Many-Core Clique Enumeration with Fast Set Intersections

Listing all maximal cliques of a given graph has important applications in the analysis of social and biological networks. Parallelisation of maximal clique enumeration (MCE) algorithms on modern manycore processors is challenging due to the task-level parallelism that unfolds dynamically. Moreover, the execution time of such algorithms is known to be dominated by intersections between dynamically-created vertex sets. In this paper, we prove that the use of hashjoin-based set-intersection algorithms within MCE leads to Pareto-optimal implementations in terms of runtime and memory space compared to those based on merge joins. Building on this theoretical result, we develop a scalable parallel implementation of MCE that exploits both data parallelism, by using SIMD-accelerated hash-join-based set intersections, and task parallelism, by using a shared-memory parallel processing framework that supports dynamic load balancing. Overall, our implementation is an order of magnitude faster than a state-of-the-art manycore MCE algorithm. We also show that a careful scheduling of the execution of the tasks leads to a two orders of magnitude reduction of the peak dynamic memory usage. In practice, we can execute MCE on graphs with tens of millions of vertices and up to two billion edges in just a few minutes on a single CPU.