Parallel Algorithms for Core Maintenance in Dynamic Graphs

TL;DR

This paper introduces the first parallel algorithms for core maintenance in dynamic graphs, enabling faster updates of core numbers after graph modifications, with proven efficiency and scalability through extensive experiments.

Contribution

The paper proposes novel parallel algorithms for core maintenance in dynamic graphs, utilizing the superior edge set structure to achieve significant speedup over sequential methods.

Findings

Algorithms demonstrate high speedup in processing time.

Effective on real-world and synthetic datasets.

Showcase scalability and stability of the approach.

Abstract

This paper initiates the studies of parallel algorithms for core maintenance in dynamic graphs. The core number is a fundamental index reflecting the cohesiveness of a graph, which are widely used in large-scale graph analytics. The core maintenance problem requires to update the core numbers of vertices after a set of edges and vertices are inserted into or deleted from the graph. We investigate the parallelism in the core update process when multiple edges and vertices are inserted or deleted. Specifically, we discover a structure called superior edge set, the insertion or deletion of edges in which can be processed in parallel. Based on the structure of superior edge set, efficient parallel algorithms are then devised for incremental and decremental core maintenance respectively. To the best of our knowledge, the proposed algorithms are the first parallel ones for the fundamental core maintenance problem. The algorithms show a significant speedup in the processing time compared with previous results that sequentially handle edge and vertex insertions/deletions. Finally, extensive experiments are conducted on different types of real-world and synthetic datasets, and the results illustrate the efficiency, stability and scalability of the proposed algorithms.