The K-Core Decomposition Algorithm Under the Framework of GraphBLAS

A graph's k-core is the unique largest induced subgraph where all nodes' degrees are greater than or equal to k. The k-core decomposition algorithm is to find the coreness value for each node in a graph, which is the maximum value of k all the k-core containing this node. K-core is one of the most commonly used references to evaluate the node importance in various scientific disciplines. The widely used classical k-core decomposition algorithm has O(n + m) complexity [1] However, it is not suitable for parallelization. In this paper, we propose an algebraic k-core decomposition algorithm that is O(k(max)n + m) in computational complexity and can be efficiently parallelized on GPU under the GraphBLAS framework [2]. We can efficiently parallelize and calculate the coreness value for graphs with billions of edges. On a 14-core CPU server and a large scale sparse datasets, our algebraic algorithm outperforms the state-of-the-art ParK [3] and PK C [4] algorithms. The algebraic algorithm, in particular, achieves up to 4x acceleration in CPU, whereas our parallel GPU implementation on several large scale graphs achieves up to 6x acceleration over our CPU version.