Finding a Summary for All Maximal Cliques

The number of maximal cliques could be exponentially large with respect to the number of vertices. A clique summary is a subset of all the maximal cliques and can somehow represent all the maximal cliques. Finding such a summary is deemed important in information distribution, influence estimation, cost-effective marketing, etc. The existing approach that finds a maximal clique summary suffers from long running time due to the excessive number of costly bound calculations that are used to estimate the size of to-be-found cliques during the enumeration process. Furthermore, we found that, sometimes, the bound calculation is not necessary at all. As a result, in order to provide the best study of the problem, we propose four strategies in two directions to speed up the process of finding a maximal clique summary by (1) restricting the bound calculation operation to a particular subset of all search branches and (2) making the best use of the bounds that have been previously calculated. Extensive experiments are conducted on eight real-world datasets to validate our strategies. Results demonstrate that the proposed method can reduce the number of bound calculations by 3 ∼ 5 orders of magnitude, and each run of our algorithm can be up to 2.x times faster than the state-of-the-art algorithm while still keeping the summary concise. Our method can potentially benefit other large-output enumeration based problems, such as frequent itemset mining, when a summary of results is needed.