Download This PaperIdentifying Maximal Cliques on Large Scale Network using the Genetic Algorithm
6 Pages Posted: 17 Apr 2020
Date Written: April 16, 2020
Abstract
In graph theory, definition of clique is given as sub-graph(complete) where each node is connected to each other . Identifying functional units in complex network, modelling evolution of social network and community detection are some of the applications of maximum clique problem under graph theory. This problems comprises of a NP-Hard problem where all cliques are enumerating in large scale complex network . However, by applying heuristic based optimisation algorithms it may be possible to identify maximal clique in complex network in reasonable amount of time. The problem can be solved in polynomial time whereas, other NP-hard problems like Travelling Salesman Problem(TSP), graph colouring problem, 3-SAT problem etc. could be diminished to maximal clique problem in order to process in polynomial amount of time. Maximal Cliques are not subset of any other cliques. Out of all the maximal cliques, the clique with maximum cardinality or maximum weight is treated as maximum cliques in the network. Detection of maximum clique problem is formulated by combining the optimal problem where the aim is to maximize sum of weights or the cardinality of the sub graph. A number of approaches have been presented in literature to identify cliques in the network. Most of them are computationally expensive in analyzing large scale network. In this paper, an efficient genetic algorithm has been proposed to enumerate all the cliques in large scale network.The effectiveness of the proposed algorithm has been verified by comparing computational complexity with other existing algorithms.
Keywords: Maximal Clique, 3-SAT ,Graph Coloring, Mutation, Crossover, Genetic - Algorithm
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