# Set1 - IE 514 Network Flows MIT Slides (Adapted) WELCOME! x...

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IE 514 Network Flows MIT Slides (Adapted)

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2 WELCOME! Network Flows and Applications The Koenigsberg Bridge Problem Introduces Networks and Network Algorithms Computational Complexity Overall goal of today’s lecture: set the tone for the rest of the subject provide background provide motivation handle some class logistics
3 Grading Homework Sets 5-8 assignments much of it is “theorem/proof” Grading homework: 10 % Midterm I 20 % Midterm II 20 % final: 25 % project 25% (INCENTIVE!!) Textbook: Network Flows: Theory, Algorithms, and Applications by Ahuja, Magnanti, and Orlin referred to as AMO

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4 On the background of students Requirement for this class Linear Programming Data Structures
5 Some aspects of the class Fondness for PowerPoint animations Class time: used for presenting theory, algorithms, applications mostly outlines of proofs illustrated by examples (not detailed proofs) detailed proofs are in the text

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6 Network Flows and Routing Models Phone network: route calls, messages, data Power network: transmit power from power plants to consumers Highway, street, rail, airline, shipping networks: transport people, vehicles, goods Computer networks: transmit info, data, messages Pipeline networks: transport crude oil, gasoline Satellite networks: worldwide communication system
7 History 1735: Euler’s work on the Koenisgsberg Bridges 1800s: Kirchoff constructed network flow models to analyze current flows 1940s: Kantorovich, Hitchhock & Koopmans considered transportation problems 1947: Dantzig pioneered Linear Programming 1956: Ford & Fulkerson proved max flow min cut theorem and developed a labelling algorithm for max flow. (Start of algorithmic developments)

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8 The Bridges of Koenigsberg: Euler 1735 “Graph Theory” began in 1735 Leonard Eüler Visited Koenigsberg People wondered whether it is possible to take a walk, end up where you started from, and cross each bridge in Koenigsberg exactly once Generally it was believed to be impossible Presented the proof to Russian Academy
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## Set1 - IE 514 Network Flows MIT Slides (Adapted) WELCOME! x...

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