# NOintro - ESI6417 Introduction Page 1 Introduction Four...

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ESI6417 Introduction Page 1 Introduction Four problems in Network Flows and Graphs: (AMO = Ahuja, Magnanti, and Orlin’s Network Flows) 1) Minimum Cost Flow Problem (AMO: Chapters 9 and 11.) 2) Shortest Path Problem (AMO: Chapter 4 and 5.) 3) Maximum Flow Problem (AMO: Chapter 6.) 4) Minimum Spanning Tree Problem (AMO: Chapter 13.) What is a network or graph? ± In operations research, it is more common to use the term ‘network’. In mathematics, the term ‘graph’ is more common. ± A network is a collection of nodes, some of which are connected by arcs. Arcs may or may not have a direction. Arcs without any direction are called undirected arcs . Otherwise, they are directed arcs . ± Note: In graph theory, node = vertex (nodes = vertices) and arcs = edges.

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ESI6417 Introduction Page 2 Example of networks City maps: nodes = road intersections, arcs = road segments between intersections, flow on the network = cars on road segments. State maps: nodes = cities, arcs = highways between cities, and flow = cars on
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NOintro - ESI6417 Introduction Page 1 Introduction Four...

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