Implementation of a maximum clique search procedure on CUDA

We present a novel implementation of a Motzkin–Straus-based iterative clique-finding algorithm for GPUs. The well-known iterative approach is enhanced by an annealing variant, where better convergence is obtained by introducing an additional parameter that eliminates certain local maxima, and by an attenuation variant, where the search is repeated several times and known cliques are attenuated by reducing the edge weights. The proposed solution belongs to a global optimization class of methods. It is particularly well suited to large and/or dense graphs, and outperforms other popular clique-finding methods. Therefore, it could be useful in many practical applications related to graph representations of the structures and/or dynamics of complex systems. The proposed algorithm was chosen on the basis of its portability to GPUs. Our implementation includes optimizations aimed at maximizing utilization of GPU cores by delaying some auxiliary computations and performing them simultaneously with the main matrix-vector multiplication. It achieves an average speedup of up to \(20\,\times \) over the CPU version, depending on the graph size and density. CUDA-MS is available under the GPL license.