This is a java program to implement Hungarian Algorithm for Bipartite Matching. The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.
Here is the source code of the Java Program to Implement the Hungarian Algorithm for Bipartite Matching. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.
package com.maixuanviet.graph; import java.util.Arrays; import java.util.Scanner; public class HungarianBipartiteMatching { private final double[][] costMatrix; private final int rows, cols, dim; private final double[] labelByWorker, labelByJob; private final int[] minSlackWorkerByJob; private final double[] minSlackValueByJob; private final int[] matchJobByWorker, matchWorkerByJob; private final int[] parentWorkerByCommittedJob; private final boolean[] committedWorkers; public HungarianBipartiteMatching(double[][] costMatrix) { this.dim = Math.max(costMatrix.length, costMatrix[0].length); this.rows = costMatrix.length; this.cols = costMatrix[0].length; this.costMatrix = new double[this.dim][this.dim]; for (int w = 0; w < this.dim; w++) { if (w < costMatrix.length) { if (costMatrix[w].length != this.cols) { throw new IllegalArgumentException("Irregular cost matrix"); } this.costMatrix[w] = Arrays.copyOf(costMatrix[w], this.dim); } else { this.costMatrix[w] = new double[this.dim]; } } labelByWorker = new double[this.dim]; labelByJob = new double[this.dim]; minSlackWorkerByJob = new int[this.dim]; minSlackValueByJob = new double[this.dim]; committedWorkers = new boolean[this.dim]; parentWorkerByCommittedJob = new int[this.dim]; matchJobByWorker = new int[this.dim]; Arrays.fill(matchJobByWorker, -1); matchWorkerByJob = new int[this.dim]; Arrays.fill(matchWorkerByJob, -1); } protected void computeInitialFeasibleSolution() { for (int j = 0; j < dim; j++) { labelByJob[j] = Double.POSITIVE_INFINITY; } for (int w = 0; w < dim; w++) { for (int j = 0; j < dim; j++) { if (costMatrix[w][j] < labelByJob[j]) { labelByJob[j] = costMatrix[w][j]; } } } } public int[] execute() { /* * Heuristics to improve performance: Reduce rows and columns by their * smallest element, compute an initial non-zero dual feasible solution * and * create a greedy matching from workers to jobs of the cost matrix. */ reduce(); computeInitialFeasibleSolution(); greedyMatch(); int w = fetchUnmatchedWorker(); while (w < dim) { initializePhase(w); executePhase(); w = fetchUnmatchedWorker(); } int[] result = Arrays.copyOf(matchJobByWorker, rows); for (w = 0; w < result.length; w++) { if (result[w] >= cols) { result[w] = -1; } } return result; } protected void executePhase() { while (true) { int minSlackWorker = -1, minSlackJob = -1; double minSlackValue = Double.POSITIVE_INFINITY; for (int j = 0; j < dim; j++) { if (parentWorkerByCommittedJob[j] == -1) { if (minSlackValueByJob[j] < minSlackValue) { minSlackValue = minSlackValueByJob[j]; minSlackWorker = minSlackWorkerByJob[j]; minSlackJob = j; } } } if (minSlackValue > 0) { updateLabeling(minSlackValue); } parentWorkerByCommittedJob[minSlackJob] = minSlackWorker; if (matchWorkerByJob[minSlackJob] == -1) { /* * An augmenting path has been found. */ int committedJob = minSlackJob; int parentWorker = parentWorkerByCommittedJob[committedJob]; while (true) { int temp = matchJobByWorker[parentWorker]; match(parentWorker, committedJob); committedJob = temp; if (committedJob == -1) { break; } parentWorker = parentWorkerByCommittedJob[committedJob]; } return; } else { /* * Update slack values since we increased the size of the * committed * workers set. */ int worker = matchWorkerByJob[minSlackJob]; committedWorkers[worker] = true; for (int j = 0; j < dim; j++) { if (parentWorkerByCommittedJob[j] == -1) { double slack = costMatrix[worker][j] - labelByWorker[worker] - labelByJob[j]; if (minSlackValueByJob[j] > slack) { minSlackValueByJob[j] = slack; minSlackWorkerByJob[j] = worker; } } } } } } protected int fetchUnmatchedWorker() { int w; for (w = 0; w < dim; w++) { if (matchJobByWorker[w] == -1) { break; } } return w; } protected void greedyMatch() { for (int w = 0; w < dim; w++) { for (int j = 0; j < dim; j++) { if (matchJobByWorker[w] == -1 && matchWorkerByJob[j] == -1 && costMatrix[w][j] - labelByWorker[w] - labelByJob[j] == 0) { match(w, j); } } } } protected void initializePhase(int w) { Arrays.fill(committedWorkers, false); Arrays.fill(parentWorkerByCommittedJob, -1); committedWorkers[w] = true; for (int j = 0; j < dim; j++) { minSlackValueByJob[j] = costMatrix[w][j] - labelByWorker[w] - labelByJob[j]; minSlackWorkerByJob[j] = w; } } protected void match(int w, int j) { matchJobByWorker[w] = j; matchWorkerByJob[j] = w; } protected void reduce() { for (int w = 0; w < dim; w++) { double min = Double.POSITIVE_INFINITY; for (int j = 0; j < dim; j++) { if (costMatrix[w][j] < min) { min = costMatrix[w][j]; } } for (int j = 0; j < dim; j++) { costMatrix[w][j] -= min; } } double[] min = new double[dim]; for (int j = 0; j < dim; j++) { min[j] = Double.POSITIVE_INFINITY; } for (int w = 0; w < dim; w++) { for (int j = 0; j < dim; j++) { if (costMatrix[w][j] < min[j]) { min[j] = costMatrix[w][j]; } } } for (int w = 0; w < dim; w++) { for (int j = 0; j < dim; j++) { costMatrix[w][j] -= min[j]; } } } protected void updateLabeling(double slack) { for (int w = 0; w < dim; w++) { if (committedWorkers[w]) { labelByWorker[w] += slack; } } for (int j = 0; j < dim; j++) { if (parentWorkerByCommittedJob[j] != -1) { labelByJob[j] -= slack; } else { minSlackValueByJob[j] -= slack; } } } public static void main(String[] args) { Scanner sc = new Scanner(System.in); System.out.println("Enter the dimentsions of the cost matrix: "); System.out.println("r:"); int r = sc.nextInt(); System.out.println("c:"); int c = sc.nextInt(); System.out.println("Enter the cost matrix: <row wise>"); double[][] cost = new double[r]; for (int i = 0; i < r; i++) { for (int j = 0; j < c; j++) { cost[i][j] = sc.nextDouble(); } } HungarianBipartiteMatching hbm = new HungarianBipartiteMatching(cost); int[] result = hbm.execute(); System.out.println("Bipartite Matching: " + Arrays.toString(result)); sc.close(); } }
Output:
$ javac HungarianBipartiteMatching.java $ java HungarianBipartiteMatching Enter the dimentsions of the cost matrix: r: 4 c: 4 Enter the cost matrix: <row wise> 82 83 69 92 77 37 49 92 11 69 5 86 8 9 98 23 Bipartite Matching: [2, 1, 0, 3] //worker 1 should perform job 3, worker 2 should perform job 2 and so on...
Related posts:
Java Program to Find Number of Spanning Trees in a Complete Bipartite Graph
Converting Strings to Enums in Java
Java Streams vs Vavr Streams
Assertions in JUnit 4 and JUnit 5
Tìm hiểu về xác thực và phân quyền trong ứng dụng
Guide to the Volatile Keyword in Java
Java Program to Implement Insertion Sort
Java Program to Perform Right Rotation on a Binary Search Tree
Allow user:password in URL
Java Program to Compute Discrete Fourier Transform Using Naive Approach
Java List UnsupportedOperationException
Hướng dẫn Java Design Pattern – Factory Method
Annotation trong Java 8
Java Program to Construct an Expression Tree for an Prefix Expression
The DAO with JPA and Spring
Java Program to Implement Stack using Two Queues
Java Program to Implement Cartesian Tree
Java Program to Implement ArrayList API
Truyền giá trị và tham chiếu trong java
Compact Strings in Java 9
So sánh HashSet, LinkedHashSet và TreeSet trong Java
Java Program to Implement Hash Tables Chaining with Binary Trees
Java Program to Implement Tarjan Algorithm
Java Program to Implement Dijkstra’s Algorithm using Priority Queue
Java Program to Implement Self Balancing Binary Search Tree
Java Program to Perform Partition of an Integer in All Possible Ways
Generating Random Dates in Java
Guide to the Fork/Join Framework in Java
Reversing a Linked List in Java
Java Program to Implement Quick Sort Using Randomization
Hướng dẫn Java Design Pattern – Chain of Responsibility
Java 9 Stream API Improvements