Network flow problem (original) (raw)
In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, 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. Specific types of network flow problems include: Algorithms for constructing flows include
| Property | Value |
|---|---|
| dbo:abstract | In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, 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. Specific types of network flow problems include: * The maximum flow problem, in which the goal is to maximize the total amount of flow out of the source terminals and into the sink terminals * The minimum-cost flow problem, 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 * The multi-commodity flow problem, in which one must construct multiple flows for different commodities whose total flow amounts together respect the capacities * Nowhere-zero flow, a type of flow studied in combinatorics in which the flow amounts are restricted to a finite set of nonzero values The max-flow min-cut theorem equates the value of a maximum flow to the value of a minimum cut, 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. Approximate max-flow min-cut theorems provide an extension of this result to multi-commodity flow problems. The Gomory–Hu tree of an undirected flow network provides a concise representation of all minimum cuts between different pairs of terminal vertices. Algorithms for constructing flows include * Dinic's algorithm, a strongly polynomial algorithm for maximum flow * The Edmonds–Karp algorithm, a faster strongly polynomial algorithm for maximum flow * The Ford–Fulkerson algorithm, a greedy algorithm for maximum flow that is not in general strongly polynomial * The network simplex algorithm, a method based on linear programming but specialized for network flow * The out-of-kilter algorithm for minimum-cost flow * The push–relabel maximum flow algorithm, one of the most efficient known techniques for maximum flow Otherwise the problem can be formulated as a more conventional linear program or similar and solved using a general purpose optimization solver. This article includes a list of related items that share the same name (or similar names). If an internal link incorrectly led you here, you may wish to change the link to point directly to the intended article. (en) |
| dbo:wikiPageID | 3171800 (xsd:integer) |
| dbo:wikiPageLength | 2606 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1006876099 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Push–relabel_maximum_flow_algorithm dbr:Nowhere-zero_flow dbr:Algorithm dbr:Approximate_max-flow_min-cut_theorem dbc:Network_flow_problem dbc:Combinatorial_optimization dbr:Max-flow_min-cut_theorem dbr:Maximum_flow_problem dbr:Gomory–Hu_tree dbr:Combinatorial_optimization dbc:Graph_algorithms dbc:Directed_graphs dbr:Network_simplex_algorithm dbr:Minimum-cost_flow_problem dbr:Minimum_cut dbr:Flow_network dbr:Dinic's_algorithm dbr:Edmonds–Karp_algorithm dbr:Ford–Fulkerson_algorithm dbr:Multi-commodity_flow_problem dbr:Out-of-kilter_algorithm dbr:Linear_program |
| dbp:wikiPageUsesTemplate | dbt:Short_description dbt:Unreferenced dbt:Sia |
| dcterms:subject | dbc:Network_flow_problem dbc:Combinatorial_optimization dbc:Graph_algorithms dbc:Directed_graphs |
| rdfs:comment | In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities on its edges), and the goal is to construct a flow, 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. Specific types of network flow problems include: Algorithms for constructing flows include (en) |
| rdfs:label | Network flow problem (en) |
| owl:sameAs | wikidata:Network flow problem https://global.dbpedia.org/id/5ENFk |
| prov:wasDerivedFrom | wikipedia-en:Network_flow_problem?oldid=1006876099&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Network_flow_problem |
| is dbo:wikiPageDisambiguates of | dbr:Network_flow |
| is dbo:wikiPageWikiLink of | dbr:Leximin_order dbr:Network_flow dbr:Shannon_switching_game dbr:Laman_graph dbr:Linear_programming dbr:Minimum-cost_flow_problem dbr:Multi-commodity_flow_problem dbr:List_of_terms_relating_to_algorithms_and_data_structures dbr:The_Art_of_Computer_Programming dbr:Simultaneous_eating_algorithm |
| is foaf:primaryTopic of | wikipedia-en:Network_flow_problem |