Module35Worksheet

# Module35Worksheet - – Task: Output a maximum sized clique...

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Module 35 Worksheet In Class Questions 1) (S3): Give a vertex cover of size 3. 2) (S3): Give a quick proof that there is no vertex cover of size 2. 3) (S4): Give a satisfying truth assignment for the example input 4) (S11): Suppose that the input graph G is given as an adjacency matrix. Prove that solving the maximum clique problem requires Ω(V 2 ) time. Consider the case where k=2. Clique Input: Undirected graph G = (V,E), integer k Y/N Question: Does G contain a clique of size ≥ k? Optimization to Decision Example problems with Clique Optimization Problem 1 Input: Graph G=(V,E) Task: Output size of maximum clique in G Optimization Problem 2 Input: Graph G=(V,E)

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Unformatted text preview: – Task: Output a maximum sized clique of G – Decision Problem – Input: Graph G=(V,E), integer k ≤ |V| – Y/N Question: Does G contain a clique of size k? (5) (S19) Show that if we can solve the decision problem, we can solve optimization problem 1. (6) (S19) Show that if we can solve optimization problem 1, we can solve optimization problem 2. Take home review questions 1) What is the definition of complexity class P? 2) How do we prove a problem belongs to P? 3) How does a polynomial-time answer-preserving input transformation differ from the answer-preserving input transformations we studied in module 11?...
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## This note was uploaded on 07/25/2008 for the course CSE 460 taught by Professor Torng during the Fall '07 term at Michigan State University.

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Module35Worksheet - – Task: Output a maximum sized clique...

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