Exercise 3 Consider Graph G V E Independent Set Graph G Set Vertices S V X Y S X Y Edge G Q43853681
Exercise 3 Consider a graph G = (V, E). An independent set ofthe graph G is a set of vertices S⊆V such that for all x, y ∈S thex,y is not an edge of the graph G. A set D⊆X is said to be adominating set if for every x ∈ X /D there exists y ∈ D such thatxy ∈ E.
it is a Dominating and Independent sets (DIS) problem
Instance : A graph G = (V, E) and an integer k ∈ (1,|X|].
Question :
1. Are there a dominating set of size ≥ k and an independent setof size ≥ k
2. Show that DIS is in NP?
3. Show that DIS is NP-Hard? Hint: Maximal independent set.
3. Suppose that P= NP and given a polynomial-time black-boxalgorithm for solving the decision problem DIS. Give apolynomial-time algorithm to solve the associated optimizationproblem.
Expert Answer
Answer to Exercise 3 Consider a graph G = (V, E). An independent set of the graph G is a set of vertices S⊆V such that for all x…
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