Connectivity queries, which check whether vertices belong to the same connected component, are fundamental in graph computations. Sliding window connectivity processes these queries over sliding windows, facilitating real-time streaming graph analytics. However, existing methods struggle with low-latency processing due to the significant overhead of continuously updating index structures as edges are inserted and deleted. We introduce a novel approach that leverages spanning trees to efficiently process queries. The novelty of this method lies in its ability to maintain spanning trees efficiently as window updates occur. Notably, our approach completely eliminates the need for replacement edge searches, a traditional bottleneck in managing spanning trees during edge deletions. We also present several optimizations to maximize the potential of spanning-tree-based indexes. Our comprehensive experimental evaluation shows that index update latency in spanning trees can be reduced by up to 458x while maintaining query performance, leading to an 8x improvement in throughput. Our approach also significantly outperforms the state-of-the-art in both query processing and index updates. Additionally, our methods use significantly less memory and demonstrate consistent efficiency across various settings.

翻译：连通性查询用于检查顶点是否属于同一连通分量，是图计算中的基础操作。滑动窗口连通性在滑动窗口上处理此类查询，为实时流图分析提供支持。然而，现有方法因边插入和删除时持续更新索引结构带来的显著开销，难以实现低延迟处理。本文提出一种利用生成树高效处理查询的新方法。该方法的核心创新在于能够在窗口更新时高效维护生成树。特别值得注意的是，我们的方法完全避免了替代边搜索——这是传统方法在边删除过程中管理生成树的主要瓶颈。我们还提出了若干优化策略，以充分发挥基于生成树的索引的潜力。全面的实验评估表明，在保持查询性能的同时，生成树索引的更新延迟最高可降低458倍，吞吐量提升8倍。我们的方法在查询处理和索引更新两方面均显著优于现有最优技术。此外，该方法内存占用显著更少，并在多种设置下均表现出稳定的高效性。