Design & Analysis of Algorithms - Vol 3 | 12. Intractability: Checking Algorithms by Abraham | Learn Smarter
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12. Intractability: Checking Algorithms

The chapter delves into the concept of intractability in algorithms, emphasizing the distinction between generating and checking solutions. It highlights important problems such as Boolean satisfiability and the traveling salesman problem, noting that while finding efficient solutions may be difficult or impossible, checking their validity often is not. The chapter concludes by illustrating the relationship between various computational problems and their checking algorithms.

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Sections

  • 12

    Intractability: Checking Algorithms

    This section discusses the concepts of intractability and the differences between generating solutions and checking solutions in algorithms.

    Learning Practice

  • 12.1

    Understanding Intractability

    This section introduces intractability, emphasizing the importance of recognizing problems for which no known efficient solutions exist.

    Learning Practice

  • 12.2

    Checking Algorithms Explained

    This section discusses checking algorithms, emphasizing their role in verifying solutions to problems that may not have efficient algorithms available for generating solutions.

    Learning Practice

  • 12.3

    Boolean Satisfiability Problem

    The section discusses the Boolean satisfiability problem, a significant issue in computer science regarding the existence of solutions to specific Boolean formulas.

    Learning Practice

  • 12.4

    Traveling Salesman Problem

    The section discusses the Traveling Salesman Problem (TSP), emphasizing its significance in algorithm design and analysis due to its NP-hard nature despite the existence of efficient checking algorithms.

    Learning Practice

  • 12.5

    Independent Set Problem

    This section explores the Independent Set Problem, emphasizing the challenge of identifying the largest subset of vertices in a graph where no two vertices are adjacent.

    Learning Practice

  • 12.6

    Vertex Cover Problem

    The Vertex Cover Problem involves finding the smallest set of vertices that can cover all edges in a graph, and it falls under problems for which no efficient solution is currently known.

    Learning Practice

  • 12.7

    Reduction Between Problems

    This section discusses the concepts of intractability and how checking algorithms differ from generating algorithms.

    Learning Practice

References

ch55.pdf

Class Notes

Memorization

What we have learnt

  • Not all problems have known...
  • Checking algorithms can oft...
  • Problems can be transformed...

Final Test

Revision Tests