380CT: Theoretical Aspects of Computer Science Assignment, CU, Malaysia You are assigned to the problem stated above and you are required to develop a computer program to try and solve it

Task Description

Consider one of the following problems:

Problem: Clique Problem

Given an undirected graph 𝐺, determine whether a 𝑘-clique exists in the graph, where a 𝑘- clique is a subgraph containing 𝑘 nodes in 𝐺 where every two nodes in the subgraph are connected by an edge.

Instructions

You are assigned to the problem stated above and you are required to develop a computer program to try and solve it. You have to choose two main methods to find the best solutions: one exact method and one non-exact/approximation method.

Exact Methods:
a) Exhaustive Search
b) Dynamic Programming
Non-exact Methods:
a) Genetic Algorithm
b) Tabu Search
c) GRASP
d) Simulated Annealing

You must apply a suitable testing methodology (choosing the appropriate sample size,

obtaining average results) to compare the various methods in terms of their
performance. Based on the results that you have obtained, you will be required to prepare a portfolio to analyse the capabilities and limitations of the algorithms that you have implemented.

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