Lecture1

# Lecture1 - Graphs and Network Flows IE411 Lecture 1 Dr Ted...

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Graphs and Network Flows IE411 Lecture 1 Dr. Ted Ralphs

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IE411 Lecture 1 1 References for Today’s Lecture Required reading Sections 17.1, 19.1 References AMO Chapter 1 and Section 2.1 and 2.2
IE411 Lecture 1 2 Introduction to Graphs and Network Flows What is a graph ? What does network flow mean? The word network can be interpreted according to the dictionary definition. electrical networks communication networks transportation networks (highways, railways, airline) The word flow comes from the movement of something from one point to another. electricity information person or vehicle inventory money Physical goods We will rigorously define the word graph shortly.

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IE411 Lecture 1 3 Graph Problems Graphs model the connectivity relationships between items in a set. Specifically, we will specify that there is a direct link between certain pairs of items. In some cases, there will be a direction to the link. This will allow us to ask questions such as the following. Is x connected “directly” to y ? Is x connected to y “indirectly,” i.e., through a sequence of direct connections ? What is the set of of all items connected to x , directly or indirectly ? What is the shortest number of connections needed to get from x to y ?
IE411 Lecture 1 4 Applications of Graphs Maps Social Networks World Wide Web Circuits Scheduling Communication Networks Matching and Assignment

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IE411 Lecture 1 5 Network Flow Problems Network flow problems arise in many, many contexts travel/transportation logistics manufacturing telecommunications chemistry/biology finance Much of early work was descriptive . Our interest is in prescriptive models.
IE411 Lecture 1 6 Basic Categories of Network Flow Problems Most of the problems we will encounter involve analyzing an existing network. Problem types What is the shortest path from point to point? What is the maximum throughput that can be achieved? What is the minimum cost of moving a fixed quantity of goods from point to point?

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• Spring '14
• TedRalphs
• Graph Theory, Shortest path problem, undirected graph, communication networks

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