Problem 2In a graph a Clique is a fully connected subgraph. An example of a clique isgiven below.I have an idea for a greedy algorithm to find the largest clique. First Istart 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 ourclique, 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

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.

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

Problem 1PE

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Concept explainers

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.

Question

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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