ass07

# ass07 - (IS is NPC 3 Let Minimum Degree Spanning Tree(MDST...

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Fall 2011 CS 513: #07 Farach-Colton Due by the beginning of class, Dec. 6. 1. A boolean formula α is in Disjunctive Normal Form if α = α 1 ... α k , where each α i = α i 1 ∧ ··· α ij i . That is, it is the disjunction of a sequence of conjunctions. The DNF problem is deﬁned as: Input: A formula α in disjunctive normal form. Output: Yes, if α is satisﬁable, and No otherwise. (a) Is DNF ∈ P ? Prove your answer. (b) Is DNF ∈ NP ? Prove your answer. (c) Is DNF NP-complete? Prove your answer. 2. Show that Vertex Cover (VC) is NPC. You may assume that Independent Set
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Unformatted text preview: (IS) is NPC. 3. Let Minimum Degree Spanning Tree (MDST) problem be: Input: A graph G = ( V,E ). Output: A spanning tree of G with minimum degree. (a) How would you modify this problem so that it is in NP? (b) Show that your modiﬁcation is NP-Complete. You may assume HC is NPC. (c) Show that if you had a polynomial time algorithm for your modiﬁcation of MSC, then you could also solve MSC in polynomial time....
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