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Maximum Independent Set problem is known to be NP-Complete. Suppose we have a graph G in which the maximum degree of each node is some constant c. Then, is the following greedy algorithm guaranteed to find an independent set whose size is within a constant factor of the optimal? 1) Initialize S = empty 2) Arbitrarily pick a vertex v, add v to S delete v and its neighbors from G 3) Repeat step 2 until G is empty Return S Yes No

Maximum Independent Set problem is known to be NP-Complete. Suppose we have a graph G in which the maximum degree of each node is some constant c. Then, is the following greedy algorithm guaranteed to find an independent set whose size is within a constant factor of the optimal? 1) Initialize S = empty 2) Arbitrarily pick a vertex v, add v to S delete v and its neighbors from G 3) Repeat step 2 until G is empty Return S Yes No

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter8: Network Models
Section8.6: Minimum Spanning Tree Problems
Problem 3P
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Maximum Independent Set problem is known to be NP-Complete. Suppose we have a graph G in which the maximum degree of each node is some constant c. Then, is the following greedy algorithm guaranteed to find an independent set whose size is within a constant factor of the optimal? 1) Initialize S = empty 2) Arbitrarily pick a vertex v, add v to S delete v and its neighbors from G 3) Repeat step 2 until G is empty Return S Yes No
Transcribed Image Text:Maximum Independent Set problem is known to be NP-Complete. Suppose we have a graph G in which the maximum degree of each node is some constant c. Then, is the following greedy algorithm guaranteed to find an independent set whose size is within a constant factor of the optimal? 1) Initialize S = empty 2) Arbitrarily pick a vertex v, add v to S delete v and its neighbors from G 3) Repeat step 2 until G is empty Return S Yes No
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