Question: Dominating Set. In a graph G = (V, E), we define a dominating set as a set of vertices D CV such that every vertex

Dominating Set. In a graph G = (V, E), we define

Dominating Set. In a graph G = (V, E), we define a dominating set as a set of vertices D CV such that every vertex in V is in D or has a neighbor in D. Consider the following relative of the Vertex Cover Problem: Given a graph G = (AUB, E) and a positive integer k, decide whether G has an dominating set of size at most k Describe a polynomial-time algorithm that solves this problem, or show that the prob- lem is NP-complete. Provide a proof of correctness (that is, correctness of either a polynomial-time algorithm, or a polynomial-time reduction from a problem that was shown to be NP-hard at class) Dominating Set. In a graph G = (V, E), we define a dominating set as a set of vertices D CV such that every vertex in V is in D or has a neighbor in D. Consider the following relative of the Vertex Cover Problem: Given a graph G = (AUB, E) and a positive integer k, decide whether G has an dominating set of size at most k Describe a polynomial-time algorithm that solves this problem, or show that the prob- lem is NP-complete. Provide a proof of correctness (that is, correctness of either a polynomial-time algorithm, or a polynomial-time reduction from a problem that was shown to be NP-hard at class)

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