Article

Contraction hierarchies: faster and simpler hierarchical routing in road networks

Authors:

Robert Geisberger,

Dominik Schultes,

Daniel DellingAuthors Info & Claims

WEA'08: Proceedings of the 7th international conference on Experimental algorithms

Pages 319 - 333

Published: 30 May 2008 Publication History

Abstract

We present a route planning technique solely based on the concept of node contraction. The nodes are first ordered by 'importance'. A hierarchy is then generated by iteratively contracting the least important node. Contracting a node υ means replacing shortest paths going through v by shortcuts. We obtain a hierarchical query algorithm using bidirectional shortest-path search. The forward search uses only edges leading to more important nodes and the backward search uses only edges coming from more important nodes. For fastest routes in road networks, the graph remains very sparse throughout the contraction process using rather simple heuristics for ordering the nodes. We have five times lower query times than the best previous hierarchical Dijkstra-based speedup techniques and a negative space overhead, i.e., the data structure for distance computation needs less space than the input graph. CHs can be combined with many other route planning techniques, leading to improved performance for many-to-many routing, transit-node routing, goal-directed routing or mobile and dynamic scenarios.

References

[1]

Sanders, P., Schultes, D.: Engineering fast route planning algorithms. In: Demetrescu, C. (ed.)WEA 2007. LNCS, vol. 4525, pp. 23-36. Springer, Heidelberg (2007)

Digital Library

[2]

Schultes, D.: Route Planning in Road Networks. PhD thesis (2008)

[3]

Schultes, D., Sanders, P.: Dynamic highway-node routing. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 66-79. Springer, Heidelberg (2007)

Digital Library

[4]

Sanders, P., Schultes, D.: Highway hierarchies hasten exact shortest path queries. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 568-579. Springer, Heidelberg (2005)

Digital Library

[5]

Sanders, P., Schultes, D.: Engineering highway hierarchies. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 804-816. Springer, Heidelberg (2006)

Digital Library

[6]

Goldberg, A.V., Kaplan, H., Werneck, R.F.: Better landmarks within reach. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 38-51. Springer, Heidelberg (2007)

Digital Library

[7]

Bauer, R., Delling, D.: SHARC: Fast and robust unidirectional routing. In: Workshop on Algorithm Engineering and Experiments (ALENEX) (2008)

[8]

Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast routing in road networks with transit nodes. Science 316(5824), 566 (2007)

[9]

Bauer, R., Delling, D., Sanders, P., Schieferdecker, D., Schultes, D., Wagner, D.: Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm. In: WEA 2008. LNCS, vol. 5038, Springer, Heidelberg (2008)

Digital Library

[10]

Knopp, S., Sanders, P., Schultes, D., Schulz, F., Wagner, D.: Computing many-to-many shortest paths using highway hierarchies. In: Workshop on Algorithm Engineering and Experiments (ALENEX) (2007)

[11]

Maue, J., Sanders, P., Matijevic, D.: Goal directed shortest path queries using Precomputed Cluster Distances. In: À lvarez, C., Serna, M.J. (eds.) WEA 2006. LNCS, vol. 4007, pp. 316-328. Springer, Heidelberg (2006)

Digital Library

[12]

Geisberger, R., Sanders, P., Schultes, D.: Better approximation of betweenness centrality. In: Workshop on Algorithm Engineering and Experiments (ALENEX) (2008)

[13]

Gutman, R.: Reach-based routing: A new approach to shortest path algorithms optimized for road networks. In: Workshop on Algorithm Engineering and Experiments (ALENEX)., pp. 100-111 (2004)

[14]

Lauther, U.: 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, pp. 219-230. IfGI prints, Institut für Geoinformatik, Münster (2004)

[15]

Köhler, E., Möhring, R.H., Schilling, H.: Acceleration of shortest path and constrained shortest path computation. In: WEA 2005. LNCS, vol. 3503, Springer, Heidelberg (2005)

Digital Library

[16]

Delling, D., Sanders, P., Schultes, D., Wagner, D.: Highway hierarchies star. In: 9th DIMACS Implementation Challenge {20} (2006)

[17]

Goldberg, A.V., Kaplan, H., Werneck, R.F.: Better landmarks within reach. In: 9th DIMACS Implementation Challenge {20} (2006)

[18]

Sanders, P., Schultes, D., Vetter, C.: Mobile Route Planning (2008) in preparation, http://algo2.iti.uka.de/schultes/hwy/

[19]

R Development Core Team: R: A Language and Environment for Statistical Computing (2004), http://www.r-project.org

[20]

9th DIMACS Implementation Challenge: Shortest Paths (2006), http://www.dis.uniroma1.it/~challenge9/

Cited By

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Published In

cover image Guide Proceedings

WEA'08: Proceedings of the 7th international conference on Experimental algorithms

May 2008

362 pages

ISBN:3540685480

Editor:
Catherine C. McGeoch
Department of Mathematics and Computer Science, Amherst College, Amherst, MA

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 30 May 2008

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Cited By

Sivagnanam APettet ALee HMukhopadhyay ADubey ALaszka ASalakhutdinov RKolter ZHeller KWeller AOliver NScarlett JBerkenkamp F(2024)Multi-agent reinforcement learning with hierarchical coordination for emergency responder stationingProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3693934(45813-45834)Online publication date: 21-Jul-2024
https://dl.acm.org/doi/10.5555/3692070.3693934
Fahmin ACheema MEunus Ali MNadjaran Toosi ALu HLi HTaniar DA. Rakha HShen B(2024)Eco-Friendly Route Planning Algorithms: Taxonomies, Literature Review and Future DirectionsACM Computing Surveys10.1145/369162457:1(1-42)Online publication date: 2-Sep-2024
https://dl.acm.org/doi/10.1145/3691624
Farhan MKoehler HOhms RWang Q(2023)Hierarchical Cut Labelling - Scaling Up Distance Queries on Road NetworksProceedings of the ACM on Management of Data10.1145/36267311:4(1-25)Online publication date: 12-Dec-2023
https://dl.acm.org/doi/10.1145/3626731
Liu ZLi LZhang MHua WZhou X(2022)FHL-cubeProceedings of the VLDB Endowment10.14778/3551793.355185615:11(3112-3125)Online publication date: 1-Jul-2022
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Zhang JLi WYuan LQin LZhang YChang L(2022)Shortest-path queries on complex networksProceedings of the VLDB Endowment10.14778/3551793.355182015:11(2640-2652)Online publication date: 29-Sep-2022
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Qiu YWen DQin LLi WLi RZhang Y(2022)Efficient shortest path counting on large road networksProceedings of the VLDB Endowment10.14778/3547305.354731515:10(2098-2110)Online publication date: 1-Jun-2022
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Zhang JYuan LLi WQin LZhang Y(2022)Efficient label-constrained shortest path queries on road networksProceedings of the VLDB Endowment10.14778/3494124.349414815:3(686-698)Online publication date: 4-Feb-2022
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Baur LFunke SRupp TRenz MSarwat M(2022)PATHFINDERVISProceedings of the 30th International Conference on Advances in Geographic Information Systems10.1145/3557915.3560990(1-4)Online publication date: 1-Nov-2022
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