Directed graphs | Combinatorial optimization | Graph algorithms | Network flow problem
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. (Wikipedia).
Bipartite Matching | Elementary Math problem | Network Flow | Graph Theory
Network flow problem example: The Elementary Math problem! Support me by purchasing the full graph theory course on Udemy which includes additional problems, exercises and quizzes not available on YouTube: https://www.udemy.com/course/graph-theory-algorithms Previous video: https://youtu
From playlist Network Flow playlist
OCR MEI MwA K: LP Solvers: 08 Network Flows Example 1
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From playlist TEACHING OCR MEI Modelling with Algorithms
OCR MEI MwA H: Network Flows: 01 Introduction
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From playlist OCR MEI MwA H: Network Flows
Linear Algebra - Lecture 14 - Applications to Networks
In this lecture, we study how to apply linear algebra techniques to flow networks.
From playlist Linear Algebra Lectures
Max Flow Ford Fulkerson | Network Flow | Graph Theory
Explanation of how to find the maximum flow with the Ford-Fulkerson method Next video: https://youtu.be/Xu8jjJnwvxE Algorithms repository: https://github.com/williamfiset/algorithms#network-flow Video slides: https://github.com/williamfiset/Algorithms/tree/master/slides 0:00 Intro and
From playlist Network Flow playlist
Computer Networks. Part Six: The TCP/IP Protocol Stack and Routers
This is the sixth in a series about computer networks. This video describes the role of a network protocol, and specifically details the TCP/IP suite of protocols. The need for a layered approach to networking software is discussed including the four layer TCP/IP stack and the relevance
From playlist Computer Networks
離散数学入門#8: 最大流問題(1):フローネットワークの基礎知識
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From playlist 離散数学入門Ⅲ
Lecture 10 | Convex Optimization II (Stanford)
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd introduces a new topic, Decomposition Applications. This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentral
From playlist Lecture Collection | Convex Optimization
Mean Curvature Flow, Neural Networks, and Applications
40th Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk Date: March 2, 10:00am Eastern Time Zone (US & Canada) / 2:00pm GMT Speaker: Elie Bretin, Institut Camille Jourdan and INSA Lyon Abstract: Many applications in image processing (denoising, segmentation)
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
A New Balancing Method for Solving Parametric Max Flow
March 14, 2007 lecture by Bin Zhang for the Stanford University Computer Systems Colloquium (EE 380). A new, simple and fast algorithm finds a sequence of nested minimum cuts of a bipartite parametric flow network. Instead of working with the original parametric flow-network, the new meth
From playlist Course | Computer Systems Laboratory Colloquium (2006-2007)
離散数学入門#9: 最大流問題(2):増加道アルゴリズムと最大流最小カット定理
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From playlist 離散数学入門Ⅲ
Nexus Trimester - Giacomo Como (Lund University)
Resilient control of dynamic flow networks Giacomo Como (Lund University) february 29, 2016 Abstract: This talk focuses on distributed control of dynamical flow networks. These are modeled as dynamical systems derived from mass conservation laws on directed capacitated networks. The flow
From playlist Nexus Trimester - 2016 - Central Workshop
Petar Veličković: "Reasoning on Natural Inputs"
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Stanford Seminar - Security and the Software Defined Network
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The (Counter-Intuitive) Geometry of Cut and Flow Polytopes - Ankur Moitra
Ankur Moitra Massachusetts Institute of Technology; Institute for Advanced Study October 3, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Gabriele Steidl: Stochastic normalizing flows and the power of patches in inverse problems
CONFERENCE Recording during the thematic meeting : "Learning and Optimization in Luminy" the October 4, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on C
From playlist Probability and Statistics