Approximation Algorithm 2. (**) Consider a k-center clustering algorithm via par

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Approximation Algorithm

2. (**) Consider a k-center clustering algorithm via partitioning: The input vertex set V is arbitrarily partitioned into n sets, Vi, ½, , V n, each of size v n. We run the Gonzalez's algorithm on each Vi and let Si be the resulting 2-approximate k-center clustering of Then, we run the same algorithm on S- S1US2U...USyn and return the resulting k-center clustering of S, which is denoted as C. What is the approximation ratio of this new k-center clustering algorithm? The tighter (smaller), the better. Needless to say, you must prove the approximation ratio you claim

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