We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the problem by identifying \emph{source-target} ($s$--$t$) overlaps of hop-distance spheres. Selecting an anchor node $a$ within this overlap partitions the task into independent induced subgraphs for $s\to a$ and $a\to t$, each restricted to its own induced subgraph. If resulting subgraphs remain large, the procedure recurses on that specific subgraph. We provide a formal guarantee that by using the partition cut within the shared overlap, the resulting subpaths preserve feasibility, thereby avoiding the need for boundary repair. Furthermore, \emph{SPHERE} acts as a solver-agnostic framework that naturally exposes parallelism across subproblems. On million-scale road networks, \emph{SPHERE} achieves faster runtimes and smaller optimality gaps than contemporary state-of-the-art partitioning and community-based routing pipelines. Crucially, it also substantially mitigates heavy-tail runtime outliers suffered by standard exact methods, yielding highly stable and predictable execution times across varying queries.

翻译：本文研究大规模加权无向图中的最短路径路由问题，其中搜索边界的扩展导致精确求解器的时间和内存成本增加。我们提出一种查询感知的划分启发式方法——SPHERE，该方法通过识别跳距球面的源-目标（s–t）重叠区域来自适应地分割问题。在此重叠区域内选择锚点a可将任务划分为s→a和a→t两个独立的诱导子图，每个子图的计算被限制在各自的诱导子图内。若所得子图规模仍然较大，则在该特定子图上递归执行此过程。我们提供严格的理论保证：通过在共享重叠区域内进行划分切割，所得子路径将保持可行性，从而避免边界修复的必要性。此外，SPHERE作为求解器无关的框架，天然支持子问题间的并行计算。在百万级规模的道路网络上，SPHERE相比当前最先进的划分方法与基于社区的路由流程，实现了更快的运行速度和更小的最优性差距。更重要的是，该方法显著缓解了标准精确方法常出现的重尾运行时间异常值问题，在不同查询条件下均能产生高度稳定且可预测的执行时间。