Article

Preprocessing speed-up techniques is hard

Authors:

Reinhard Bauer,

Tobias Columbus,

Dorothea WagnerAuthors Info & Claims

CIAC'10: Proceedings of the 7th international conference on Algorithms and Complexity

Pages 359 - 370

https://doi.org/10.1007/978-3-642-13073-1_32

Published: 26 May 2010 Publication History

Abstract

During the last years, preprocessing-based techniques have been developed to compute shortest paths between two given points in a road network. These speed-up techniques make the computation a matter of microseconds even on huge networks. While there is a vast amount of experimental work in the field, there is still large demand on theoretical foundations. The preprocessing phases of most speed-up techniques leave open some degree of freedom which, in practice, is filled in a heuristical fashion. Thus, for a given speed-up technique, the problem arises of how to fill the according degree of freedom optimally. Until now, the complexity status of these problems was unknown. In this work, we answer this question by showing NP-hardness for the recent techniques.

References

[1]

Delling, D., Sanders, P., Schultes, D., Wagner, D.: Engineering Route Planning Algorithms. In: Lerner, J., Wagner, D., Zweig, K.A. (eds.) Algorithmics of Large and Complex Networks. LNCS, vol. 5515, pp. 117-139. Springer, Heidelberg (2009).

Digital Library

[2]

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 (SODA 2005), pp. 156-165 (2005).

Digital Library

[3]

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. IfGI prints. vol. 22. pp. 219-230 (2004).

[4]

Hilger, M., Köhler, E., Möhring, R.H., Schilling, H.: Fast Point-to-Point Shortest Path Computations with Arc-Flags. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) The Shortest Path Problem: Ninth DIMACS Implementation Challenge. DIMACS Book, vol. 74, pp. 41-72. American Mathematical Society, Providence (2009).

[5]

Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. ACM Journal of Experimental Algorithmics 14 (May 2009); 2.4 Special Section on Selected Papers from ALENEX 2008.

Digital Library

[6]

Schulz, F., Wagner, D., Weihe, K.: Dijkstra's Algorithm On-Line: An Empirical Case Study from Public Railroad Transport. In: Vitter, J.S., Zaroliagis, C.D. (eds.) WAE 1999. LNCS, vol. 1668, pp. 110-123. Springer, Heidelberg (1999).

Digital Library

[7]

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

[8]

Holzer, M., Schulz, F., Wagner, D.: Engineering Multi-Level Overlay Graphs for Shortest-Path Queries. In: Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX 2006), pp. 156-170. SIAM, Philadelphia (2006).

[9]

Geisberger, R., Sanders, P., Schultes, D., Delling, D.: Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 319-333. Springer, Heidelberg (2008).

Digital Library

[10]

Wagner, D., Willhalm, T.: Geometric Speed-Up Techniques for Finding Shortest Paths in Large Sparse Graphs. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 776-787. Springer, Heidelberg (2003).

[11]

Wagner, D., Willhalm, T., Zaroliagis, C.: Geometric Containers for Efficient Shortest-Path Computation. ACM Journal of Experimental Algorithmics 10, 1.3 (2005).

Digital Library

[12]

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

[13]

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

[14]

Gutman, R.J.: 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 2004), pp. 100-111. SIAM, Philadelphia (2004).

[15]

Goldberg, A.V., Kaplan, H., Werneck, R.F.: Reach for A*: Efficient Point-to-Point Shortest Path Algorithms. In: Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX 2006), pp. 129-143. SIAM, Philadelphia (2006).

[16]

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

[17]

Sanders, P., Schultes, D.: Robust, Almost Constant Time Shortest-Path Queries in Road Networks. In: Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.) 9th DIMACS Implementation Challenge - Shortest Paths (November 2006).

[18]

Bast, H., Funke, S., Matijevic, D., Sanders, P., Schultes, D.: In Transit to Constant Shortest-Path Queries in Road Networks. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments (ALENEX 2007), pp. 46-59. SIAM, Philadelphia (2007).

[19]

Bauer, R., D'Angelo, G., Delling, D., Wagner, D.: The Shortcut Problem - Complexity and Approximation. In: Nielsen, M., Kucera, A., Miltersen, P.B., Palamidessi, C., Tuma, P., Valencia, F.D. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 105-116. Springer, Heidelberg (2009).

Digital Library

[20]

Abraham, I., Fiat, A., Goldberg, A.V., Werneck, R.F.: Highway Dimension, Shortest Paths, and Provably Efficient Algorithms. In: Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), pp. 782-793 (2010).

Digital Library

[21]

Bauer, R., Columbus, T., Katz, B., Krug, M., Wagner, D.: Preprocessing Speed-Up Techniques is Hard. Technical Report 2010-04, ITI Wagner, Faculty of Informatics, Universität Karlsruhe, TH (2010), http://digbib.ubka.uni-karlsruhe.de/volltexte/1000016080

[22]

Eppstein, D., Goodrich, M.T.: Studying (non-planar) road networks through an algorithmic lens. In: Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems. ACM Press, New York (2008).

Digital Library

Cited By

Farhan MKoehler HWang Q(2025)Dual-Hierarchy Labelling: Scaling Up Distance Queries on Dynamic Road NetworksProceedings of the ACM on Management of Data10.1145/37096853:1(1-25)Online publication date: 11-Feb-2025
https://dl.acm.org/doi/10.1145/3709685
Storandt SLarson K(2024)Scalable landmark hub labeling for optimal and bounded suboptimal pathfindingProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/750(6788-6795)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/750
Funke SStorandt S(2024)Parameterized Upper Bounds for Path-Consistent Hub LabelingCombinatorial Algorithms10.1007/978-3-031-63021-7_34(446-459)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-63021-7_34
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Preprocessing speed-up techniques is hard
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation

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Information

Published In

cover image Guide Proceedings

CIAC'10: Proceedings of the 7th international conference on Algorithms and Complexity

May 2010

384 pages

ISBN:3642130720

Editors:
Tiziana Calamoneri
Department of Computer Science, Sapienza University of Rome, Via Salaria 113, Rome, Italy
,
Josep Diaz
Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega 240, Jordi Girona Salgado 1-3, Barcelona, Spain

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Università di Roma 'La Sapienza': Università di Roma 'La Sapienza'
EATCS: European Association for Theoretical Computer Science

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Berlin, Heidelberg

Publication History

Published: 26 May 2010

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Cited By

Farhan MKoehler HWang Q(2025)Dual-Hierarchy Labelling: Scaling Up Distance Queries on Dynamic Road NetworksProceedings of the ACM on Management of Data10.1145/37096853:1(1-25)Online publication date: 11-Feb-2025
https://dl.acm.org/doi/10.1145/3709685
Storandt SLarson K(2024)Scalable landmark hub labeling for optimal and bounded suboptimal pathfindingProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/750(6788-6795)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/750
Funke SStorandt S(2024)Parameterized Upper Bounds for Path-Consistent Hub LabelingCombinatorial Algorithms10.1007/978-3-031-63021-7_34(446-459)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-63021-7_34
Hamann MStrasser B(2018)Graph Bisection with Pareto OptimizationACM Journal of Experimental Algorithmics10.1145/317304523(1-34)Online publication date: 12-Feb-2018
https://dl.acm.org/doi/10.1145/3173045
Dibbelt JStrasser BWagner D(2016)Customizable Contraction HierarchiesACM Journal of Experimental Algorithmics10.1145/288684321(1-49)Online publication date: 5-Apr-2016
https://dl.acm.org/doi/10.1145/2886843
Bauer RColumbus TRutter IWagner D(2016)Search-space size in contraction hierarchiesTheoretical Computer Science10.1016/j.tcs.2016.07.003645:C(112-127)Online publication date: 13-Sep-2016
https://dl.acm.org/doi/10.1016/j.tcs.2016.07.003
Sommer C(2014)Shortest-path queries in static networksACM Computing Surveys10.1145/253053146:4(1-31)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1145/2530531
Mozes SSommer C(2012)Exact distance oracles for planar graphsProceedings of the twenty-third annual ACM-SIAM symposium on Discrete algorithms10.5555/2095116.2095135(209-222)Online publication date: 17-Jan-2012
https://dl.acm.org/doi/10.5555/2095116.2095135
Geisberger RSanders PSchultes DVetter C(2012)Exact Routing in Large Road Networks Using Contraction HierarchiesTransportation Science10.1287/trsc.1110.040146:3(388-404)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1287/trsc.1110.0401
Milosavljević NWinter SMüller-Hannemann M(2012)On optimal preprocessing for contraction hierarchiesProceedings of the 5th ACM SIGSPATIAL International Workshop on Computational Transportation Science10.1145/2442942.2442949(33-38)Online publication date: 6-Nov-2012
https://dl.acm.org/doi/10.1145/2442942.2442949
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