🤖 AI Summary
This work addresses the problem of efficiently maintaining rooted spanning forests in dynamic graphs by proposing four novel GPU-oriented fully dynamic parallel algorithms that support batch edge insertions and deletions without requiring forest reconstruction after each update. As the first approach specifically designed for GPUs to maintain fully dynamic rooted spanning trees, it fills a critical gap in the literature. By integrating dynamic graph update strategies with GPU parallelism, the system achieves throughputs of up to 2 million insertions and 1.4 million deletions per second on real-world datasets, significantly outperforming existing static parallel algorithms.
📝 Abstract
Spanning trees are fundamental structures in graph theory, essential for various applications such as network maintenance, routing adjustments, and many more. The dynamic nature of real-world networks requires efficient updates to these structures as the underlying graph evolves. Maintaining rooted spanning trees dynamically is particularly crucial for algorithms addressing 2-connected components and minimum-weighted spanning trees. In this paper, we address the challenge of maintaining a rooted spanning forest when a batch of edges are inserted or deleted. We present four novel fully dynamic parallel algorithms to update the spanning forest without reconstructing it from scratch. To the best of our knowledge, parallel algorithms for this problem remain largely unexplored. Our experiments on a diverse collection of real-world graphs using a GPU environment demonstrate a throughput of 2 million insertions and 1.4 million deletions per second, significantly outperforming state-of-the-art parallel static algorithms.