SPHERE: Spherical partitioning for large-scale routing optimization

Abstract

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.