Abstract
We study the computation of good alternatives to the shortest path in road networks. Our approach is based on single via-node routing on top of contraction hierarchies and achieves superior quality and efficiency compared to previous methods. We present a fast preprocessing method for computing multiple good alternatives and apply this result in an online setting. This setting makes our result applicable in legacy systems with negligible memory overhead. An extensive experimental analysis on a continental-sized real- world road network proves the performance of our algorithm and supports the general systematic algorithm engineering approach. We also show how to combine our results with the competing concept of alternative graphs that encode many alternative paths at once.
- Ittai Abraham, Daniel Delling, Amos Fiat, Andrew V. Goldberg, and Renato F. Werneck. 2011a. VC-Dimension and Shortest Path Algorithms. In International Colloquium on Automata, Languages, and Programming (ICALP’11). Google ScholarDigital Library
- Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2011b. A Hub-Based Labeling Algorithm for Shortest Paths in Road Networks. In International Symposium on Experimental Algorithms (SEA’11). 230--241. Google ScholarDigital Library
- Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2012. Hierarchical Hub Labelings for Shortest Paths. In European Symposium on Algorithms (ESA’12) (LNCS), Leah Epstein and Paolo Ferragina (Eds.), Vol. 7501. Springer, 24--35. Google ScholarDigital Library
- Ittai Abraham, Daniel Delling, Andrew V. Goldberg, and Renato F. Werneck. 2013. Alternative Routes in Road Networks. ACM Journal of Experimental Algorithmics 18, 1 (2013), 1--17. Google ScholarDigital Library
- Ittai Abraham, Amos Fiat, Andrew V. Goldberg, and Renato F. Werneck. 2010. Highway Dimension, Shortest Paths, and Provably Efficient Algorithms. In ACM--SIAM Symposium on Discrete Algorithms (SODA’10). Google ScholarDigital Library
- Roland Bader, Jonathan Dees, Robert Geisberger, and Peter Sanders. 2011. Alternative Route Graphs in Road Networks. In Theory and Practice of Algorithms in (Computer) Systems (TAPAS’11). Google ScholarDigital Library
- Holger Bast, Stefan Funke, Peter Sanders, and Dominik Schultes. 2007. Fast Routing in Road Networks with Transit Nodes. Science 316 (2007), 566.Google ScholarCross Ref
- Gernot Veit Batz, Robert Geisberger, Dennis Luxen, Peter Sanders, and Roman Zubkov. 2012. Efficient Route Compression for Hybrid Route Planning. In 1st Mediterranean Conference on Algorithms. Springer. Google ScholarDigital Library
- Gernot Veit Batz, Robert Geisberger, Peter Sanders, and Christian Vetter. 2013. Minimum Time-Dependent Travel Times with Contraction Hierarchies. ACM Journal of Experimental Algorithmics 18, 1.4 (2013), 1--43. Google ScholarDigital Library
- Reinhard Bauer, Daniel Delling, Peter Sanders, Dennis Schieferdecker, Dominik Schultes, and Dorothea Wagner. 2010. Combining Hierarchical and Goal-Directed Speed-Up Techniques for Dijkstra’s Algorithm. ACM Journal of Experimental Algorithmics 15, 2.3 (2010), 1--31. Google ScholarDigital Library
- Cambridge Vehicle Information Tech. Ltd. 2005. Choice Routing. Retrieved from http://camvit.com.Google Scholar
- Yanyan Chen, Michael G. H. Bell, and Klaus Bogenberger. 2007. Reliable Pretrip Multipath Planning and Dynamic Adaptation for a Centralized Road Navigation System. IEEE Transactions on Intelligent Transportation Systems 8, 1 (2007), 14--20. Google ScholarDigital Library
- Gianlorenzo D’Angelo, Mattia D’Emidio, Daniele Frigioni, and Camillo Vitale. 2012. Fully Dynamic Maintenance of Arc-Flags in Road Networks. In International Symposium on Experimental Algorithms (SEA’12) (LNCS), Vol. 7276. Springer, 135--147. Google ScholarDigital Library
- Daniel Delling, Andrew V. Goldberg, Andreas Nowatzyk, and Renato F. Werneck. 2013. PHAST: Hardware-Accelerated Shortest Path Trees. Journal of Parallel and Distributed Computing 73, 7 (2013), 940--952.Google ScholarCross Ref
- Daniel Delling, Andrew V. Goldberg, Ilya Razenshteyn, and Renato F. Werneck. 2011. Graph Partitioning with Natural Cuts. In International Parallel and Distributed Processing Symposium (IPDPS’11). IEEE Computer Society. Google ScholarDigital Library
- Daniel Delling, Moritz Kobitzsch, Dennis Luxen, and Renato F. Werneck. 2012. Robust Mobile Route Planning with Limited Connectivity. In Meeting on Algorithm Engineering and Experiments (ALENEX’12). SIAM, 150--159.Google Scholar
- Daniel Delling, Peter Sanders, Dominik Schultes, and Dorothea Wagner. 2009. Engineering Route Planning Algorithms. In Algorithmics of Large and Complex Networks. Springer, 117--139. Google ScholarDigital Library
- Daniel Delling and Dorothea Wagner. 2009. Pareto Paths with SHARC. In International Symposium on Experimental Algorithms (SEA’09) (LNCS), Vol. 5526. Springer. Google ScholarDigital Library
- Camil Demetrescu, Andrew V. Goldberg, and David S. Johnson (Eds.). 2006. The 9th DIMACS Implementation Challenge—Shortest Paths. American Mathematical Society.Google Scholar
- Edsger W. Dijkstra. 1959. A Note on Two Problems in Connexion with Graphs. Numerische Mathematik 1 (1959), 269--271. Google ScholarDigital Library
- David Eppstein. 1998. Finding the k Shortest Paths. SIAM Journal of Computing 28, 2 (1998), 652--673. Google ScholarDigital Library
- Robert Geisberger, Moritz Kobitzsch, and Peter Sanders. 2010. Route Planning with Flexible Objective Functions. In Workshop on Algorithm Engineering and Experiments (ALENEX’10). SIAM.Google Scholar
- Robert Geisberger, Peter Sanders, Dominik Schultes, and Christian Vetter. 2012. Exact Routing in Large Road Networks Using Contraction Hierarchies. Transportation Science 46, 3 (2012), 388--404. Google ScholarDigital Library
- Andrew V. Goldberg and Chris Harrelson. 2005. Computing the Shortest Path: A* Search Meets Graph Theory. In ACM--SIAM Symposium on Discrete Algorithms (SODA’05). SIAM. Google ScholarDigital Library
- Andrew V. Goldberg, Haim Kaplan, and Renato F. Werneck. 2009. Reach for A*: Shortest Path Algorithms with Preprocessing. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, Camil Demetrescu, Andrew V. Goldberg, and David S. Johnson (Eds.). DIMACS Book, Vol. 74. American Mathematical Society, 93--139.Google Scholar
- P. Hansen. 1980. Bicriterion Path Problems. In Multiple Criteria Decision Making: Theory and Applications.Google Scholar
- P. E. Hart, N. J. Nilsson, and B. Raphael. 1968. A Formal Basis for the Heuristic Determination of Minimum Cost Paths. IEEE Transactions on Systems Science and Cybernetics 4, 2 (1968). DOI: http://dx.doi.org/10.1109/TSSC.1968.300136Google ScholarCross Ref
- Moritz Hilger, Ekkehard Köhler, Rolf H. Möhring, and Heiko Schilling. 2009. Fast Point-to-Point Shortest Path Computations with Arc-Flags. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, Camil Demetrescu, Andrew V. Goldberg, and David S. Johnson (Eds.). DIMACS Book, Vol. 74. American Mathematical Society, 41--72.Google Scholar
- Sebastian Knopp, Peter Sanders, Dominik Schultes, Frank Schulz, and Dorothea Wagner. 2007. Computing Many-to-Many Shortest Paths Using Highway Hierarchies. In Workshop on Algorithm Engineering and Experiments (Alenex’07).Google Scholar
- Ulrich Lauther. 2009. An Experimental Evaluation of Point-To-Point Shortest Path Calculation on Roadnetworks with Precalculated Edge-Flags. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, Camil Demetrescu, Andrew V. Goldberg, and David S. Johnson (Eds.). DIMACS Book, Vol. 74. American Mathematical Society, 19--40.Google Scholar
- Dennis Luxen and Dennis Schieferdecker. 2012. Candidate Sets for Alternative Routes in Road Networks. In International Symposium on Experimental Algorithms (SEA’12) (LNCS), Vol. 7276. Springer, 260--270. Google ScholarDigital Library
- Ernesto Queiros Vieira Martins. 1984. On a Multicriteria Shortest Path Problem. European Journal of Operational Research 16, 2 (1984), 236--245. http://ideas.repec.org/a/eee/ejores/v16y1984i2p236-245.html.Google ScholarCross Ref
- Francois Pellegrini and Jean Roman. 1996. SCOTCH: A Software Package for Static Mapping by Dual Recursive Bipartitioning of Process and Architecture Graphs. In High-Performance Computing and Networking (LNCS). Springer. Google ScholarDigital Library
- Ira Pohl. 1970. Heuristic search viewed as path finding in a graph. Artificial Intelligence 1, 3--4 (1970), 193--204.Google ScholarCross Ref
- Peter Sanders and Dominik Schultes. 2012. Engineering Highway Hierarchies. ACM Journal of Experimental Algorithmics 17, 1 (2012), 1--40. Google ScholarDigital Library
- Peter Sanders and Christian Schulz. 2011. Engineering Multilevel Graph Partitioning Algorithms. In European Symposium on Algorithms (ESA’11) (LNCS), Vol. 6942. Springer, 469--480. Google ScholarDigital Library
- Dominik Schultes. 2008. Route Planning in Road Networks. Ph.D. Dissertation. Universität Karlsruhe. Retrieved from http://algo2.iti.uka.de/schultes/hwy/schultes_diss.pdf.Google Scholar
- Dominik Schultes and Peter Sanders. 2007. Dynamic Highway-Node Routing. In Workshop on Experimental Algorithms (WEA’07) (LNCS), Vol. 4525. Springer, 66--79. Google ScholarDigital Library
- Christian Vetter. 2009. Parallel Time-Dependent Contraction Hierarchies. Student Research Project. Retrieved from http://algo2.iti.kit.edu/download/vetter_sa.pdf.Google Scholar
- Jin Y. Yen. 1971. Finding the K Shortest Loopless Paths in a Network. Management Science 17, 11 (1971), 712--716.Google ScholarDigital Library
Index Terms
- Candidate Sets for Alternative Routes in Road Networks
Recommendations
Alternative Routes for Next Generation Traffic Shaping
IWCTS'19: Proceedings of the 12th ACM SIGSPATIAL International Workshop on Computational Transportation ScienceAlternative route computations so far have mostly been considered as producing a small set of reasonable routes for a human driver to select from. In the not too distant future most cars will be self-driving, and choosing from a very large set of ...
Alternative routes in road networks
We study the problem of finding good alternative routes in road networks. We look for routes that are substantially different from the shortest path, have small stretch, and are locally optimal. We formally define the problem of finding alternative ...
Exact Routing in Large Road Networks Using Contraction Hierarchies
Contraction hierarchies are a simple approach for fast routing in road networks. Our algorithm calculates exact shortest paths and handles road networks of whole continents. During a preprocessing step, we exploit the inherent hierarchical structure of ...
Comments