Counting k-cliques in a graph is an important problem in graph analysis with many applications. Counting k-cliques is typically done by traversing search trees starting at each vertex in the graph. An important optimization is to eliminate search tree branches that discover the same clique redundantly. Eliminating redundant clique discovery is typically done via graph orientation or pivoting. Parallel implementations for both of these approaches have demonstrated promising performance on CPUs. In this paper, we present our GPU implementations of k-clique counting for both the graph orientation and pivoting approaches. Our implementations explore both vertex-centric and edge-centric parallelization schemes, and replace recursive search tree traversal with iterative traversal based on an explicitly-managed shared stack. We also apply various optimizations to reduce memory consumption and improve the utilization of parallel execution resources. Our evaluation shows that our best GPU implementation outperforms the best state-of-the-art parallel CPU implementation by a geometric mean speedup of 12.39x, 6.21x, and 18.99x for k = 4, 7, and 10, respectively. We also evaluate the impact of the choice of parallelization scheme and the incremental speedup of each optimization. Our code will be open-sourced to enable further research on parallelizing k-clique counting on GPUs.
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