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Understanding Network Flow Models: Shortest Route, Minimal Spanning Tree, and Maximal Flow Problems

This chapter explores key concepts of network flow models, focusing on the Shortest Route Problem, Minimal Spanning Tree Problem, and Maximal Flow Problem. It discusses the use of distances and costs between nodes to find optimal paths and networks. Methods such as Dijkstra's algorithm and QM are introduced for problem-solving within these contexts. The text outlines specific applications, input formats, and distinguishes between different problem types, ensuring a practical understanding for handling real-world networking challenges.

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Understanding Network Flow Models: Shortest Route, Minimal Spanning Tree, and Maximal Flow Problems

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  1. Chapter 7 Network Flow Models

  2. Shortest Route Problem • Given distances between nodes, find the shortest route between any pair of nodes.

  3. Example: p.282 (291)

  4. Solution Methods • Dijkstra algorithm: • Introduced in book. • Not required for this course • Using QM: • Required for this course • Data input format -

  5. Discussion • What if the ‘cost’, instead of ‘distance’, between two nodes are given, and we want to find the ‘lowest-cost route’ from a starting node to a destination node? • What if the cost from a to b is different from the cost from b to a? (QM does not handle this situation.)

  6. Minimal Spanning Tree Problem • Given costs (distances) between nodes, find a network (actually a “tree”) that covers all the nodes with minimum total cost. • Applications:

  7. Example: p.290 (299) Solution Method: Using QM.

  8. Shortest Route vs. Minimal Spanning • The minimal spanning tree problem is to identify a set of connected arcs that cover all nodes. • The shortest route problem is to identify a route from a particular node to another, which typically does not pass through every node.

  9. Maximal Flow Problem • Given flow-capacities between nodes, find the maximum amount of flows that can go from the origin node to the destination node through the network. • Applications:

  10. Example: p.294 (303) Solution Method: Using QM.

  11. Network Flow Problem Solving • Given a problem, we need to tell what ‘problem’ it is (shortest route, minimal spanning tree, or maximal flow); then use the corresponding module in QM to solve it.

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