assignment5 - CSIS 0250B Design and Analysis of Algorithms...

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CSIS 0250B Design and Analysis of Algorithms Assignment 4 Due: 11:55 PM, Apr 16, 2009 1. Consider the CLIQUE problem restricted to graphs in which every vertex has degree at most 3. Call this problem CLIQUE-3. (a) Prove that CLIQUE-3 is in NP. (b) What is wrong with the following proof of NP-completeness for CLIQUE-3? We know that the CLIQUE problem in general graphs is NP-complete, so it is enough to present a reduction from CLIQUE-3 to CLIQUE. Given a graph G with vertices of degree at most 3, and a parameter g, the reduction leaves the graph and the parameter unchanged: clearly the output of the reduction is a possible input for the CLIQUE problem. Furthermore, the answer to both problems is identical. This proves the correctness of the reduction and, therefore, the NP-completeness of CLIQUE-3. (c) It is true that the VERTEX COVER problem remains NP-complete even when restricted to graphs in which every vertex has degree at most 3. Call this problem VC-3. What is wrong with the following proof of NP-completeness for CLIQUE-3? We present a reduction
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This note was uploaded on 03/01/2010 for the course CS 1234 taught by Professor Chan during the Spring '10 term at University of the Bío-Bío.

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assignment5 - CSIS 0250B Design and Analysis of Algorithms...

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