Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm

Published: 17 March 2010 Publication History

Abstract

In recent years, highly effective hierarchical and goal-directed speed-up techniques for routing in large road networks have been developed. This article makes a systematic study of combinations of such techniques. These combinations turn out to give the best results in many scenarios, including graphs for unit disk graphs, grid networks, and time-expanded timetables. Besides these quantitative results, we obtain general insights for successful combinations.

References

[1]
Bast, H., Funke, S., Matijevic, D., Sanders, P., and Schultes, D. 2007. In transit to constant shortest-path queries in road networks. In Proceedings of the 9th Workshop on Algorithm Engineering and Experiments (ALENEX'07). SIAM, Philadelphia, 46--59.
[2]
Bast, H., Funke, S., Sanders, P., and Schultes, D. 2007. Fast routing in road networks with transit modes. Science 316, 5824, 566.
[3]
Batz, G. V., Delling, D., Sanders, P., and Vetter, C. 2009. Time-dependent contraction hierarchies. In Proceedings of the 11th Workshop on Algorithm Engineering and Experiments (ALENEX'09). SIAM, Philadelphia, 97--105.
[4]
Bauer, R. and Delling, D. 2008. SHARC: Fast and robust unidirectional routing. In Proceedings of the 10th Workshop on Algorithm Engineering and Experiments (ALENEX'08). SIAM, Philadelphia, 13--26.
[5]
Bauer, R. and Delling, D. 2009. SHARC: Fast and robust unidirectional routing. ACM J. Exp. Algorithmics 14, 2.4--2.29.
[6]
Bauer, R., Delling, D., Sanders, P., Schieferdecker, D., Schultes, D., and Wagner, D. 2008. Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm. In Proceedings of the 7th Workshop on Experimental Algorithms (WEA'08). Springer, Berlin, 303--318.
[7]
Bauer, R., Delling, D., and Wagner, D. 2007. Experimental study on speed-up techniques for timetable information systems. In Proceedings of the 7th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'07).
[8]
Beier, R., Funke, S., Matijevic, D., and Sanders, P. 2009. Energy-efficient paths in radio networks. Algorithmica.
[9]
Chan, T. M., Efrat, A., and Har-Peled, S. 2001. Fly cheaply: On the minimum fuel consumption problem. J. Algorithms 41, 2, 330--337.
[10]
Dantzig, G. B. 1962. Linear Programming and Extensions. Princeton University Press.
[11]
Delling, D. 2008. Time-dependent SHARC-routing. In Proceedings of the 16th Annual European Symposium on Algorithms (ESA'08). Springer, Berlin, 332--343.
[12]
Delling, D. 2009. Time-dependent SHARC-routing. Algorithmica.
[13]
Delling, D. and Nannicini, G. 2008. Bidirectional core-based routing in dynamic time-dependent road networks. In Proceedings of the 19th International Symposium on Algorithms and Computation (ISAAC'08). Springer, Berlin, 813--824.
[14]
Delling, D., Pajor, T., and Wagner, D. 2008. Engineering time-expanded graphs for faster timetable information. In Proceedings of the 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS'08).
[15]
Delling, D., Sanders, P., Schultes, D., and Wagner, D. 2009a. Engineering route planning algorithms. In Algorithmics of Large and Complex Networks. Springer, Berlin, 117--139.
[16]
Delling, D., Sanders, P., Schultes, D., and Wagner, D. 2009b. Highway hierarchies star. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, C. Demetrescu, A. V. Goldberg, and D. S. Johnson, Eds. DIMACS Book, vol. 74. American Mathematical Society, Providence, RI, 141--174.
[17]
Delling, D. and Wagner, D. 2007. Landmark-based routing in dynamic graphs. In Proceedings of the 6th Workshop on Experimental Algorithms (WEA'07). Springer, Berlin, 52--65.
[18]
Delling, D. and Wagner, D. 2009. Pareto paths with SHARC. In Proceedings of the 8th International Symposium on Experimental Algorithms (SEA'09). Springer, Berlin, 125--136.
[19]
Demetrescu, C., Goldberg, A. V., and Johnson, D. S., Eds. 2006. Proceedings of the 9th DIMACS Implementation Challenge—Shortest Paths. American Mathematical Society, Providence, RI.
[20]
Dijkstra, E. W. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1, 269--271.
[21]
Geisberger, R., Sanders, P., Schultes, D., and Delling, D. 2008. Contraction hierarchies: Faster and simpler hierarchical routing in road networks. In Proceedings of the 7th Workshop on Experimental Algorithms (WEA'08).Springer, Berlin, 319--333.
[22]
Goldberg, A. V. and Harrelson, C. 2005. Computing the shortest path: A* search meets graph theory. In Proceedings of the 16th Annual ACM--SIAM Symposium on Discrete Algorithms (SODA'05). ACM, New York, 156--165.
[23]
Goldberg, A. V., Kaplan, H., and Werneck, R. F. 2006. Reach for A*: Efficient point-to-point shortest path algorithms. In Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX'06). SIAM, Philadelphia, 129--143.
[24]
Goldberg, A. V., Kaplan, H., and Werneck, R. F. 2007. Better landmarks within reach. In Proceedings of the 6th Workshop on Experimental Algorithms (WEA'07). Springer, Berlin, 38--51.
[25]
Goldberg, A. V., Kaplan, H., and Werneck, R. F. 2009. Reach for A*: shortest path algorithms with preprocessing. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, C. Demetrescu, A. V. Goldberg, and D. S. Johnson, Eds. DIMACS Book, vol. 74. American Mathematical Society, Providence, RI, 93--139.
[26]
Goldberg, A. V. and Werneck, R. F. 2005. Computing point-to-point shortest paths from external, emory. In Proceedings of the 7th Workshop on Algorithm Engineering and Experiments (ALENEX'05). SIAM, Philadelphia, 26--40.
[27]
Gutman, R. J. 2004. Reach-based routing: A new approach to shortest path algorithms optimized for road networks. In Proceedings of the 6th Workshop on Algorithm Engineering and Experiments (ALENEX'04). SIAM, Philadelphia, 100--111.
[28]
Hilger, M., Köhler, E., Möhring, R. H., and Schilling, H. 2009. Fast point-to-point shortest path computations with ArcFlags. In The Shortest Path Problem: Ninth DIMACS Implementation Challenge, C. Demetrescu, A. V. Goldberg, and D. S. Johnson, Eds. DIMACS Book, vol. 74. American Mathematical Society, Providence, RI, 41--72.
[29]
Holzer, M., Schulz, F., and Wagner, D. 2006. Engineering multi-level overlay graphs for shortest-path queries. In Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX'06). SIAM, Philadelphia, 156--170.
[30]
Holzer, M., Schulz, F., Wagner, D., and Willhalm, T. 2006. Combining speed-up techniques for shortest-path computations. ACM J. Exp. Algorithmics 10, 2.5.
[31]
Holzer, M., Schulz, F., and Willhalm, T. 2004. Combining speed-up techniques for Shortest path computations. In Proceedings of the 3rd Workshop on Experimental Algorithms (WEA'04). Springer, Berlin, 269--284.
[32]
Köhler, E., Möhring, R. H., and Schilling, H. 2005. Acceleration of shortest path and constrained shortest path computation. In Proceedings of the 4th Workshop on Experimental Algorithms (WEA'05). Springer, Berlin, 126--138.
[33]
Lauther, U. 2004. An extremely fast, exact algorithm for finding shortest paths in static networks with geographical background. In Geoinformation und Mobilität - von der Forschung zur praktischen Anwendung. vol. 22. IfGI, 219--230.
[34]
Möhring, R. H., Schilling, H., Schütz, B., Wagner, D., and Willhalm, T. 2005. Partitioning graphs to speed up Dijkstra's algorithm. In Proceedings of the 4th Workshop on Experimental Algorithms (WEA'05). Springer, Berlin, 189--202.
[35]
Pellegrini, F. 2007. SCOTCH: Static mapping, graph, mesh and hyper-graph partitioning, and parallel and sequential sparse matrix ordering package. http://www.labri.fr/perso/pelegrin/scotch/.
[36]
Sanders, P. and Schultes, D. 2005. Highway hierarchies hasten exact shortest path queries. In Proceedings of the 13th Annual European Symposium on Algorithms (ESA'05). Springer, Berlin, 568--579.
[37]
Sanders, P. and Schultes, D. 2006. Engineering highway hierarchies. In Proceedings of the 14th Annual European Symposium on Algorithms (ESA'06). Springer, Berlin, 804--816.
[38]
Schieferdecker, D. 2008. Systematic combination of speed-up techniques for exact shortest path queries. M.S. thesis, Universität Karlsruhe (TH), Fakultät für Informatik.
[39]
Schultes, D. 2008. Route planning in road networks. Ph.D. thesis, Universitäat Karlsruhe (TH), Fakultät für Informatik. http://algo2.iti.uka.de/schultes/hwy/schultes_diss.pdf.
[40]
Schultes, D. and Sanders, P. 2007. Dynamic highway-node routing. In Proceedings of the 6th Workshop on Experimental Algorithms (WEA'07). Springer, Berlin, 66--79.
[41]
Schulz, F., Wagner, D., and Weihe, K. 2000. Dijkstra's algorithm online: An empirical case study from public railroad transport. ACM J. Exp. Algorithmics 5,12.
[42]
Schulz, F., Wagner, D., and Zaroliagis, C. 2002. Using multi-level graphs for timetable information in railway systems. In Proceedings of the 4th Workshop on Algorithm Engineering and Experiments (ALENEX'02). Springer, Berlin, 43--59.
[43]
Wagner, D., Willhalm, T., and Zaroliagis, C. 2005. Geometric containers for efficient shortest path computation. ACM J. Exp. Algorithmics 10, 1.3.

Cited By

View all
  • (2024)A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) SchemesSIAM Journal on Numerical Analysis10.1137/22M149894262:2(622-645)Online publication date: 1-Mar-2024
  • (2024)Complex Words as Shortest Paths in the Network of Lexical KnowledgeCognitive Science10.1111/cogs.7000548:11Online publication date: 28-Oct-2024
  • (2024)Global Optimal Travel Planning for Massive Travel Queries in Road NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.343940936:12(8377-8394)Online publication date: 1-Dec-2024
  • Show More Cited By

Index Terms

  1. Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Journal of Experimental Algorithmics
    ACM Journal of Experimental Algorithmics  Volume 15, Issue
    2010
    387 pages
    ISSN:1084-6654
    EISSN:1084-6654
    DOI:10.1145/1671970
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 17 March 2010
    Accepted: 01 November 2009
    Revised: 01 July 2009
    Received: 01 December 2008
    Published in JEA Volume 15

    Author Tags

    1. Dijkstra's algorithm
    2. speed-up technique

    Qualifiers

    • Research-article
    • Research
    • Refereed

    Funding Sources

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)39
    • Downloads (Last 6 weeks)2
    Reflects downloads up to 15 Jan 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2024)A Numerical Framework for Nonlinear Peridynamics on Two-Dimensional Manifolds Based on Implicit P-(EC)\(^{ {\boldsymbol k}}\) SchemesSIAM Journal on Numerical Analysis10.1137/22M149894262:2(622-645)Online publication date: 1-Mar-2024
    • (2024)Complex Words as Shortest Paths in the Network of Lexical KnowledgeCognitive Science10.1111/cogs.7000548:11Online publication date: 28-Oct-2024
    • (2024)Global Optimal Travel Planning for Massive Travel Queries in Road NetworksIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.343940936:12(8377-8394)Online publication date: 1-Dec-2024
    • (2024)Space-time tree: a spatiotemporal construct for efficient similarity matrix calculations among network-constrained trajectoriesInternational Journal of Geographical Information Science10.1080/13658816.2024.2431906(1-36)Online publication date: 2-Dec-2024
    • (2023)Optimizing Utilization of Transport Capacities in the Cold Chain by Introducing Dynamic Allocation of Semi-TrailersLogistics10.3390/logistics70401017:4(101)Online publication date: 14-Dec-2023
    • (2023)ULTRA: Unlimited Transfers for Efficient Multimodal Journey PlanningTransportation Science10.1287/trsc.2022.0198Online publication date: 30-Aug-2023
    • (2023)Dynamic Path Optimization Based on Improved Ant Colony AlgorithmJournal of Advanced Transportation10.1155/2023/76511002023(1-11)Online publication date: 17-Apr-2023
    • (2023)A Novel Real-Time Algorithm for Optimizing Train Speed Profiles Under Complex ConstraintsIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.326479524:8(7987-8002)Online publication date: Aug-2023
    • (2023)Multi-Level Elliptic Dijkstra's Algorithm for Finding Optimal Trajectory of Aircrafts2023 15th International Conference on Knowledge and Systems Engineering (KSE)10.1109/KSE59128.2023.10299413(1-6)Online publication date: 18-Oct-2023
    • (2023)Top-k Distance Queries on Large Time-Evolving GraphsIEEE Access10.1109/ACCESS.2023.331660211(102228-102242)Online publication date: 2023
    • Show More Cited By

    View Options

    Login options

    Full Access

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media