Core Maintenance on Dynamic Graphs: A Distributed Approach Built on H-Index

Core number is an essential tool for analyzing graph structure. Graphs in the real world are typically large and dynamic, requiring the development of distributed algorithms to refrain from expensive I/O operations and the maintenance algorithms to address dynamism. Core maintenance updates the core number of each vertex upon the insertion/deletion of vertices/edges. Although the state-of-the-art distributed maintenance algorithm (Weng et al.~2022) can handle multiple edge insertions/deletions simultaneously, it still has two aspects to improve. (I) Parallel processing is not allowed when inserting/removing edges with the same core number, reducing the degree of parallelism and raising the number of rounds. (II) During the implementation phase, only one thread is assigned to the vertices with the same core number, leading to the inability to fully utilize the distributed computing power. Furthermore, the h-index (Lü, et al. 2016) based distributed core decomposition algorithm (Montresor et al. 2013) can fully utilize the distributed computing power where all vertices can be processed in parallel. However, it requires all vertices to recompute their core numbers upon graph changes. In this article, we propose a distributed core maintenance algorithm based on h-index, which circumvents the issues of algorithm (Weng et al.~2022). In addition, our algorithm avoids core numbers recalculation where the numbers do not change. In comparison to the state-of-the-art distributed maintenance algorithm (Weng et al.~2022), the time speedup ratio is at least 100 in the scenarios of both insertion and deletion. Compared to the distributed core decomposition algorithm (Montresor et al. 2013), the average time speedup ratios are 2 and 8 for the cases of insertion and deletion, respectively.