311 lines
11 KiB
Java
311 lines
11 KiB
Java
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/*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.*/
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import java.util.Arrays;
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import java.util.Scanner;
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public class HungarianBipartiteMatching
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{
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private final double[][] costMatrix;
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private final int rows, cols, dim;
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private final double[] labelByWorker, labelByJob;
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private final int[] minSlackWorkerByJob;
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private final double[] minSlackValueByJob;
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private final int[] matchJobByWorker, matchWorkerByJob;
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private final int[] parentWorkerByCommittedJob;
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private final boolean[] committedWorkers;
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public HungarianBipartiteMatching(double[][] costMatrix)
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{
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this.dim = Math.max(costMatrix.length, costMatrix[0].length);
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this.rows = costMatrix.length;
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this.cols = costMatrix[0].length;
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this.costMatrix = new double[this.dim][this.dim];
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for (int w = 0; w < this.dim; w++)
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{
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if (w < costMatrix.length)
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{
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if (costMatrix[w].length != this.cols)
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{
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throw new IllegalArgumentException("Irregular cost matrix");
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}
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this.costMatrix[w] = Arrays.copyOf(costMatrix[w], this.dim);
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}
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else
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{
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this.costMatrix[w] = new double[this.dim];
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}
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}
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labelByWorker = new double[this.dim];
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labelByJob = new double[this.dim];
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minSlackWorkerByJob = new int[this.dim];
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minSlackValueByJob = new double[this.dim];
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committedWorkers = new boolean[this.dim];
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parentWorkerByCommittedJob = new int[this.dim];
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matchJobByWorker = new int[this.dim];
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Arrays.fill(matchJobByWorker, -1);
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matchWorkerByJob = new int[this.dim];
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Arrays.fill(matchWorkerByJob, -1);
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}
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protected void computeInitialFeasibleSolution()
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{
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for (int j = 0; j < dim; j++)
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{
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labelByJob[j] = Double.POSITIVE_INFINITY;
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}
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for (int w = 0; w < dim; w++)
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{
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for (int j = 0; j < dim; j++)
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{
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if (costMatrix[w][j] < labelByJob[j])
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{
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labelByJob[j] = costMatrix[w][j];
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}
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}
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}
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}
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public int[] execute()
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{
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/*
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* Heuristics to improve performance: Reduce rows and columns by their
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* smallest element, compute an initial non-zero dual feasible solution
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* and
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* create a greedy matching from workers to jobs of the cost matrix.
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*/
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reduce();
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computeInitialFeasibleSolution();
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greedyMatch();
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int w = fetchUnmatchedWorker();
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while (w < dim)
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{
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initializePhase(w);
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executePhase();
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w = fetchUnmatchedWorker();
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}
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int[] result = Arrays.copyOf(matchJobByWorker, rows);
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for (w = 0; w < result.length; w++)
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{
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if (result[w] >= cols)
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{
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result[w] = -1;
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}
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}
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return result;
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}
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protected void executePhase()
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{
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while (true)
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{
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int minSlackWorker = -1, minSlackJob = -1;
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double minSlackValue = Double.POSITIVE_INFINITY;
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for (int j = 0; j < dim; j++)
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{
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if (parentWorkerByCommittedJob[j] == -1)
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{
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if (minSlackValueByJob[j] < minSlackValue)
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{
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minSlackValue = minSlackValueByJob[j];
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minSlackWorker = minSlackWorkerByJob[j];
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minSlackJob = j;
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}
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}
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}
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if (minSlackValue > 0)
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{
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updateLabeling(minSlackValue);
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}
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parentWorkerByCommittedJob[minSlackJob] = minSlackWorker;
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if (matchWorkerByJob[minSlackJob] == -1)
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{
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/*
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* An augmenting path has been found.
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*/
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int committedJob = minSlackJob;
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int parentWorker = parentWorkerByCommittedJob[committedJob];
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while (true)
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{
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int temp = matchJobByWorker[parentWorker];
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match(parentWorker, committedJob);
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committedJob = temp;
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if (committedJob == -1)
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{
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break;
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}
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parentWorker = parentWorkerByCommittedJob[committedJob];
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}
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return;
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}
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else
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{
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/*
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* Update slack values since we increased the size of the
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* committed
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* workers set.
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*/
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int worker = matchWorkerByJob[minSlackJob];
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committedWorkers[worker] = true;
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for (int j = 0; j < dim; j++)
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{
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if (parentWorkerByCommittedJob[j] == -1)
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{
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double slack = costMatrix[worker][j]
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- labelByWorker[worker] - labelByJob[j];
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if (minSlackValueByJob[j] > slack)
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{
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minSlackValueByJob[j] = slack;
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minSlackWorkerByJob[j] = worker;
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}
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}
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}
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}
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}
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}
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protected int fetchUnmatchedWorker()
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{
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int w;
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for (w = 0; w < dim; w++)
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{
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if (matchJobByWorker[w] == -1)
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{
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break;
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}
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}
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return w;
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}
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protected void greedyMatch()
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{
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for (int w = 0; w < dim; w++)
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{
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for (int j = 0; j < dim; j++)
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{
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if (matchJobByWorker[w] == -1
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&& matchWorkerByJob[j] == -1
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&& costMatrix[w][j] - labelByWorker[w] - labelByJob[j] == 0)
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{
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match(w, j);
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}
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}
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}
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}
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protected void initializePhase(int w)
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{
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Arrays.fill(committedWorkers, false);
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Arrays.fill(parentWorkerByCommittedJob, -1);
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committedWorkers[w] = true;
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for (int j = 0; j < dim; j++)
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{
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minSlackValueByJob[j] = costMatrix[w][j] - labelByWorker[w]
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- labelByJob[j];
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minSlackWorkerByJob[j] = w;
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}
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}
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protected void match(int w, int j)
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{
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matchJobByWorker[w] = j;
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matchWorkerByJob[j] = w;
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}
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protected void reduce()
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{
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for (int w = 0; w < dim; w++)
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{
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double min = Double.POSITIVE_INFINITY;
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for (int j = 0; j < dim; j++)
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{
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if (costMatrix[w][j] < min)
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{
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min = costMatrix[w][j];
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}
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}
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for (int j = 0; j < dim; j++)
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{
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costMatrix[w][j] -= min;
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}
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}
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double[] min = new double[dim];
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for (int j = 0; j < dim; j++)
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{
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min[j] = Double.POSITIVE_INFINITY;
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}
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for (int w = 0; w < dim; w++)
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{
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for (int j = 0; j < dim; j++)
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{
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if (costMatrix[w][j] < min[j])
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{
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min[j] = costMatrix[w][j];
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}
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}
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}
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for (int w = 0; w < dim; w++)
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{
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for (int j = 0; j < dim; j++)
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{
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costMatrix[w][j] -= min[j];
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}
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}
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}
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protected void updateLabeling(double slack)
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{
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for (int w = 0; w < dim; w++)
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{
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if (committedWorkers[w])
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{
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labelByWorker[w] += slack;
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}
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}
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for (int j = 0; j < dim; j++)
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{
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if (parentWorkerByCommittedJob[j] != -1)
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{
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labelByJob[j] -= slack;
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}
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else
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{
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minSlackValueByJob[j] -= slack;
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}
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}
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}
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public static void main(String[] args)
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{
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Scanner sc = new Scanner(System.in);
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System.out.println("Enter the dimentsions of the cost matrix: ");
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System.out.println("r:");
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int r = sc.nextInt();
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System.out.println("c:");
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int c = sc.nextInt();
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System.out.println("Enter the cost matrix: <row wise>");
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double[][] cost = new double[r][c];
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for (int i = 0; i < r; i++)
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{
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for (int j = 0; j < c; j++)
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{
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cost[i][j] = sc.nextDouble();
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}
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}
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HungarianBipartiteMatching hbm = new HungarianBipartiteMatching(cost);
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int[] result = hbm.execute();
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System.out.println("Bipartite Matching: " + Arrays.toString(result));
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sc.close();
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}
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}
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/*
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Enter the dimentsions of the cost matrix:
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r: 4
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c: 4
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Enter the cost matrix: <row wise>
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82 83 69 92
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77 37 49 92
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11 69 5 86
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8 9 98 23
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Bipartite Matching: [2, 1, 0, 3] //worker 1 should perform job 3, worker 2 should perform job 2 and so on...
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