Design & Analysis of Algorithms - Vol 3 | 11. Reductions by Abraham | Learn Smarter
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11. Reductions

The concept of reductions in problem-solving is explored, specifically in relation to bipartite matching and network flows. A course allocation problem is used as an example, demonstrating how to match teachers with courses based on their preferences. It emphasizes the importance of using existing efficient algorithms for related problems to indirectly solve more complex issues, showcasing the process of translating problems into forms suitable for established algorithms.

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Sections

  • 11.1

    Reductions

    This section explores the concept of reductions in algorithm design, specifically how bipartite matching problems can be transformed into network flow problems for efficient solutions.

    Learning Practice

  • 11.1.1

    Matching Problem

    This section introduces the matching problem in the context of assigning teachers to courses they prefer using a bipartite graph.

    Learning Practice

  • 11.1.2

    Bipartite Graph

    This section covers the concept of bipartite graphs and their use in solving matching problems through reductions to network flows.

    Learning Practice

  • 11.1.3

    Perfect Match And Network Flows

    This section explores the relationship between matching problems in bipartite graphs and how they can be solved using network flow techniques.

    Learning Practice

  • 11.1.4

    Reduction Process

    This section discusses the concept of reductions in algorithm design, specifically focusing on how to reduce problems to network flows.

    Learning Practice

  • 11.1.5

    Efficiency Of Reductions

    This section explores the concept of reductions in problem-solving, especially in the context of matching problems and network flows.

    Learning Practice

  • 11.1.2

    Big Hammers In Algorithms

    This section discusses the concept of reductions in algorithm design, particularly how bipartite matching can be transformed into network flow problems.

    Learning Practice

  • 11.2.1

    Linear Programming

    This section discusses linear programming and its application in solving bipartite matching problems through network flows.

    Learning Practice

  • 11.2.2

    Network Flows

    This section discusses the bipartite matching problem and how it can be reduced to a network flow problem, illustrating the concept of problem reduction in algorithm design.

    Learning Practice

  • 11.2.3

    Expressing Problems As Linear Programs Or Network Flows

    This section discusses how problems can be modeled using linear programming and network flows, illustrating this process through a course allocation problem.

    Learning Practice

References

ch54.pdf

Class Notes

Memorization

What we have learnt

  • Bipartite matching is defin...
  • Efficient solutions for one...
  • The efficiency of algorithm...

Final Test

Revision Tests