Randomized heuristic for the maximum clique problem

A clique in a graph is a set of vertices that are all directly connected

to each other i.e. a complete sub-graph. A clique of the largest size is

called a maximum clique. Finding the maximum clique in a graph is an

NP-hard problem and it cannot be solved by an approximation algorithm

that returns a solution within a constant factor of the optimum. In this

work, we present a simple and very fast randomized algorithm for the

maximum clique problem. We also provide Java code of the algorithm

in our git repository. Results show that the algorithm is able to find

reasonably good solutions to some randomly chosen DIMACS benchmark

graphs. Rather than aiming for optimality, we aim to find good solutions

very fast.