I have an idea for a greedy algorithm to find the largest clique. First I with a vertex u, then I grow the clique like we did with Prim's algo- We check each neighbor, and if it's connected to everything in our then we add it to our clique.

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
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Problem 2
In a graph a Clique is a fully connected subgraph. An example of a clique is
given below.
I have an idea for a greedy algorithm to find the largest clique. First I
start with a vertex v, then I grow the clique like we did with Prim's algo-
rithm. We check each neighbor, and if it's connected to everything in our
clique, then we add it to our clique.
For the above graph I started with b, then added c, d, and e to my clique.
Since a isn't connected the algorithm terminates.
Is this a good idea for an algorithm?
If it is, explain why it gives me the maximum clique,
and give the running time.
If not, then give an example where it would fail.
OC
Transcribed Image Text:Problem 2 In a graph a Clique is a fully connected subgraph. An example of a clique is given below. I have an idea for a greedy algorithm to find the largest clique. First I start with a vertex v, then I grow the clique like we did with Prim's algo- rithm. We check each neighbor, and if it's connected to everything in our clique, then we add it to our clique. For the above graph I started with b, then added c, d, and e to my clique. Since a isn't connected the algorithm terminates. Is this a good idea for an algorithm? If it is, explain why it gives me the maximum clique, and give the running time. If not, then give an example where it would fail. OC
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