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CLIQUE Problem and NP-Completeness Proof Homework, Assignments of Algorithms and Programming

Oregon State University (OSU)Algorithms and Programming

A university-level homework assignment focused on the clique problem in computer science. The assignment includes four problems, the first of which requires students to prove that the clique problem is np-complete. The document also references several exercises from a textbook for additional problems to solve. This homework is optional and can be used to improve the final grade for the corresponding written homework.

Typology: Assignments

Pre 2010

Uploaded on 08/30/2009

koofers-user-uet 🇺🇸

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HW8 Due in class on March 16th.

Note: the submission of this homework is optional. If you do submit it, please indicate on

your submission which written homework you want to use this submission toward. The

maximum percentage points of the two will be used as the final grade for that homework.

Problem 1. Below is the definition of the CLIQUE problem.

Given an undirected graph G=(V,E), a CLIQUE is S, a subset of V such that there

is an edge between every pair of nodes of S.

Question: is there a CLIQUE of size k or larger?

Please prove that CLIQUE is in NP-complete

Note that the book provides a sketchy description of the reduction from independent set

to CLIQUE. For this homework question, you need to extend this and provide the

complete proof that CLIQUE is in NP-Complete.

Problem 2. Exercise 8.4 in book.

Discover Assignments of Algorithms and Programming Oregon State University (OSU)

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HW8 Due in class on March 16th. Note: the submission of this homework is optional. If you do submit it, please indicate on your submission which written homework you want to use this submission toward. The maximum percentage points of the two will be used as the final grade for that homework.

Problem 1. Below is the definition of the CLIQUE problem. Given an undirected graph G=(V,E), a CLIQUE is S, a subset of V such that there is an edge between every pair of nodes of S. Question: is there a CLIQUE of size k or larger? Please prove that CLIQUE is in NP-complete

Note that the book provides a sketchy description of the reduction from independent set to CLIQUE. For this homework question, you need to extend this and provide the complete proof that CLIQUE is in NP-Complete.

Problem 2. Exercise 8.4 in book.

Problem 3. Exercise 8.10 (b) and (c)

Problem 4. Exercise 9.2 in book.