Parallel k-Core Decomposition: Theory and Practice

This paper proposes efficient solutions for 𝑘-core decomposition with high parallelism. The problem of 𝑘-core decomposition is fundamental in graph analysis and has applications across various domains. However, existing algorithms face significant challenges in achieving work-efficiency in theory and/or high parallelism in practice, and suffer from various performance bottlenecks.

We present a simple, work-efficient parallel framework for 𝑘core decomposition that is easy to implement and adaptable to various strategies for improving work-efficiency. We introduce two techniques to enhance parallelism: a sampling scheme to reduce contention on high-degree vertices, and vertical granularity control (VGC) to mitigate scheduling overhead for low-degree vertices. Furthermore, we design a hierarchical bucket structure to optimize performance for graphs with high coreness values.

We evaluate our algorithm on a diverse set of real-world and synthetic graphs. Compared to state-of-the-art parallel algorithms, including ParK, PKC, and Julienne, our approach demonstrates superior performance on 23 out of 25 graphs when tested on a 96-core machine. Our algorithm shows speedups of up to 315× over ParK, 33.4× over PKC, and 52.5× over Julienne. 1 The work of a parallel algorithm is its time complexity running on one core. A parallel algorithm is work-efficient if its work is the same as the best sequential time complexity.