Incremental Maintenance of Maximal Cliques in a Dynamic Graph

We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as the first change-sensitive algorithms for clique maintenance, whose runtime is proportional to the magnitude of the change in the set of maximal cliques. We present experimental results showing these algorithms are efficient in practice and are faster than prior work by two to three orders of magnitude.Comment: 18 pages, 8 figure

GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra

We propose GraphMineSuite (GMS): the first benchmarking suite for graph mining that facilitates evaluating and constructing high-performance graph mining algorithms. First, GMS comes with a benchmark specification based on extensive literature review, prescribing representative problems, algorithms, and datasets. Second, GMS offers a carefully designed software platform for seamless testing of different fine-grained elements of graph mining algorithms, such as graph representations or algorithm subroutines. The platform includes parallel implementations of more than 40 considered baselines, and it facilitates developing complex and fast mining algorithms. High modularity is possible by harnessing set algebra operations such as set intersection and difference, which enables breaking complex graph mining algorithms into simple building blocks that can be separately experimented with. GMS is supported with a broad concurrency analysis for portability in performance insights, and a novel performance metric to assess the throughput of graph mining algorithms, enabling more insightful evaluation. As use cases, we harness GMS to rapidly redesign and accelerate state-of-the-art baselines of core graph mining problems: degeneracy reordering (by up to >2x), maximal clique listing (by up to >9x), k-clique listing (by 1.1x), and subgraph isomorphism (by up to 2.5x), also obtaining better theoretical performance bounds