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Maximum weight matching

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25: 284: 194: 145:, and the matching constrained to be have cardinality that of the smaller of the two partitions. Another special case is the problem of finding a 349: 93: 65: 35: 72: 325: 344: 79: 196:
time algorithm to find a maximum matching or a maximum weight matching in a graph that is not bipartite; it is due to
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More elaborate algorithms exist and are reviewed by Duan and Pettie (see Table III). Their work proposes an
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for the maximum weight matching problem, which runs in linear time for any fixed error bound.
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on an unweighted graph: this corresponds to the case where all edge weights are the same.
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Graph theory problem: find a matching with max total weight
246:"Linear-Time Approximation for Maximum Weight Matching" 163: 188: 336: 319: 51:introducing citations to additional sources 141:, in which the input is restricted to be a 326: 312: 243: 134:in which the sum of weights is maximized. 126:problem is the problem of finding, in a 41:Relevant discussion may be found on the 350:Computational problems in graph theory 337: 244:Duan, Ran; Pettie, Seth (2014-01-01). 278: 18: 13: 14: 366: 282: 34:relies largely or entirely on a 23: 237: 183: 167: 1: 230: 152: 298:. You can help Knowledge by 147:maximum cardinality matching 137:A special case of it is the 7: 10: 371: 345:Combinatorial optimization 277: 202:paths, trees, and flowers 189:{\displaystyle O(V^{2}E)} 62:"Maximum weight matching" 214:maximum independent sets 225:approximation algorithm 124:maximum weight matching 294:-related article is a 190: 191: 161: 47:improve this article 355:Graph theory stubs 253:Journal of the ACM 206:Edmonds' algorithm 186: 139:assignment problem 307: 306: 204:method or simply 112: 111: 97: 362: 328: 321: 314: 286: 279: 269: 268: 250: 241: 218:claw-free graphs 210:bidirected edges 200:, is called the 195: 193: 192: 187: 179: 178: 116:computer science 107: 104: 98: 96: 55: 27: 19: 370: 369: 365: 364: 363: 361: 360: 359: 335: 334: 333: 332: 275: 273: 272: 265:10.1145/2529989 248: 242: 238: 233: 174: 170: 162: 159: 158: 155: 143:bipartite graph 108: 102: 99: 56: 54: 40: 28: 17: 12: 11: 5: 368: 358: 357: 352: 347: 331: 330: 323: 316: 308: 305: 304: 287: 271: 270: 235: 234: 232: 229: 185: 182: 177: 173: 169: 166: 154: 151: 128:weighted graph 110: 109: 45:. Please help 31: 29: 22: 15: 9: 6: 4: 3: 2: 367: 356: 353: 351: 348: 346: 343: 342: 340: 329: 324: 322: 317: 315: 310: 309: 303: 301: 297: 293: 288: 285: 281: 280: 276: 266: 262: 258: 254: 247: 240: 236: 228: 226: 221: 219: 215: 211: 207: 203: 199: 180: 175: 171: 164: 150: 148: 144: 140: 135: 133: 129: 125: 121: 117: 106: 95: 92: 88: 85: 81: 78: 74: 71: 67: 64: –  63: 59: 58:Find sources: 52: 48: 44: 38: 37: 36:single source 32:This article 30: 26: 21: 20: 300:expanding it 292:graph theory 289: 274: 256: 252: 239: 222: 201: 198:Jack Edmonds 156: 136: 123: 120:graph theory 113: 100: 90: 83: 76: 69: 57: 33: 208:, and uses 157:There is a 339:Categories 231:References 153:Algorithms 103:April 2024 73:newspapers 43:talk page 259:: 1–23. 132:matching 87:scholar 122:, the 89:  82:  75:  68:  60:  290:This 249:(PDF) 94:JSTOR 80:books 296:stub 130:, a 118:and 66:news 261:doi 216:in 114:In 49:by 341:: 257:61 255:. 251:. 220:. 327:e 320:t 313:v 302:. 267:. 263:: 184:) 181:E 176:2 172:V 168:( 165:O 105:) 101:( 91:· 84:· 77:· 70:· 53:. 39:.

Index


single source
talk page
improve this article
introducing citations to additional sources
"Maximum weight matching"
news
newspapers
books
scholar
JSTOR
computer science
graph theory
weighted graph
matching
assignment problem
bipartite graph
maximum cardinality matching
Jack Edmonds
Edmonds' algorithm
bidirected edges
maximum independent sets
claw-free graphs
approximation algorithm
"Linear-Time Approximation for Maximum Weight Matching"
doi
10.1145/2529989
Stub icon
graph theory
stub

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