Parallel $k$-Core Decomposition: Theory and Practice

TL;DR

This paper introduces a highly parallel, work-efficient framework for $k$-core decomposition that significantly outperforms existing algorithms in speed and scalability across diverse graph datasets.

Contribution

The paper presents a novel parallel framework with techniques like sampling, vertical granularity control, and hierarchical buckets, improving work-efficiency and parallelism in $k$-core decomposition.

Findings

Achieves up to 315x speedup over ParK

Outperforms state-of-the-art algorithms on 23/25 graphs

Demonstrates superior scalability on multi-core systems

Abstract

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 $k$-core 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$\times$ over ParK, 33.4$\times$ over PKC, and 52.5$\times$ over Julienne.