5. Consider the following modification of the independent set problem. As input, you receive an undirected graph G = (V, E). As output, you must decide if G contains an independent set UCV such that U contains at least 99% of the vertices in V (that is, |U| > 0.99|V|). Prove that this modification of the independent set problem is NP-Complete.
5. Consider the following modification of the independent set problem. As input, you receive an undirected graph G = (V, E). As output, you must decide if G contains an independent set UCV such that U contains at least 99% of the vertices in V (that is, |U| > 0.99|V|). Prove that this modification of the independent set problem is NP-Complete.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![5. Consider the following modification of the independent set problem. As input, you receive an
undirected graph G = (V, E). As output, you must decide if G contains an independent set
UCV such that U contains at least 99% of the vertices in V (that is, JU| > 0.99|V|).
Prove that this modification of the independent set problem is NP-Complete.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F271641c2-cc1c-4149-b3cf-f5dba485eb1a%2Fee33a865-6cf7-43f8-b2dc-4c3418508434%2Fmbm1i5q_processed.png&w=3840&q=75)
Transcribed Image Text:5. Consider the following modification of the independent set problem. As input, you receive an
undirected graph G = (V, E). As output, you must decide if G contains an independent set
UCV such that U contains at least 99% of the vertices in V (that is, JU| > 0.99|V|).
Prove that this modification of the independent set problem is NP-Complete.
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