Design & Analysis of Algorithms - Vol 3 | 10. Network Flows by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
10. Network Flows

The chapter delves into the concept of network flows, specifically in the context of linear programming and the Ford-Fulkerson algorithm. It explains the representation of network flows using directed graphs containing source and sink vertices, and highlights the significance of flow conservation and optimization. Additionally, it discusses the relationship between maximum flow and minimum cut, demonstrating how these principles are crucial for efficiently managing resources in a network.

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

  • 10

    Network Flows

    This section introduces the concept of network flows and their representation in linear programming, focusing on the Ford-Fulkerson algorithm for optimizing flow from a source to a sink in a network.

    Learning Practice

  • 10.1

    Bandwidth Allocation Problem

    The bandwidth allocation problem involves determining the maximum flow through a network from a source to a sink while adhering to edge capacities.

    Learning Practice

  • 10.2

    Flow Properties

    This section discusses the flow properties in network flow problems, focusing on the algorithms used to optimize flow from source to sink in directed graphs.

    Learning Practice

  • 10.3

    Special Graph Type

    This section delves into network flow problems, specifically the mechanisms of the Ford-Fulkerson algorithm, its formulation through linear programming, and the importance of maximum flow and minimum cut theorems.

    Learning Practice

  • 10.4

    Setting Up Linear Program

    This section explains how to set up a linear program to model network flow problems, particularly focusing on the bandwidth allocation problem.

    Learning Practice

  • 10.5

    Ford-Fulkerson Algorithm

    The Ford-Fulkerson algorithm is a method for computing the maximum flow in a flow network.

    Learning Practice

  • 10.6

    Residual Graph

    This section introduces the concept of residual graphs used in network flow problems, particularly in the context of the Ford-Fulkerson algorithm.

    Learning Practice

  • 10.7

    Max Flow Min Cut Theorem

    The Max Flow Min Cut Theorem states that the maximum flow in a network equals the minimum capacity that can separate the source from the sink.

    Learning Practice

  • 10.8

    Choosing Paths In Ford-Fulkerson

    This section discusses the Ford-Fulkerson algorithm for maximizing flow in a network, illustrating how paths are chosen and flows are augmented within a directed graph.

    Learning Practice

References

ch53.pdf

Class Notes

Memorization

What we have learnt

  • Network flows are represent...
  • Flow conservation must ensu...
  • The maximum flow from the s...

Final Test

Revision Tests