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Network flow problem

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257: 25: 145:, numerical values on each edge that respect the capacity constraints and that have incoming flow equal to outgoing flow at all vertices except for certain designated terminals. 163:, in which the edges have costs as well as capacities and the goal is to achieve a given amount of flow (or a maximum flow) that has the minimum possible cost 241: 188:, a partition of the vertices of the flow network that minimizes the total capacity of edges crossing from one side of the partition to the other. 46: 189: 304: 116: 97: 196:
of an undirected flow network provides a concise representation of all minimum cuts between different pairs of terminal vertices.
69: 170:, in which one must construct multiple flows for different commodities whose total flow amounts together respect the capacities 50: 76: 294: 220: 265: 167: 289: 83: 213: 176:, a type of flow studied in combinatorics in which the flow amounts are restricted to a finite set of nonzero values 156:, in which the goal is to maximize the total amount of flow out of the source terminals and into the sink terminals 130: 299: 227: 160: 65: 309: 181: 35: 234: 54: 39: 206: 153: 275:
incorrectly led you here, you may wish to change the link to point directly to the intended article.
193: 90: 173: 249: 283: 142: 138: 141:(a graph with numerical capacities on its edges), and the goal is to construct a 223:, a greedy algorithm for maximum flow that is not in general strongly polynomial 185: 24: 268:
includes a list of related items that share the same name (or similar names).
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provide an extension of this result to multi-commodity flow problems. The
230:, a method based on linear programming but specialized for network flow 252:
or similar and solved using a general purpose optimization solver.
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Otherwise the problem can be formulated as a more conventional
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are a class of computational problems in which the input is a
18: 244:, one of the most efficient known techniques for maximum flow 216:, a faster strongly polynomial algorithm for maximum flow 272: 184:
equates the value of a maximum flow to the value of a
209:, a strongly polynomial algorithm for maximum flow 148:Specific types of network flow problems include: 262:Index of articles associated with the same name 8: 53:. Unsourced material may be challenged and 117:Learn how and when to remove this message 190:Approximate max-flow min-cut theorems 7: 51:adding citations to reliable sources 242:push–relabel maximum flow algorithm 14: 255: 23: 202:for constructing flows include 16:Class of computational problems 1: 168:multi-commodity flow problem 326: 305:Combinatorial optimization 254: 131:combinatorial optimization 228:network simplex algorithm 161:minimum-cost flow problem 221:Ford–Fulkerson algorithm 182:max-flow min-cut theorem 235:out-of-kilter algorithm 214:Edmonds–Karp algorithm 66:"Network flow problem" 237:for minimum-cost flow 135:network flow problems 295:Network flow problem 154:maximum flow problem 47:improve this article 290:Set index articles 266:set index article 207:Dinic's algorithm 174:Nowhere-zero flow 127: 126: 119: 101: 317: 300:Graph algorithms 276: 259: 122: 115: 111: 108: 102: 100: 59: 27: 19: 325: 324: 320: 319: 318: 316: 315: 314: 310:Directed graphs 280: 279: 278: 277: 270: 269: 263: 123: 112: 106: 103: 60: 58: 44: 28: 17: 12: 11: 5: 323: 321: 313: 312: 307: 302: 297: 292: 282: 281: 261: 260: 250:linear program 246: 245: 238: 231: 224: 217: 210: 194:Gomory–Hu tree 178: 177: 171: 164: 157: 125: 124: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 322: 311: 308: 306: 303: 301: 298: 296: 293: 291: 288: 287: 285: 274: 273:internal link 267: 258: 253: 251: 243: 239: 236: 232: 229: 225: 222: 218: 215: 211: 208: 205: 204: 203: 201: 197: 195: 191: 187: 183: 175: 172: 169: 165: 162: 158: 155: 151: 150: 149: 146: 144: 140: 136: 132: 121: 118: 110: 99: 96: 92: 89: 85: 82: 78: 75: 71: 68: â€“  67: 63: 62:Find sources: 56: 52: 48: 42: 41: 37: 32:This article 30: 26: 21: 20: 247: 198: 179: 147: 139:flow network 134: 128: 113: 104: 94: 87: 80: 73: 61: 45:Please help 33: 186:minimum cut 284:Categories 200:Algorithms 107:April 2018 77:newspapers 34:does not 91:scholar 55:removed 40:sources 271:If an 93:  86:  79:  72:  64:  264:This 98:JSTOR 84:books 240:The 233:The 226:The 219:The 212:The 180:The 166:The 159:The 152:The 143:flow 70:news 38:any 36:cite 129:In 49:by 286:: 133:, 120:) 114:( 109:) 105:( 95:· 88:· 81:· 74:· 57:. 43:.

Index


cite
sources
improve this article
adding citations to reliable sources
removed
"Network flow problem"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
combinatorial optimization
flow network
flow
maximum flow problem
minimum-cost flow problem
multi-commodity flow problem
Nowhere-zero flow
max-flow min-cut theorem
minimum cut
Approximate max-flow min-cut theorems
Gomory–Hu tree
Algorithms
Dinic's algorithm
Edmonds–Karp algorithm
Ford–Fulkerson algorithm
network simplex algorithm
out-of-kilter algorithm

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