Practice Reduction Between Problems (12.7) - Intractability: Checking Algorithms

Practice: Reduction Between Problems

Lesson 12.7Intractability: Checking Algorithms

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8 questions

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6 sample questions

Question 1.
What is the difference between generating and checking algorithms?
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Think about what you do when you receive an answer to a problem.
Question 2.
Can you give an example of a problem that can be checked but not easily generated?
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Recall the definition of SAT and its verification process.
3Question 3.
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.
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Recall the definitions discussed in class.
4Question 4.
True or False: The Boolean Satisfiability problem can be generated efficiently.
- True
- False
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Think of the complexity of SAT when generating solutions.
Question 5.
Design a checking algorithm for the Traveling Salesman Problem that utilizes binary search in conjunction with a distance bound.
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Consider using approximations before refining your search with binary search.
Question 6.
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.
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Explore the relationships between nodes and edges in both problems.

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