Design & Analysis of Algorithms

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Module 5: Tractable and Intractable Problems

  1. Q1h. Hamiltonian path problem is ______? - (i) NP Problem - (ii) NP Complete - (iii) P Class Problem - (iv) N Class Problem20242m

    Module 5: Tractable and Intractable Problems

    Hamiltonian path problem is ______?

    • (i) NP Problem
    • (ii) NP Complete
    • (iii) P Class Problem
    • (iv) N Class Problem
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  2. Q1j. The choice of polynomial class has led to the development of an extensive theory called: - (i) computational complexity - (ii) time complexity - (iii) problem complexity - (iv) decision complexity20222m

    Module 5: Tractable and Intractable Problems

    The choice of polynomial class has led to the development of an extensive theory called:

    • (i) computational complexity
    • (ii) time complexity
    • (iii) problem complexity
    • (iv) decision complexity
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  3. Q5a. What is the relationship among P, NP and NP complete problems? Show with the help of a diagram.20197m

    Module 5: Tractable and Intractable Problems

    What is the relationship among P, NP and NP complete problems? Show with the help of a diagram.

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  4. Q5b. What are NP- hard and NP-complete problems?20247m

    Module 5: Tractable and Intractable Problems

    What are NP- hard and NP-complete problems?

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  5. Q8. Explain back-tracking, DFS and BFS with help of small example. Differentiate in between backtracking and dynamic programming. Apply the backtracking algorithm to solve the three-colouring problem for the following graph using state space tree. Assume three colours red, green and blue. ![Graph for Q8](https://res.cloudinary.com/djkpavwmp/image/upload/v1765793825/portfolio_assets/qoy6nsycvjnin985kjnp.png)201914m

    Module 5: Tractable and Intractable Problems

    Explain back-tracking, DFS and BFS with help of small example. Differentiate in between backtracking and dynamic programming. Apply the backtracking algorithm to solve the three-colouring problem for the following graph using state space tree. Assume three colours red, green and blue.

    Graph for Q8

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  6. Q8a. Define the classes P and NP.20232m

    Module 5: Tractable and Intractable Problems

    Define the classes PP and NPNP.

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  7. Q8b. Discuss what you mean by polynomial reduction.20232m

    Module 5: Tractable and Intractable Problems

    Discuss what you mean by polynomial reduction.

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  8. Q8c. Discuss diagrammatically the relation among P class, NP class, NP hard and NP complete.20232m

    Module 5: Tractable and Intractable Problems

    Discuss diagrammatically the relation among PP class, NPNP class, NPNP hard and NPNP complete.

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  9. Q8d. Describe Clique Decision Problem (CDP).20232m

    Module 5: Tractable and Intractable Problems

    Describe Clique Decision Problem (CDP).

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  10. Q9a. Write short notes on: Cook's Theorem20247m

    Module 5: Tractable and Intractable Problems

    Write short notes on: Cook's Theorem

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  12. Q9b. Write short notes on: Branch and bound technique20197m

    Module 5: Tractable and Intractable Problems

    Write short notes on: Branch and bound technique

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  13. Q9b. Write short notes on: Approximation algorithms20227m

    Module 5: Tractable and Intractable Problems

    Write short notes on: Approximation algorithms

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