'Residual network' presentation slideshows

Lecture 16

Lecture 16. Max Flows 3 Preflow-Push Algorithms. Review. The Ford Fulkerson Maximum Flow Algorithm. Begin x := 0; create the residual network G(x); while there is some directed path from s to t in G(x) do begin let P be a path from s to t in G(x); ? := ? (P);

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Overlay Network Creation and Maintenance with Selfish Users

Overlay Network Creation and Maintenance with Selfish Users. Georgios Smaragdakis. Dissertation committee members: Azer Bestavros, Nikolaos Laoutaris, John Byers. Overlays & Neighbor Selection. Overlay node. Overlay links.

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Max Flow

Max Flow. Jose Rolim University of Geneva. Graph Models. Graphs (used as models of "transportation" networks) have the following components: Links / edges: carrier of some sort of traffic and have capacities Nodes: - source nodes: generate traffic

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Flow Networks

Flow Networks. zichun@comp.nus.edu.sg. Formalization. Basic Results. Min-cut. Ford-Fulkerson. Edmunds-Karp. Bipartite Matching. Flow Network. Directed Graph G = (V, E) Each edge has a capacity. Properties of Flow. Capacity Constraint Skew Symmetry Flow Conservation. Maximum Flow.

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Network Flow

Network Flow. What is a network? Flow network and flows Ford-Fulkerson method - Residual networks - Augmenting paths - Cuts of flow networks Max-flow min-cut theorem. Chapter 26: Maximum Flow. A directed graph is interpreted as a flow network:

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Introduction to Operations Research

Maximum Flow Problem. Introduction to Operations Research. Maximum flow problem description All flow through a directed and connected network originates at one node ( source ) and terminates at one another node ( sink ) All the remaining nodes are transshipment nodes

476 views • 34 slides

Introduction to Operations Research

Maximum Flow Problem. Introduction to Operations Research. Maximum flow problem description All flow through a directed and connected network originates at one node ( source ) and terminates at one another node ( sink ) All the remaining nodes are transshipment nodes

580 views • 34 slides

Maximum Flow

Maximum Flow. Maximum Flow Problem The Ford-Fulkerson method Maximum bipartite matching. material coursing through a system from a source to a sink. 12. 20. 16. s. t. 7. 9. 10. 4. 4. 13. 14. Flow networks:.

580 views • 33 slides

Logistics Routing Plans: Max Flow Problem

Logistics Routing Plans: Max Flow Problem. Objectives and Agenda: 1. Examples for flow of materials over limited capacity channels 2. Finding maximum flows: Ford-Fulkerson Method. WanChai. NorthPoint. Western. 5. Central. 20. 15. 10. 20. 15. 25. 15. PokFuLam. 40. HappyValley.

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Logistics Routing Plans: Max Flow Problem

Logistics Routing Plans: Max Flow Problem. Objectives and Agenda: 1. Examples for flow of materials over limited capacity channels 2. Finding maximum flows: Ford-Fulkerson Method. WanChai. NorthPoint. Western. 5. Central. 20. 15. 10. 20. 15. 25. 15. PokFuLam. 40. HappyValley.

227 views • 22 slides

Algorithms ( and Datastructures )

Algorithms ( and Datastructures ). Lecture 12 MAS 714 part 2 Hartmut Klauck. Ford Fulkerson. Input: flow network N=(G,C,s,t) Set f(u,v)=0 for all pairs u,v While there is an augmenting path p in N f : Compute C f (p) For all edges u,v on p: set f(u,v):=f(u,v)+C f (p)

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Maximum Flow Algorithms

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The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem

The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem. Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3. 1. 1. 2. 2. s. 4. t. 3. 2. 1. 3. This is the original network, and the original residual network. Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3. 1. 1. 2. 2. s.

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15.082 and 6.855J

15.082 and 6.855J. The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem. Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3. 1. 1. 2. 2. s. 4. t. 3. 2. 1. 3. This is the original network, and the original residual network. Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3.

241 views • 15 slides

15.082 and 6.855J

15.082 and 6.855J. The Ford-Fulkerson Augmenting Path Algorithm for the Maximum Flow Problem. Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3. 1. 1. 2. 2. s. 4. t. 3. 2. 1. 3. This is the original network, and the original residual network. Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3.

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Network Optimization Models: Maximum Flow Problems

Network Optimization Models: Maximum Flow Problems. In this handout: The problem statement Augmenting path algorithm for solving the problem. A. 4. 4. 6. B. O. D. 5. 5. T. 4. 4. 5. C. Maximum Flow Problem. Given : Directed graph G=(V, E),

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Ford-Fulkerson algorithm for the Maximum F low problem

Ford-Fulkerson algorithm for the Maximum F low problem. Maximum Flow Problem Given a connected graph G=(V,E), a capacity c:E->R+, and two nodes s and t, find a maximum s-t flow. Minimum Cut Problem

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Complexity of Ford-Fulkerson

Complexity of Ford-Fulkerson. Let U = max {(i,j) in A} u ij . If S = {s} and T = N{s}, then u[S,T] is at most nU. The maximum flow is at most nU. At most nU augmentations. Each iteration of the inner while loop is O(m): Each arc is inspected at most once Finding ? is O(n)

265 views • 9 slides