Randomized heuristic for the maximum clique problem
- Shalin Shah
Abstract
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.