Assignment Problem Hungarian Method C++ Code Examples

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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.

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.

Output:

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  1.  
  2. packagecom.hinguapps.graph;
  3.  
  4. importjava.util.Arrays;
  5. importjava.util.Scanner;
  6.  
  7. publicclass HungarianBipartiteMatching
  8. {
  9. privatefinaldouble[][] costMatrix;
  10. privatefinalint rows, cols, dim;
  11. privatefinaldouble[] labelByWorker, labelByJob;
  12. privatefinalint[] minSlackWorkerByJob;
  13. privatefinaldouble[] minSlackValueByJob;
  14. privatefinalint[] matchJobByWorker, matchWorkerByJob;
  15. privatefinalint[] parentWorkerByCommittedJob;
  16. privatefinalboolean[] committedWorkers;
  17.  
  18. public HungarianBipartiteMatching(double[][] costMatrix)
  19. {
  20. this.dim=Math.max(costMatrix.length, costMatrix[0].length);
  21. this.rows= costMatrix.length;
  22. this.cols= costMatrix[0].length;
  23. this.costMatrix=newdouble[this.dim][this.dim];
  24. for(int w =0; w <this.dim; w++)
  25. {
  26. if(w < costMatrix.length)
  27. {
  28. if(costMatrix[w].length!=this.cols)
  29. {
  30. thrownewIllegalArgumentException("Irregular cost matrix");
  31. }
  32. this.costMatrix[w]=Arrays.copyOf(costMatrix[w], this.dim);
  33. }
  34. else
  35. {
  36. this.costMatrix[w]=newdouble[this.dim];
  37. }
  38. }
  39. labelByWorker =newdouble[this.dim];
  40. labelByJob =newdouble[this.dim];
  41. minSlackWorkerByJob =newint[this.dim];
  42. minSlackValueByJob =newdouble[this.dim];
  43. committedWorkers =newboolean[this.dim];
  44. parentWorkerByCommittedJob =newint[this.dim];
  45. matchJobByWorker =newint[this.dim];
  46. Arrays.fill(matchJobByWorker, -1);
  47. matchWorkerByJob =newint[this.dim];
  48. Arrays.fill(matchWorkerByJob, -1);
  49. }
  50.  
  51. protectedvoid computeInitialFeasibleSolution()
  52. {
  53. for(int j =0; j < dim; j++)
  54. {
  55. labelByJob[j]=Double.POSITIVE_INFINITY;
  56. }
  57. for(int w =0; w < dim; w++)
  58. {
  59. for(int j =0; j < dim; j++)
  60. {
  61. if(costMatrix[w][j]< labelByJob[j])
  62. {
  63. labelByJob[j]= costMatrix[w][j];
  64. }
  65. }
  66. }
  67. }
  68.  
  69. publicint[] execute()
  70. {
  71. /*
  72.   * Heuristics to improve performance: Reduce rows and columns by their
  73.   * smallest element, compute an initial non-zero dual feasible solution
  74.   * and
  75.   * create a greedy matching from workers to jobs of the cost matrix.
  76.   */
  77. reduce();
  78. computeInitialFeasibleSolution();
  79. greedyMatch();
  80. int w = fetchUnmatchedWorker();
  81. while(w < dim)
  82. {
  83. initializePhase(w);
  84. executePhase();
  85. w = fetchUnmatchedWorker();
  86. }
  87. int[] result =Arrays.copyOf(matchJobByWorker, rows);
  88. for(w =0; w < result.length; w++)
  89. {
  90. if(result[w]>= cols)
  91. {
  92. result[w]=-1;
  93. }
  94. }
  95. return result;
  96. }
  97.  
  98. protectedvoid executePhase()
  99. {
  100. while(true)
  101. {
  102. int minSlackWorker =-1, minSlackJob =-1;
  103. double minSlackValue =Double.POSITIVE_INFINITY;
  104. for(int j =0; j < dim; j++)
  105. {
  106. if(parentWorkerByCommittedJob[j]==-1)
  107. {
  108. if(minSlackValueByJob[j]< minSlackValue)
  109. {
  110. minSlackValue = minSlackValueByJob[j];
  111. minSlackWorker = minSlackWorkerByJob[j];
  112. minSlackJob = j;
  113. }
  114. }
  115. }
  116. if(minSlackValue >0)
  117. {
  118. updateLabeling(minSlackValue);
  119. }
  120. parentWorkerByCommittedJob[minSlackJob]= minSlackWorker;
  121. if(matchWorkerByJob[minSlackJob]==-1)
  122. {
  123. /*
  124.   * An augmenting path has been found.
  125.   */
  126. int committedJob = minSlackJob;
  127. int parentWorker = parentWorkerByCommittedJob[committedJob];
  128. while(true)
  129. {
  130. int temp = matchJobByWorker[parentWorker];
  131. match(parentWorker, committedJob);
  132. committedJob = temp;
  133. if(committedJob ==-1)
  134. {
  135. break;
  136. }
  137. parentWorker = parentWorkerByCommittedJob[committedJob];
  138. }
  139. return;
  140. }
  141. else
  142. {
  143. /*
  144.   * Update slack values since we increased the size of the
  145.   * committed
  146.   * workers set.
  147.   */
  148. int worker = matchWorkerByJob[minSlackJob];
  149. committedWorkers[worker]=true;
  150. for(int j =0; j < dim; j++)
  151. {
  152. if(parentWorkerByCommittedJob[j]==-1)
  153. {
  154. double slack = costMatrix[worker][j]
  155. - labelByWorker[worker]- labelByJob[j];
  156. if(minSlackValueByJob[j]> slack)
  157. {
  158. minSlackValueByJob[j]= slack;
  159. minSlackWorkerByJob[j]= worker;
  160. }
  161. }
  162. }
  163. }
  164. }
  165. }
  166.  
  167. protectedint fetchUnmatchedWorker()
  168. {
  169. int w;
  170. for(w =0; w < dim; w++)
  171. {
  172. if(matchJobByWorker[w]==-1)
  173. {
  174. break;
  175. }
  176. }
  177. return w;
  178. }
  179.  
  180. protectedvoid greedyMatch()
  181. {
  182. for(int w =0; w < dim; w++)
  183. {
  184. for(int j =0; j < dim; j++)
  185. {
  186. if(matchJobByWorker[w]==-1
  187. && matchWorkerByJob[j]==-1
  188. && costMatrix[w][j]- labelByWorker[w]- labelByJob[j]==0)
  189. {
  190. match(w, j);
  191. }
  192. }
  193. }
  194. }
  195.  
  196. protectedvoid initializePhase(int w)
  197. {
  198. Arrays.fill(committedWorkers, false);
  199. Arrays.fill(parentWorkerByCommittedJob, -1);
  200. committedWorkers[w]=true;
  201. for(int j =0; j < dim; j++)
  202. {
  203. minSlackValueByJob[j]= costMatrix[w][j]- labelByWorker[w]
  204. - labelByJob[j];
  205. minSlackWorkerByJob[j]= w;
  206. }
  207. }
  208.  
  209. protectedvoid match(int w, int j)
  210. {
  211. matchJobByWorker[w]= j;
  212. matchWorkerByJob[j]= w;
  213. }
  214.  
  215. protectedvoid reduce()
  216. {
  217. for(int w =0; w < dim; w++)
  218. {
  219. double min =Double.POSITIVE_INFINITY;
  220. for(int j =0; j < dim; j++)
  221. {
  222. if(costMatrix[w][j]< min)
  223. {
  224. min = costMatrix[w][j];
  225. }
  226. }
  227. for(int j =0; j < dim; j++)
  228. {
  229. costMatrix[w][j]-= min;
  230. }
  231. }
  232. double[] min =newdouble[dim];
  233. for(int j =0; j < dim; j++)
  234. {
  235. min[j]=Double.POSITIVE_INFINITY;
  236. }
  237. for(int w =0; w < dim; w++)
  238. {
  239. for(int j =0; j < dim; j++)
  240. {
  241. if(costMatrix[w][j]< min[j])
  242. {
  243. min[j]= costMatrix[w][j];
  244. }
  245. }
  246. }
  247. for(int w =0; w < dim; w++)
  248. {
  249. for(int j =0; j < dim; j++)
  250. {
  251. costMatrix[w][j]-= min[j];
  252. }
  253. }
  254. }
  255.  
  256. protectedvoid updateLabeling(double slack)
  257. {
  258. for(int w =0; w < dim; w++)
  259. {
  260. if(committedWorkers[w])
  261. {
  262. labelByWorker[w]+= slack;
  263. }
  264. }
  265. for(int j =0; j < dim; j++)
  266. {
  267. if(parentWorkerByCommittedJob[j]!=-1)
  268. {
  269. labelByJob[j]-= slack;
  270. }
  271. else
  272. {
  273. minSlackValueByJob[j]-= slack;
  274. }
  275. }
  276. }
  277.  
  278. publicstaticvoid main(String[] args)
  279. {
  280. Scanner sc =new Scanner(System.in);
  281. System.out.println("Enter the dimentsions of the cost matrix: ");
  282. System.out.println("r:");
  283. int r = sc.nextInt();
  284. System.out.println("c:");
  285. int c = sc.nextInt();
  286. System.out.println("Enter the cost matrix: <row wise>");
  287. double[][] cost =newdouble[r][c];
  288. for(int i =0; i < r; i++)
  289. {
  290. for(int j =0; j < c; j++)
  291. {
  292. cost[i][j]= sc.nextDouble();
  293. }
  294. }
  295. HungarianBipartiteMatching hbm =new HungarianBipartiteMatching(cost);
  296. int[] result = hbm.execute();
  297. System.out.println("Bipartite Matching: "+Arrays.toString(result));
  298. sc.close();
  299. }
  300. }
$ 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...

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