A fast parallel maximum clique algorithm for large sparse graphs and temporal strong components


We propose a fast, parallel, maximum clique algorithm for large, sparse graphs that is designed to exploit characteristics of social and information networks. We observe roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices. In a test with a 1.8 billion-edge social network, the algorithm finds the largest clique in about 20 minutes. For social networks, in particular, we found that using the core number of a vertex in combination with a good heuristic clique finder efficiently removes the vast majority of the search space. In addition, we parallelize the exploration of the search tree. In the algorithm, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with especially large search spaces can be pruned by other processes. We use this clique finder to investigate the size of the largest temporal strong components in dynamic networks, which requires finding the largest clique in a particular temporal reachability graph.


large sparce graphs, social and information networks, maximum clique

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Cornell University Library, Social and Information Networks