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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Introduction
Page 2
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Example of networks
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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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 Spring '07
 SIRIPHONGLAWPHONGPANICH
 Shortest path problem, Flow network, telephone lines, ARCs, Magnanti

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