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Travel-time computation with large transportation networks is often computationally intensive for two main reasons: 1) large computer memory is required to handle large networks; and 2) calculating shortest-distance paths over large networks is computing intensive. Therefore, previous research tends to limit their spatial extent to reduce computational intensity or resolve computational intensity with advanced cyberinfrastructure. In this context, this article describes a new Spatial Partitioning Algorithm for Scalable Travel-time Computation (SPASTC) that is designed based on spatial domain decomposition with computer memory limit explicitly considered. SPASTC preserves spatial relationships required for travel-time computation and respects a user-specified memory limit, which allows efficient and large-scale travel-time computation within the given memory limit. We demonstrate SPASTC by computing spatial accessibility to hospital beds across the conterminous United States. Our case study shows that SPASTC achieves significant efficiency and scalability making the travel-time computation tens of times faster.