Efficient Parallel D-Core Decomposition at Scale

Directed graphs are prevalent in social networks, web networks, and communication networks. A well-known concept of the directed graph is the D-core, or ( k, l )-core, which is the maximal subgraph in which each vertex has an in-degree not less than k and an out-degree not less than l. Computing the non-empty D-cores for all possible values of k and l , a.k.a. D-core decomposition, has found versatile applications spanning social network analysis, community search, and graph visualization. However, existing algorithms of D-core decomposition suffer from efficiency and scalability issues on large graphs, because serial peeling-based algorithms are limited by single-core utilization, while skyline coreness-based methods exhibit notably high time complexity. To tackle these issues, in this paper, we propose efficient parallel algorithms for D-core decomposition by leveraging the computational prowess of multicore CPUs. Specifically, we first propose a novel algorithm that computes the D-cores for each possible k value, by exploiting an implicit level-by-level vertex removal strategy, which not only diminishes dependencies between vertices but also maintains a time complexity akin to that of sequential algorithms. We further develop an advanced algorithm by introducing a novel concept of D-shell, which allows us to curtail redundant computations by reducing the necessary k values when computing corresponding D-cores, and deriving D-cores with larger k values from the D-cores currently computed based on D-shell. Extensive experiments on ten real-world large graphs show that our algorithms are highly efficient and scalable, and the advanced algorithm is up to two orders of magnitude faster than the state-of-the-art parallel decomposition algorithm with 32 threads.