Listing k-cliques in Sparse Real-World Graphs

Maximilien Danisch, Oana Balalau and Mauro Sozio

WWW, 2018

Motivated by recent studies in the data mining community whichrequire to efficiently list allk-cliques, we revisit the iconic algorithmof Chiba and Nishizeki and develop the most efficient parallel algo-rithm for such a problem. Our theoretical analysis provides the bestasymptotic upper bound on the running time of our algorithm forthe case when the input graph is sparse. Our experimental evalua-tion on large real-world graphs shows that our parallel algorithm isfaster than state-of-the-art algorithms, while boasting an excellentdegree of parallelism. In particular, we are able to list allk-cliques(for anyk) in graphs containing up to tens of millions of edges aswell as all10-cliques in graphs containing billions of edges, withina few minutes and a few hours respectively. Finally, we show howour algorithm can be employed as an effective subroutine for find-ing thek-clique core decomposition and an approximatek-clique densest subgraphs in very large real-world graphs.