Practice The Concept Of Np-hardness (8.2.4.1) - Undecidability and Introduction to Complexity Theory
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The Concept of NP-Hardness

Practice - The Concept of NP-Hardness

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Practice Questions

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Question 1 Easy

What does NP-hard mean?

💡 Hint: Think about problems in NP and their relationships.

Question 2 Easy

Give a brief definition of NP-complete.

💡 Hint: Focus on the two conditions for NP-completeness.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What are NP-hard problems?

Problems that can be solved in polynomial time
Problems that are atleast as hard as the hardest in NP
Problems restricted to linear time solutions

💡 Hint: Think of NP problems in terms of efficiency.

Question 2

True or False: A problem is NP-complete if it is in NP and it is NP-hard.

💡 Hint: Recall the two criteria for NP-completeness.

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Challenge Problems

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Challenge 1 Hard

Consider the Clique problem. Create a polynomial-time reduction from a known NP-complete problem to show it is NP-complete.

💡 Hint: Think of how positions in the graph relate to true assignments of variables.

Challenge 2 Hard

Examine the implications if any NP-complete problem were found to have a polynomial-time solution.

💡 Hint: Consider the broad impacts in cryptography and algorithm design.

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Reference links

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