Abstract
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a “travel time” value, are becoming a standard feature of many navigation-related applications. To support this, very efficient computation of these paths in very large road networks is critical. Fastest paths may be computed as minimal-cost paths in a weighted directed graph, but traditional minimal-cost path algorithms based on variants of the classical Dijkstra algorithm do not scale well, as in the worst case they may traverse the entire graph. A common improvement, which can dramatically reduce the number of graph vertices traversed, is the A* algorithm, which requires a good heuristic lower bound on the minimal cost. We introduce a simple, but very effective, heuristic function based on a small number of values assigned to each graph vertex. The values are based on graph separators and are computed efficiently in a preprocessing stage. We present experimental results demonstrating that our heuristic provides estimates of the minimal cost superior to those of other heuristics. Our experiments show that when used in the A* algorithm, this heuristic can reduce the number of vertices traversed by an order of magnitude compared to other heuristics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bast, H.; Delling, D.; Goldberg, A.; Müeller-Hannemann, M.; Pajor, T.; Sanders, P.; Wagner, D.; Werneck, R. Route planning in transportation networks. In: Algorithm Engineering. Lecture Notes in Computer Science, Vol. 9220. Kliemann, L.; Sanders, P. Eds. Springer Cham, 19–80, 2016.
Dijkstra, E. W. A note on two problems in connexion with graphs. Numerische Mathematik Vol. 1, No. 1, 269–271, 1959.
Fredman, M. L.; Tarjan, R. E. Fibonacci heaps and their uses in improved network optimization algorithms. In: Proceedings of the 25th Annual Symposium on Foundations of Computer Science, 338–346, 1984.
Hart, P. E.; Nilsson, N. J.; Raphael, B. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics Vol. 4, No. 2, 100–107, 1968.
Rayner, C.; Bowling, M.; Sturtevant, N. Euclideanheuristic optimization. In: Proceedings of the 25th AAAI Conference on Artificial Intelligence, 81–86, 2011.
Goldberg, A. V.; Harrelson, C. Computing the shortest path: A* search meets graph theory. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, 156–165, 2003.
Chow, E. A graph search heuristic for shortest distance paths. In: Proceedings of the Association for the Advance of Artificial Intelligence, 2005.
Cohen, L.; Uras, T.; Jahangiri, S.; Arunasalam, A.; Koenig, S.; Kumar, T. K. S. The FastMap algorithm for shortest path computations. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence, 1427–1433, 2018.
Lipton, R. J.; Tarjan, R. E. A separator theorem for planar graphs. SIAM Journal on Applied Mathematics Vol. 36, No. 2, 177–189, 1979.
Karypis, G.; Kumar, V. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing Vol. 20, No. 1, 359–392, 1998.
Information on http://www.diag.uniroma1.it/challenge9/.
Information on https://www.openstreetmap.org/.
Dibbelt, J.; Strasser, B.; Wagner, D. Customizable contraction hierarchies. In: Experimental Algorithms. Lecture Notes in Computer Science, Vol. 8504. Gudmundsson, J.; Katajainen, J. Eds. Springer Cham, 271–282, 2014.
Geisberger, R.; Sanders, P.; Schultes, D.; Vetter, C. Exact routing in large road networks using contraction hierarchies. Transportation Science Vol. 46, No. 3, 388–404, 2012.
Geisberger, R.; Sanders, P.; Schultes, D.; Delling, D. Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In: Experimental Algorithms. Lecture Notes in Computer Science, Vol. 5038. McGeoch, C. C. Ed. Springer Berlin Heidelberg, 319–333, 2008.
Delling, D.; Goldberg, A. V.; Pajor, T.; Werneck, R. F. Customizable route planning. In: Experimental Algorithms. Lecture Notes in Computer Science, Vol. 6630. Pardalos, P. M.; Rebennack, S. Eds. Springer Berlin Heidelberg, 376–387, 2011.
Delling, D.; Goldberg, A. V.; Pajor, T.; Werneck, R. F. Customizable route planning in road networks. Transportation Science Vol. 51, No. 2, 566–591, 2017.
Maue, J.; Sanders, P.; Matijevic, D. Goal directed shortest path queries using precomputed cluster distances. In: Experimental Algorithms. Lecture Notes in Computer Science, Vol. 4007. Álvarez, C.; Serna, M. Eds. Springer Berlin Heidelberg, 316–327, 2009.
Efentakis, A.; Pfoser, D. Optimizing landmark-based routing and preprocessing. In: Proceedings of the 6th ACM SIGSPATIAL International Workshop on Computational Transportation Science, 25–30, 2013.
Delling, D.; Wagner, D. Landmark-based routing in dynamic graphs. In: Experimental Algorithms. Lecture Notes in Computer Science, Vol. 4525. Demetrescu, C. Ed. Springer Berlin Heidelberg, 52–65, 2007.
Acknowledgements
We would like to thank the anonymous reviewers for their constructive suggestions and comments. This work was partly supported by the Anhui Provincial Natural Science Foundation (2008085MF195), the National Natural Science Foundation of China (62072422), and Zhejiang Lab (2019NB0AB03).
Author information
Authors and Affiliations
Corresponding author
Additional information
Renjie Chen is a professor at the University of Science and Technology of China (USTC). He holds a Ph.D. degree from Zhejiang University, China. Before joining USTC, he was a postdoctoral fellow at the Technion Israel Institute of Technology, a postdoctoral research associate at the University of North Carolina at Chapel Hill, a key researcher in the BeingThere Center in Nanyang Technological University, Singapore, and a senior researcher heading a research group working on 3D geometry and images at the Max Planck Institute for Informatics (MPII) in Saarbrucken, Germany. His research interests include computer graphics, geometric modeling, computational geometry, and glasses-free 3D display.
Craig Gotsman is a Distinguished Professor and Dean of the Ying Wu College of Computing at New Jersey Institute of Technology, specializing in computer graphics and geometric modeling. He was previously a cofounder of Cornell Tech, a New York City graduate-level campus dedicated to innovation and entrepreneurship in information technologies. Prior to that, he was the Hewlett-Packard Professor of Computer Engineering at the Technion in Israel. He received his Ph.D. degree from the Hebrew University of Jerusalem in 1991. Gotsman has published over 160 papers, received eight best paper awards, and served on the editorial boards of all the leading journals and on the program committees of all the top conferences in computer graphics. Gotsman holds 11 U.S. patents, some commercialized through his four startup companies, of which three were acquired by technology giants. Gotsman is a Fellow of the U.S. National Academy of Inventors and a Fellow of the Academy of Europe.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Other papers from this open access journal are available free of charge from http://www.springer.com/journal/41095. To submit a manuscript, please go to https://www.editorialmanager.com/cvmj.
About this article
Cite this article
Chen, R., Gotsman, C. Efficient fastest-path computations for road maps. Comp. Visual Media 7, 267–281 (2021). https://doi.org/10.1007/s41095-021-0211-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41095-021-0211-2