期刊
COMMUNICATIONS OF THE ACM
卷 60, 期 11, 页码 90-99出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3131280
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类别
资金
- Google PhD Fellowship
- Fraunhofer Gesellschaft
We introduce the heat method for solving the single-or multiple-source shortest path problem on both flat and curved domains. A key insight is that distance computation can be split into two stages: first find the direction along which distance is increasing, then compute the distance itself. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard sparse linear systems. These systems can be factored once and subsequently solved in near-linear time, substantially reducing amortized cost. Real-world performance is an order of magnitude faster than state-of-the-art methods, while maintaining a comparable level of accuracy. The method can be applied in any dimension, and on any domain that admits a gradient and inner product-including regular grids, triangle meshes, and point clouds. Numerical evidence indicates that the method converges to the exact distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where greater regularity is desired.
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