Solving Dense Subgraph Problems Using Genetic Algorithm

In graph theory, the dense subgraph problem aims at finding the densest subgraph for a given graph. The subgraph is defined as a subset of a large graph and the density is calculated as the number of edges as per the number of vertices. Real-life graph networks are complicated and large in size; finding the dense subgraph is difficult as the number of subgraphs is numerous. It is an NP-hard problem and in most cases, it is infeasible to find an exact solution. Here we propose a genetic algorithm approach to solve it. The problem is a combinatorial optimization problem with a constraint that all solutions must be a subgraph of the given graph. Here, the crossover and mutation are designed to produce only feasible solutions. The proposed algorithm is able to give close approximation within a reasonable time.