Geosocial reachability queries (\textsc{RangeReach}) determine whether a given vertex in a geosocial network can reach any spatial vertex within a query region. The state-of-the-art 3DReach method answers such queries by encoding graph reachability through interval labelling and indexing spatial vertices in a 3D R-tree. We present 2DReach, a simpler approach that avoids interval labelling entirely. Like 3DReach, 2DReach collapses strongly connected components (SCCs) into a DAG, but instead of computing interval labels, it directly stores a 2D R-tree per component over all reachable spatial vertices. A query then reduces to a single 2D R-tree lookup. We further propose compressed variants that reduce storage by excluding spatial sinks and sharing R-trees between components with identical reachable sets. Experiments on four real-world datasets show that 2DReach achieves faster index construction than 3DReach, with the compressed variant yielding the smallest index size among all methods. 2DReach delivers competitive or superior query performance with more stable response times across varying query parameters.

翻译：地理社交可达性查询（\textsc{RangeReach}）用于判断地理社交网络中给定顶点能否到达查询区域内的任意空间顶点。当前最先进的3DReach方法通过区间标记编码图可达性，并在三维R树中索引空间顶点来回答此类查询。本文提出了2DReach，这是一种更简单的方法，完全避免了区间标记。与3DReach类似，2DReach将强连通分量（SCCs）压缩为有向无环图（DAG），但它不计算区间标签，而是直接为每个分量存储一个覆盖所有可达空间顶点的二维R树。查询因此简化为一次二维R树查找。我们进一步提出了压缩变体，通过排除空间汇点以及在具有相同可达集的分量间共享R树来减少存储开销。在四个真实世界数据集上的实验表明，2DReach实现了比3DReach更快的索引构建速度，其压缩变体在所有方法中获得了最小的索引大小。2DReach在不同查询参数下提供了具有竞争力或更优的查询性能，且响应时间更稳定。