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The greedy algorithm for the vertex cover problem picks a highest degree vertex v, includes v in the cover, deletes all edges incident to v, and repeats until there are no edges left. Show that this algorithm is not a c-approximation algorithm for any c.

The greedy algorithm for the vertex cover problem picks a highest degree vertex v, includes v in the cover, deletes all edges incident to v, and repeats until there are no edges left. Show that this algorithm is not a c-approximation algorithm for any c.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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2. The greedy algorithm for the vertex cover problem picks a highest degree vertex v, includes v in the cover, deletes all edges incident to v, and repeats until there are no edges left. Show that this algorithm is not a c-approximation algorithm for any c. Hint: consider a bipartite graph G = (A, B, E) with |A| = n and B ULBi, where |B;| = [n/i]. Vertices in B; have degree i, and the neigh- borhoods of different vertices are disjoint.
Transcribed Image Text:2. The greedy algorithm for the vertex cover problem picks a highest degree vertex v, includes v in the cover, deletes all edges incident to v, and repeats until there are no edges left. Show that this algorithm is not a c-approximation algorithm for any c. Hint: consider a bipartite graph G = (A, B, E) with |A| = n and B ULBi, where |B;| = [n/i]. Vertices in B; have degree i, and the neigh- borhoods of different vertices are disjoint.
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