dyGRASS: Dynamic Spectral Graph Sparsification via Localized Random Walks on GPUs

TL;DR

dyGRASS is a GPU-accelerated dynamic spectral graph sparsification algorithm that efficiently updates sparse graph representations in real-time, significantly outperforming previous methods in speed and quality across various applications.

Contribution

It introduces a novel GPU-based random walk approach for dynamic spectral sparsification, enabling fast incremental and decremental updates with high scalability.

Findings

Achieves approximately 10x speedup over inGRASS.

Effectively handles fully dynamic graphs with insertions and deletions.

Demonstrates superior solution quality across diverse graph types.

Abstract

This work presents dyGRASS, an efficient dynamic algorithm for spectral sparsification of large undirected graphs that undergo streaming edge insertions and deletions. At its core, dyGRASS employs a random-walk-based method to efficiently estimate node-to-node distances in both the original graph (for decremental update) and its sparsifier (for incremental update). For incremental updates, dyGRASS enables the identification of spectrally critical edges among the updates to capture the latest structural changes. For decremental updates, dyGRASS facilitates the recovery of important edges from the original graph back into the sparsifier. To further enhance computational efficiency, dyGRASS employs a GPU-based non-backtracking random walk scheme that allows multiple walkers to operate simultaneously across various target updates. This parallelization significantly improves both the performance and scalability of the proposed dyGRASS framework. Our comprehensive experimental evaluations reveal that dyGRASS achieves approximately a 10x speedup compared to the state-of-the-art incremental sparsification (inGRASS) algorithm while eliminating the setup overhead and improving solution quality in incremental spectral sparsification tasks. Moreover, dyGRASS delivers high efficiency and superior solution quality for fully dynamic graph sparsification, accommodating both edge insertions and deletions across a diverse range of graph instances originating from integrated circuit simulations, finite element analysis, and social networks.