Graph Partitioning

Graph partitioning is the process of dividing a graph into subsets, or partitions, in such a way that the vertices within each partition have more connections to other vertices in the same partition than to vertices in other partitions.

Graph partitioning is a fundamental problem in computer science and finds applications in various domains, such as parallel computing, network optimization, and social network analysis.

There are several algorithms to partition a graph into subsets, including the Kernighan-Lin algorithm, the Spectral bisection algorithm, and the Metis algorithm.

Here's an example Java code that demonstrates graph partitioning:

1// Example code for graph partitioning
2
3import java.util.ArrayList;
4import java.util.Arrays;
5
6public class GraphPartition {
7  public static void main(String[] args) {
8    // Create example graph
9    int[][] graph = {
10      {0, 1, 0, 1},
11      {1, 0, 1, 0},
12      {0, 1, 0, 1},
13      {1, 0, 1, 0}
14    };
15
16    // Perform graph partitioning
17    ArrayList<ArrayList<Integer>> partitions = partitionGraph(graph);
18
19    // Print the partitions
20    for (int i = 0; i < partitions.size(); i++) {
21      System.out.println("Partition " + (i + 1) + ": " + partitions.get(i));
22    }
23  }
24
25  private static ArrayList<ArrayList<Integer>> partitionGraph(int[][] graph) {
26    // Logic for graph partitioning
27    // Replace with your own implementation
28    return new ArrayList<>();
29  }
30}

The code creates an example graph represented as a 2D array and uses a placeholder function partitionGraph to partition the graph into subsets. In the code, replace the partitionGraph function with the logic for performing graph partitioning.

Feel free to modify the code and test it with different graphs to understand the concept of graph partitioning better.

xxxxxxxxxx

import java.util.ArrayList;

import java.util.Arrays;

​

public class GraphPartition {

  public static void main(String[] args) {

    // Create example graph

    int[][] graph = {

      {0, 1, 0, 1},

      {1, 0, 1, 0},

      {0, 1, 0, 1},

      {1, 0, 1, 0}

    };

​

    // Perform graph partitioning

    ArrayList<ArrayList<Integer>> partitions = partitionGraph(graph);

​

    // Print the partitions

    for (int i = 0; i < partitions.size(); i++) {

      System.out.println("Partition " + (i + 1) + ": " + partitions.get(i));

    }

  }

​

  private static ArrayList<ArrayList<Integer>> partitionGraph(int[][] graph) {

    // Logic for graph partitioning

    // Replace with your own implementation

    return new ArrayList<>();

  }

}