An efficient solution for GPUs to the ST-connectivity problem on dynamic graphs

Abstract

ST-connectivity poses a decision problem, determining whether, for vertices $s$ and $t$ within a graph, $t$ is reachable from $s$. The challenge arises in the context of dynamic real-world graphs that undergo rapid evolution over time. In these scenarios, repeatedly solving the s-t connectivity problem from the beginning after each graph modification becomes impractical. Although parallel solutions, especially designed for GPUs, have been introduced to tackle the size complexity of static graphs, none have specifically addressed the concern of work efficiency in dynamic graphs. We propose an efficient solution for GPUs to the st-connectivity problem that can handle concurrent processing of batches of graph updates. We use batch information strategically to reduce the overall workload needed for updating the connectivity result. We provide experimental results based on standard datasets and with graphs of different characteristics and batch sizes to evaluate the proposed solutions efficiency.