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.
- 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.Google Scholar
- Bast, H., Funke, S., Sanders, P., and Schultes, D. 2007. Fast routing in road networks with transit modes. Science 316, 5824, 566.Google ScholarCross Ref
- 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.Google Scholar
- 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.Google Scholar
- Bauer, R. and Delling, D. 2009. SHARC: Fast and robust unidirectional routing. ACM J. Exp. Algorithmics 14, 2.4--2.29. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 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).Google Scholar
- Beier, R., Funke, S., Matijevic, D., and Sanders, P. 2009. Energy-efficient paths in radio networks. Algorithmica.Google Scholar
- Chan, T. M., Efrat, A., and Har-Peled, S. 2001. Fly cheaply: On the minimum fuel consumption problem. J. Algorithms 41, 2, 330--337. Google ScholarDigital Library
- Dantzig, G. B. 1962. Linear Programming and Extensions. Princeton University Press.Google Scholar
- Delling, D. 2008. Time-dependent SHARC-routing. In Proceedings of the 16th Annual European Symposium on Algorithms (ESA'08). Springer, Berlin, 332--343. Google ScholarDigital Library
- Delling, D. 2009. Time-dependent SHARC-routing. Algorithmica.Google Scholar
- 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. Google ScholarDigital Library
- 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).Google Scholar
- 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. Google ScholarDigital Library
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 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.Google Scholar
- Dijkstra, E. W. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1, 269--271.Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 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/.Google Scholar
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- Schieferdecker, D. 2008. Systematic combination of speed-up techniques for exact shortest path queries. M.S. thesis, Universität Karlsruhe (TH), Fakultät für Informatik.Google Scholar
- 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.Google Scholar
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- 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. Google ScholarDigital Library
- Wagner, D., Willhalm, T., and Zaroliagis, C. 2005. Geometric containers for efficient shortest path computation. ACM J. Exp. Algorithmics 10, 1.3. Google ScholarDigital Library
Index Terms
- Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm
Recommendations
Partitioning graphs to speedup Dijkstra's algorithm
We study an acceleration method for point-to-point shortest-path computations in large and sparse directed graphs with given nonnegative arc weights. The acceleration method is called the arc-flag approach and is based on Dijkstra's algorithm. In the ...
Combining hierarchical and goal-directed speed-up techniques for Dijkstra's algorithm
WEA'08: Proceedings of the 7th international conference on Experimental algorithmsIn [1], basic speed-up techniques for Dijkstra's algorithm have been combined. The key observation in their work was that it is most promising to combine hierarchical and goal-directed speed-up techniques. However, since its publication, impressive ...
Combining speed-up techniques for shortest-path computations
In practice, computing a shortest path from one node to another in a directed graph is a very common task. This problem is classically solved by Dijkstra's algorithm. Many techniques are known to speed up this algorithm heuristically, while optimality ...
Comments