'Augmenting path' presentation slideshows

Soviet Rail Network, 1955

Soviet Rail Network, 1955. Reference: On the history of the transportation and maximum flow problems . Alexander Schrijver in Math Programming, 91: 3, 2002. Max flow and min cut. Two very rich algorithmic problems. Cornerstone problems in combinatorial optimization.

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Probabilistic Inference Lecture 3

Probabilistic Inference Lecture 3. M. Pawan Kumar pawan.kumar@ecp.fr. Slides available online http:// cvc.centrale-ponts.fr /personnel/ pawan /. Recap of lecture 1. Exponential Family. P( v ) = exp {- ? ? ? ? ? ? ( v ) - A( ? )}. Sufficient Statistics. Log-Partition Function.

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What you misses!

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Dinitz Algorithm: The Original Version & Even's Version

Dinitz Algorithm: The Original Version & Even's Version. Presentation By: Ilan Orlov. The max-flow problem Defined on a capacitated directed graph G=(V,E,c). The capacities are non-negative. 1. 1. 1. 1. 1. s. t. 2. 1. 1. 1. G.

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Lecture 16 Maximum Matching

Lecture 16 Maximum Matching. Incremental Method. Transform from a feasible solution to another feasible solution to increase (or decrease) the value of objective function. Matching in Bipartite Graph. Maximum Matching. 1. 1. Note: Every edge has capacity 1.

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Class Plan

Class Plan. 1-1 ? Graph ????? 1-2 ? Graph Search ?????? + some graph properties 1-3 ? Network Flow ???????????? 1-4 ? Algorithms ? Complexity ????????????. 2-1 ? Minimum Spanning Tree ???? ( + data structures and sorting ????????? 2-2 ? Matroid ??????.

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Maximum Flows

Maximum Flows. CONTENTS Introduction to Maximum Flows (Section 6.1) Introduction to Minimum Cuts (Section 6.1) Applications of Maximum Flows (Section 6.2) Flows and Cuts (Section 6.3) Generic Augmenting Path Algorithm (Section 6.4) Max-Flow Min-Cut Theorem (Section 6.5)

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Maximum Flow

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Advanced Algorithms

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Advanced Graph

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CSE 326: Data Structures Network Flow and APSP

CSE 326: Data Structures Network Flow and APSP. Ben Lerner Summer 2007. Network Flows. Given a weighted, directed graph G=(V,E) Treat the edge weights as capacities How much can we flow through the graph?. 1. F. 11. A. B. H. 7. 5. 3. 2. 6. 12. 9. 6. C. G. 11. 4. 10. 13.

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Introduction to Algorithms

Introduction to Algorithms. Maximum Flow My T. Thai @ UF. Flow networks. A flow network G = ( V , E ) is a directed graph Each edge ( u , v ) ? E has a nonnegative capacity If ( u , v ) ? E , then If , A source s and a sink t. Flow networks.

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Lecture 14

Lecture 14. Edmonds-Karp Algorithm. Edmonds-Karp Algorithm. The augmenting path is a shortest path from s to t in the residual graph (here, we count the number of edges for the shortest path). Ford-Fulkerson Max Flow. 4. 2. 5. 1. 3. 1. 1. 2. 2. s. 4. t. 3. 2. 1. 3.

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CSE 326: Data Structures Network Flow

CSE 326: Data Structures Network Flow. James Fogarty Autumn 2007. Network Flows. Given a weighted, directed graph G=(V,E) Treat the edge weights as capacities How much can we flow through the graph?. 1. F. 11. A. B. H. 7. 5. 3. 2. 6. 12. 9. 6. C. G. 11. 4. 10. 13. 20.

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Flow networks

Flow networks. 2. 5. 1. How much flow can we push through from s to t ? (Numbers are capacities.). 4. 7. 3. 2. 5. Flow networks. 2. 5. 1. How much flow can we push through from s to t ? (Numbers are capacities.). 4. 7. 3. 8.

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Max Flow: Shortest Augmenting Path

Max Flow: Shortest Augmenting Path. Choosing Good Augmenting Paths. Use care when selecting augmenting paths. Some choices lead to exponential algorithms. Clever choices lead to polynomial algorithms. If capacities are irrational, algorithm not guaranteed to terminate!

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Active Cuts for Real-Time Graph Partitioning in Vision

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4

3. 1. 2. 4. 3. 2. 3. 1. t. 1. 1. s. 2. 4. 2. 4. 4. the black number next to an arc is its capacity. 3. 1. 2. 4. 3. 2. 3. 1. t. 1. 1. s. 2. 4. 2. 4. 4. C ts = -1. Set costs all other arcs at 0 The minimum cost flow circulation (Af=0)

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4

3. 1. 2. 4. 3. 2. 3. 1. t. 1. 1. s. 2. 4. 2. 4. 4. the black numbers next to an arc is its capacity. 3. 1. 1 2. 2 4. 3 3. 2 2. 3. 1. t. 1 1. 1. s. 2 2. 1 4. 2. 4. 1 4. the black number next to an arc is its capacity

309 views • 16 slides