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Exercise 1 (1 point for each correct answer) For each of the following statements indicate whether...

Exercise 1 (1 point for each correct answer) For each of the following statements indicate whether it is true, false, or unknown.

1. The MIN VERTEX COVER problem is in ??.

2. The MIN VERTEX COVER problem is ??-hard.

3. The MIN VERTEX COVER problem can be solved by a 3-approximation algorithm.

4. The MIN VERTEX COVER problem can be solved by a 1-approximation algorithm.

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Answer #1

1. The MIN VERTEX COVER problem is in ??. FALSE
Explanation: MIN VERTEX COVER problem is  optimization problem of finding a minimal(least) vertex cover in the provided graph. MIN VERTEX COVER problem is NP-complete

2. The MIN VERTEX COVER problem is ??-hard. FALSE
explanation: MIN VERTEX COVER problem is  optimization problem of finding a minimal(least) vertex cover in the provided graph. MIN VERTEX COVER problem is NP-complete . where NP-hard is not a decision problem , NP-complete is exclusively a decision problem.

3. The MIN VERTEX COVER problem can be solved by a 3-approximation algorithm. FALSE

4. The MIN VERTEX COVER problem can be solved by a 1-approximation algorithm. TRUE
Explanation: We can solve it in exactly polynomial time

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