Practice Reduction Between Problems - 12.7 | 12. Intractability: Checking Algorithms | Design & Analysis of Algorithms - Vol 3
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12.7 - Reduction Between Problems

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the difference between generating and checking algorithms?

💡 Hint: Think about what you do when you receive an answer to a problem.

Question 2

Easy

Can you give an example of a problem that can be checked but not easily generated?

💡 Hint: Recall the definition of SAT and its verification process.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What distinguishes a generating algorithm from a checking algorithm?

  • A generating algorithm verifies correctness
  • while a checking algorithm generates solutions.
  • A generating algorithm finds solutions
  • while a checking algorithm verifies correctness.
  • Both generate and check solutions simultaneously.

💡 Hint: Recall the definitions discussed in class.

Question 2

True or False: The Boolean Satisfiability problem can be generated efficiently.

  • True
  • False

💡 Hint: Think of the complexity of SAT when generating solutions.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Design a checking algorithm for the Traveling Salesman Problem that utilizes binary search in conjunction with a distance bound.

💡 Hint: Consider using approximations before refining your search with binary search.

Question 2

Using the concept of reduction, show how you can demonstrate that finding a maximum independent set is at least as hard as solving the vertex cover problem.

💡 Hint: Explore the relationships between nodes and edges in both problems.

Challenge and get performance evaluation