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**Unformatted text preview: **( S ( v )), so it’s the least common ancestor in T of all leaves below v in S . Give an algorithm to compute M . 3. The Set Cover (SC) problem is deﬁned as follows: Input: A collection C of subsets of a ﬁnite set S , and a postive integer K ≤ | C | . Output: Yes, if there is a subsets C of C such that | C | ≤ K and ∪ c ∈ C c = S, No, otherwise. The Vertex Cover (VC) problem is deﬁned as follows: Input: A graph G = ( V,E ) and a postive integer K ≤ | V | . Output: Yes, if there is a subsets V of V such that | V | ≤ K and for every edge { a,b } ∈ E , { a,b } ∩ V 6 = 0 No, otherwise. Show that if there is a polynomial time algorithm for SC, there is a polynomial time algorithm for VC....

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