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Everything about Network flow problem
Class of computational problems
In combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network, 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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Network flow problemA 5-minute orientation
- Skim a recent paper: Optimal Power Flow in Distribution Network: A Review on Problem Formulation and Optimization MethodsInfluential work since 2022
- Pick up a classic book: Computer NetworksThe most-reprinted book on the subject
- Read the landmark paper: The Operator-Scheduling Problem: A Network-Flow ApproachCited 117 times
- Go sideways: Minimum cutA closely related topic
- Go sideways: Closure problemA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Operator-Scheduling Problem: A Network-Flow Approach
Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem
A composite algorithm for a concave‐cost network flow problem
The maximum flow problem of uncertain network
Solving the Convex Cost Integer Dual Network Flow Problem
Multicommodity network flow approach to the railroad crew-scheduling problem
The multi-terminal maximum-flow network-interdiction problem
A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure
🆕 Influential since 2022
Optimal Power Flow in Distribution Network: A Review on Problem Formulation and Optimization Methods
A network memetic algorithm for energy and labor-aware distributed heterogeneous hybrid flow shop scheduling problem
A network sensor location problem for link flow observability and estimation
Reliability–redundancy allocation problem in multi-state flow network: Minimal cut-based approximation scheme
Multi-Objective Flexible Flow Shop Production Scheduling Problem Based on the Double Deep Q-Network Algorithm
📚 Books worth reading
Computer NetworksAndrew S. Tanenbaum, John David Wetherall · 1981
Computer networkingJames F. Kurose, Keith W. Ross · 1900- 📕Miscellaneous problems in maritime navigation, transport and shippingAdam Weintrit, Tomasz Neumann · 2011
Graphs, Networks and AlgorithmsDieter Jungnickel · 2006
Mathematics in Industrial ProblemsAvner Friedman · 1998
Network-aware source coding and communicationNima Sarshar · 2011
Communication networksJean Walrand · 2010- 📕Gravity-driven water flow in networksGerard F. Jones · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Minimum cut In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some…
- Closure problem In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is…
- Max-flow min-cut theorem In computer 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…
- Minimum-cost flow problem The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through…
- Assignment problem The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has…
- Maximum flow problem In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum…
- Cut (graph theory) In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one…
- Matching (graph theory) In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In…