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Class of computational problems
combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical capacities
Network_flow_problem
Directed graph where edges have a capacity
network of nodes. As such, efficient algorithms for solving network flows can also be applied to solve problems that can be reduced to a flow network
Flow_network
Computational problem in graph theory
maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be
Maximum_flow_problem
Mathematical optimization problem
cast as a minimum cost flow problem and also that it can be solved efficiently using the network simplex algorithm. A flow network is a directed graph G
Minimum-cost_flow_problem
Equivalence of optimization problems
science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink
Max-flow_min-cut_theorem
Topics referred to by the same term
Network flow may refer to: Network flow problem Flow network Traffic flow (computer networking) Flow (disambiguation) This disambiguation page lists articles
Network_flow
Network flow problem (mathematics)
multi-commodity flow problem is a network flow problem with multiple commodities (flow demands) between different source and sink nodes. Given a flow network G (
Multi-commodity_flow_problem
Algorithm in graph theory
The algorithm is usually formulated in terms of a minimum-cost flow problem. The network simplex method works very well in practice, typically 200 to 300
Network_simplex_algorithm
Algorithm for solving the minimum-cost flow problem
minimum-cost flow problem in a flow network. It was published in 1961 by D. R. Fulkerson and is described here. The analog of steady state flow in a network of
Out-of-kilter_algorithm
Generalization of network flow problems
circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation
Circulation_problem
Algorithm to compute the maximum flow in a network
algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network. It is sometimes called a "method" instead of an "algorithm" as
Ford–Fulkerson_algorithm
Computational problem of graph theory
certain network flow problems, particularly when dealing with single-source, single-sink networks. In these scenarios, we can transform the network flow problem
Shortest_path_problem
Mathematical propositions in network flow theory
multi-commodity flow problems. The classic max-flow min-cut theorem states that for networks with a single type of flow (single-commodity flows), the maximum
Approximate max-flow min-cut theorem
Approximate_max-flow_min-cut_theorem
Partition of a graph by removing fewest possible edges
to max-flow min-cut theorem, 2 nodes' Minimum cut value is equal to their maxflow value. In this case, some algorithms used in maxflow problem could also
Minimum_cut
Combinatorial optimization problem
integral maximum flow of minimum cost can be found in polynomial time; see network flow problem. Every integral maximum flow in this network corresponds to
Assignment_problem
Algorithm in mathematical optimization
preflow–push algorithm) is an algorithm for computing maximum flows in a flow network. The name "push–relabel" comes from the two basic operations used
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
electrical networks which will automatically produce a solution to the minimum s–t cut problem. Alternatively, simulation of such a network will also produce
Cederbaum's maximum flow theorem
Cederbaum's_maximum_flow_theorem
Concept in graph theory
In graph theory, a nowhere-zero flow or NZ flow is a network flow that is nowhere zero. It is intimately connected (by duality) to coloring planar graphs
Nowhere-zero_flow
Disproved conjecture in network flow theory
statement about single-source unsplittable flows. It concerns the problem of converting a fractional flow, which may split each terminal's demand across
Dinitz–Garg–Goemans conjecture
Dinitz–Garg–Goemans_conjecture
Algorithm for computing the maximal flow of a network
algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist
Dinic's_algorithm
American civil engineer and academic (born 1959)
Barnhart, Cynthia (1988). A network-based primal-dual solution methodology for the multi-commodity network flow problem (Ph.D.). Massachusetts Institute
Cynthia_Barnhart
Paradox related to increasing roadway capacity
the observation that adding one or more roads to a road network can slow down overall traffic flow through it. The paradox was first discovered by Arthur
Braess's_paradox
Network packet distribution with multiple cores
the same flow will always be steered to the same core. This is usually done in the kernel, right after the NIC driver. Having handled the network interrupt
Multi-core network packet steering
Multi-core_network_packet_steering
Algorithm to compute the maximum flow in a flow network
implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in O ( | V | | E | 2 ) {\displaystyle O(|V||E|^{2})} time. The algorithm
Edmonds–Karp_algorithm
Basic concept of graph theory
related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. In an undirected graph
Connectivity_(graph_theory)
Utilization System is the first implementation of network flow monitoring, and is an ongoing open source network flow monitor project. Started by Carter Bullard
Argus – Audit Record Generation and Utilization System
Argus_–_Audit_Record_Generation_and_Utilization_System
network flow problems. In fact the preflow-push algorithm for max-flow can be derived by applying the original 1979 auction algorithm to the max flow
Auction_algorithm
Taiwanese-American computer scientist
network flow problems included the representation of all pairwise flows using the Gomory–Hu tree,[GH61] the formulation of the multi-commodity flow problem
T._C._Hu
Weighted tree representing s-t cuts of a graph
Cut (graph theory) Max-flow min-cut theorem Maximum flow problem Gomory, R. E.; Hu, T. C. (1961). "Multi-terminal network flows". Journal of the Society
Gomory–Hu_tree
Set of edges without common vertices
Finding a largest matching in a bipartite graph can be treated as a network flow problem. Finding a largest matching in a general graph is much more difficult;
Matching_(graph_theory)
American mathematician (1927–2017)
specializing in network flow problems. He was the son of mathematician Lester R. Ford Sr. Ford's paper with D. R. Fulkerson on the maximum flow problem and the
L._R._Ford_Jr.
Topics referred to by the same term
substances to and from cells Circulation problem, a generalization of network flow problems Exhaust gas recirculation, a nitrogen oxide reduction technique
Circulation
Graph with at most one cycle per component
solution of certain network flow problems. Pseudoforests also form graph-theoretic models of functions and occur in several algorithmic problems. Pseudoforests
Pseudoforest
Method to solve optimization problems
linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems, are considered
Linear_programming
Spatial analysis tools for geographic networks
infrastructure that permits and constrains movement or flow. Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts,
Transport_network_analysis
Numerical analysis of electric power flow
power-flow study is a numerical analysis of the flow of electric power in an interconnected system. It is also known as power-flow analysis, load-flow study
Power-flow_study
Type of diagram
diagram (MFD) is type of traffic flow fundamental diagram that relates space-mean flow, density and speed of an entire network with n number of links as shown
Fundamental diagram of traffic flow
Fundamental_diagram_of_traffic_flow
Analysis in fluid dynamics
The aim is to determine the flow rates and pressure drops in the individual sections of the network. This is a common problem in hydraulic design. To direct
Pipe_network_analysis
Technique to suspend transmission to avoid congestion
Ethernet flow control is a mechanism for temporarily stopping the transmission of data on the Ethernet-family of computer networks. The goal of this mechanism
Ethernet_flow_control
Graph with actively propelled particles
active flow network is a graph with edges and nodes, where particles inside this graph are propelled by an active mechanism. This type of network is used
Active_flow_network
Optimization problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a
Vehicle_routing_problem
Italian-American statistician and climate change researcher
involved a Bayesian analysis of network flow problems. She was interested in her applying her statistics to a real world problem, and she moved to the National
Claudia_Tebaldi
Data-flow programming paradigm
In computer programming, flow-based programming (FBP) is a programming paradigm that defines applications as networks of black box processes, which exchange
Flow-based_programming
18 mathematical problems stated in 1998
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 and republished in 1999. Smale composed this list
Smale's_problems
Comparison between vectors
as a rule for solving network flow problems. Given a flow network, a source s, a sink t, and a specified subset E of edges, a flow is called leximin-optimal
Leximin_order
Optimization technique
maximizing the flow through an associated image network, or graph, involving the introduction of a source and sink and Log-likelihood ratios. The problem was shown
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Optimization problem for maritime transportation
real-world problems. The problem consist of two subproblems; 1) designing feasible services, and 2) flowing the container flows through the network. An industry-standard
Liner shipping network design and scheduling problem
Liner_shipping_network_design_and_scheduling_problem
Type of artificial neural network
regulate information flow, inspired by long short-term memory (LSTM) recurrent neural networks. The advantage of the Highway Network over other deep learning
Highway_network
Integer matrices with +1 or −1 determinant; invertible over the integers. GL_n(Z)
maximum flow and minimum cost flow problems yield a coefficient matrix with these properties (and with empty C). Thus, such network flow problems with bounded
Unimodular_matrix
American computer scientist
graphs and networks, including the push–relabel maximum flow algorithm developed with Robert Tarjan, work on shortest paths and minimum-cost flow, and experimental
Andrew_V._Goldberg
Computational problem in graph theory
polynomial time using a reduction to the maximum flow problem. It may be used to model various application problems of choosing an optimal subset of tasks to
Closure_problem
Problem in combinatorial optimization
minimum-cost flow problem, the input is a flow network, with given capacities that specify lower and upper limits on the amount of flow per edge, as well
Submodular_flow
System involved in supplying a product or service to a consumer
customers, while supply chain management focuses on the optimization of the flow of goods within the supply chain's distribution channels to ensure efficiency
Supply_chain
Diagram that represents a workflow or process
network Business process mapping Data and information visualization Interactive EasyFlow Process architecture Pseudocode Recursive transition network
Flowchart
Data structure for representing a forest
n) to worst case O(log n). It has uses in solving a variety of network flow problems and to jive data sets. In the original publication, Sleator and
Link/cut_tree
Reconstruction of binary images from a small number of their projections
found the same consistency conditions, but in connection with the network flow problem. Another result of Ryser's is the definition of the switching operation
Discrete_tomography
Data transmission rate management
reservation" or "hop-to-hop" type. Open-loop flow control has inherent problems with maximizing the utilization of network resources. Resource allocation is made
Flow_control_(data)
Computational model used in machine learning
neural network (NN) or artificial neural network (ANN) is a computational model inspired by the structure and functions of biological neural networks. A neural
Neural network (machine learning)
Neural_network_(machine_learning)
Method to find shortest paths
version of the successive shortest paths algorithm for the minimum cost flow problem due to Edmonds and Karp, as well as in Suurballe's algorithm for finding
Johnson's_algorithm
Technique to solve partial differential equations
George Em (October 2022). "Physics-informed neural networks for inverse problems in supersonic flows". Journal of Computational Physics. 466 111402. arXiv:2202
Physics-informed neural networks
Physics-informed_neural_networks
Full immersion in an activity
planning, problem solving, and evaluation predicted transient flow states, but that more stable job characteristics were not found to predict flow at work
Flow_(psychology)
Polynomial-time algorithm for the assignment problem
running time. Ford and Fulkerson extended the method to general maximum flow problems in the form of the Ford–Fulkerson algorithm. In this simple example
Hungarian_algorithm
Communications protocol
NetFlow is a feature that was introduced on Cisco routers around 1996 that provides the ability to collect IP network traffic as it enters or exits an
NetFlow
Graph with edges non-crossing and upward
embedding is bimodal and modeling the consistent assignment problem as a network flow problem. The running time is linear in the size of the input graph
Upward_planar_drawing
Technique for the generative modeling of a continuous probability distribution
These linear flow formulations were independently discovered and adapted from a different perspective for supervised inverse problems. For example, Inversion
Diffusion_model
Machine learning model training problem
gradient problem is the problem of greatly diverging gradient magnitudes between earlier and later layers encountered when training neural networks with backpropagation
Vanishing_gradient_problem
Reduced quality of service due to high network traffic
The Lagrange dual of this problem decouples so that each flow sets its own rate, based only on a price signaled by the network. Each link capacity imposes
Network_congestion
American computer scientist
Engineering (BB) for his work on the role of parametric programming in network flow problems. Ahuja has held positions at several prestigious universities, including
Ravindra_K._Ahuja
Architecture of quality of service of computer networking
individual reservation. Flow specs describe what the reservation is for, while RSVP is the underlying mechanism to signal it across the network. There are two
Integrated_services
Subfield of mathematical optimization
to people optimally Designing water distribution networks Earth science problems (e.g. reservoir flow-rates) There is a large amount of literature on polynomial-time
Combinatorial_optimization
Management of the flow of resources
supply chain management that deals with the efficient forward and reverse flow of goods, services, and related information from the point of origin to the
Logistics
Pattern of motion in a visual scene due to relative motion of the observer
unknowns. This is known as the aperture problem. Therefore, additional constraints must be imposed to estimate the flow field. Perhaps the most natural approach
Optical_flow
Network that allows computers to share resources and communicate with each other
Utah. Designed principally by Bob Kahn, the network's routing, flow control, software design and network control were developed by the IMP team working
Computer_network
Graph divided into two independent sets
463: "Nonbipartite matching problems are more difficult to solve because they do not reduce to standard network flow problems." Hopcroft, John E.; Karp
Bipartite_graph
Israeli-Canadian operations researcher
University of British Columbia. Her research publications have concerned network flow problems, integer programming, cooperative game theory, and supply chains
Frieda_Granot
Computer Networking Program
general network problems with arbitrary demands is a hard problem, which can be NP-hard and even undecidable. In a linear network coding problem, a group
Linear_network_coding
Area of discrete mathematics
of flows in networks, for example: Max flow min cut theorem Museum guard problem Covering problems in graphs may refer to various set cover problems on
Graph_theory
American mathematician (1943–2024)
developing the theory of Ricci flow. Hamilton introduced the Ricci flow in 1982 and, over the next decades, he developed a network of results and ideas for
Richard_S._Hamilton
Approach to network management
OpenFlow protocol for remote communication with network plane elements to determine the path of network packets across network switches since OpenFlow's emergence
Software-defined_networking
combinatorial optimization, fractional programming, linear programming and network flow problems. He had been in the editorial board of Opsearch, an official journal
Munish_Chander_Puri
Path-finding using high-weight graph edges
algorithm for the maximum flow problem. Repeatedly augmenting a flow along a maximum capacity path in the residual network of the flow leads to a small bound
Widest_path_problem
American engineer and university president (born 1945)
Operations Research, 146: 19–39, 2006 Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs (with K. Croxton and B. Gendron), Operations
Thomas_L._Magnanti
Study of interactions between travellers and infrastructure
optimal transport network with efficient movement of traffic and minimal traffic congestion problems. The foundation for modern traffic flow analysis dates
Traffic_flow
Inventory management identifier
original on 14 December 2021. Retrieved 14 Dec 2021. Roussos, George (2008). Networked RFID: Systems, Software and Services. Springer Science & Business Media
Stock_keeping_unit
Machine learning software library
TensorFlow computations are expressed as stateful dataflow graphs. The name TensorFlow derives from the operations that such neural networks perform
TensorFlow
Data flow control switching method
Wormhole flow control, also called wormhole switching or wormhole routing, is a system of simple flow control in computer networking based on known fixed
Wormhole_switching
American mathematician
2025. "Serial and Parallel Algorithms for Large-Scale Nonlinear Network Flow Problems (Engineering)". nsf.gov. Retrieved March 18, 2021. "NSF Faculty
Anna_Nagurney
"5-flow conjecture". Open Problem Garden. Archived from the original on November 26, 2018. mdevos (March 31, 2010). "4-flow conjecture". Open Problem Garden
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Real-time networking effort
physical network. To support real-time applications, DetNet implements reservation of data plane resources in intermediate nodes along the data flow path
Deterministic_Networking
Method for determining flow in pipe network systems
method for determining the flow in pipe network systems where the inputs and outputs are known, but the flow inside the network is unknown. The method was
Hardy_Cross_method
Mathematical optimization problem restricted to integers
This problem can be formulated as an integer linear program in which binary variables indicate whether a frequency is assigned to an antenna. Cash flow matching
Integer_programming
Study of mathematical algorithms for optimization problems
A. (2003-01-01). "Modeling, Simulation, and Optimization of Traffic Flow Networks". SIAM Journal on Scientific Computing. 25 (3): 1066–1087. Bibcode:2003SJSC
Mathematical_optimization
Set of managerial and production principles
suppliers discover and fix problems to become more robust, better suppliers. The final principles embrace a philosophy of problem-solving that emphasizes
The_Toyota_Way
Soviet and Israeli computer scientist
25 December 2023. "An algorithm for the solution of the problem of maximal flow in a network with power estimation". Math-Net.Ru. Retrieved 24 December
Yefim_Dinitz
Russian-British mathematician
have simultaneous transversals, closely related to later work on network flow problems. He also was one of the first to recognize the importance of transversal
Leon_Mirsky
Knowledge base that represents semantic relations between concepts in a network
A semantic network, or frame network is a knowledge base that represents semantic relations between concepts in a network. This is often used as a form
Semantic_network
Path used to transport goods
network identified as a series of pathways and stoppages used for the commercial transport of cargo. Ancient trade routes were long-distance networks
Trade_route
Algorithm employed by process and network schedulers in computing
scheduling can be applied to other scheduling problems, such as data packet scheduling in computer networks. It is an operating system concept. The name
Round-robin_scheduling
Chinese-American mathematician
include: Efficient algorithms for structured convex programs and network flow problems, Complexity analysis of interior point methods for linear programming
Paul_Tseng
Modelling of electrical grids
rise to a large class of mathematical optimization problems. Electricity flows through an AC network according to Kirchhoff's Laws. Transmission lines
Power_system_simulation
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NETWORK FLOW-PROBLEM
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