Exercise 3 Spoints Consider Graph G V E Independent Set Graph G Set Vertices S Cv X Y Es Q43833191
the question in algorithm and complexity. please, I need step bystep solutions. thanks
Exercise 3 (Spoints Consider a graph G = (V, E). An independent set of the graph G is a set of vertices S CV such that for all x, y ES the xy is not an edge of the graph G. A set D C X is said to be a dominating set if for every x E X D there exists y E D such that xy E E. Problem 2 Dominating and Independent sets (DIS) • Instance : A graph G = (V, E) and an integer k € (1, X]. • Question : Are there a dominating set of size > k and an independent set of size > 니 1. Show that DIS is in NP? 2. * Show that DIS is NP – Hard? Hint: Maximal independent set. 3. Suppose that P= NP and given a polynomial time black-box algorithm for solving the decision problem DIS. Give a polynomial time algorithm to solve the associated optimization problem. Show transcribed image text Exercise 3 (Spoints Consider a graph G = (V, E). An independent set of the graph G is a set of vertices S CV such that for all x, y ES the xy is not an edge of the graph G. A set D C X is said to be a dominating set if for every x E X D there exists y E D such that xy E E. Problem 2 Dominating and Independent sets (DIS) • Instance : A graph G = (V, E) and an integer k € (1, X]. • Question : Are there a dominating set of size > k and an independent set of size > 니 1. Show that DIS is in NP? 2. * Show that DIS is NP – Hard? Hint: Maximal independent set. 3. Suppose that P= NP and given a polynomial time black-box algorithm for solving the decision problem DIS. Give a polynomial time algorithm to solve the associated optimization problem.
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Answer to Exercise 3 (Spoints Consider a graph G = (V, E). An independent set of the graph G is a set of vertices S CV such that f…
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