent a graph with a smaller number of bits, these include graph-based representations like adjacency lists, adjacency matrices, and graphlet frequency vectors. Graph simplification techniques can be used to remove irrelevant or redundant information from a graph, reducing its size without losing important structural properties. Examples of simplification methods include edge contraction, vertex simplification, and subgraph extraction.
Overall, graph compression, summarization, and simplification are methods to represent a large graph in a more compact form that still maintains significant information, thus reducing the number of bits needed to store or transfer it. Here is an example of a Java program that performs bandwidth reduction on a graph:
Java
import java.util.LinkedList; // Graph class represents a directed graph // using adjacency list representationpublic class Graph { // No. of vertices private int V; // Adjacency List private LinkedList<Integer> adj[]; // constructor Graph(int v) { V = v; adj = new LinkedList[v]; for (int i = 0; i < v; ++i) adj[i] = new LinkedList(); } // function to add an edge to graph void addEdge(int v, int w) { adj[v].add(w); } // prints BFS traversal from a given source s void BFS(int s) { // Mark all the vertices as not // visited(By default set as false) boolean visited[] = new boolean[V]; // Create a queue for BFS LinkedList<Integer> queue = new LinkedList<Integer>(); // Mark the current node as // visited and enqueue it visited[s] = true; queue.add(s); while (queue.size() != 0) { // Dequeue a vertex from // queue and print it s = queue.poll(); System.out.print(s + " "); // Get all adjacent vertices of the dequeued vertex s // If a adjacent has not been visited, then mark it // visited and enqueue it for (int n : adj[s]) { if (!visited[n]) { visited[n] = true; queue.add(n); } } } } // Driver method to public static void main(String args[]) { Graph g = new Graph(4); g.addEdge(0, 1); g.addEdge(0, 2); g.addEdge(1, 2); g.addEdge(2, 0); g.addEdge(2, 3); g.addEdge(3, 3); System.out.println("Following is Breadth First Traversal (starting from vertex 2)"); g.BFS(2); }} |
Following is Breadth First Traversal (starting from vertex 2) 2 0 3 1
This program creates a graph with 4 vertices and several edges between them. The BFS method performs a breadth-first search starting from a given vertex, and prints out the vertices in the order they are visited. The addEdge method is used to add edges between the vertices.
Note that this is a simple example, and the performance optimization(Bandwidth reduction) here is not visible as the graph is small, for a larger graph where the bandwidth reduction is much needed you could use other algorithms like RCM(reverse cuthill-mckee algorithm) or another permutation methods and a detailed explanation of the algorithm which is out of the scope of this answer.
