Theoretically and practically efficient parallel nucleus decomposition

This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures graphs. We present a novel parallel algorithm that is efficient both theory and practice. Our achieves work complexity matching best sequential while also having low depth (parallel running time), significantly improves upon only existing (Sariyüce et al. , PVLDB 2018). The key theoretical efficiency of our new lemma bounds amount done when peeling cliques from graph, combined with use theoretically-efficient algorithms for clique listing bucketing. introduce several practical optimizations, including multi-level hash table structure store information on space-efficiently technique traversing this cache-efficiently. On 30-core machine two-way hyper-threading real-world graphs, we achieve up 55x speedup over state-of-the-art by Sariyüce 40x self-relative speedup. are able efficiently compute larger decompositions than prior million-scale graphs first time.