Abstract
This chapter presents a method that can be used to solve the shortest path problem in large graphs, together with arc cost updates. Our approach uses a contracted graph, which is obtained from the important nodes of the original graph. Every non-important vertex has one or more assigned important nodes as references. A reference node will help us to quickly find the arcs to be updated. The advantage of our method is that we can quickly update the contracted graph, so it can be safely used for future queries. An application of these algorithms can be used by emergency vehicles.
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References
Dijkstra, E.W.: A note on two problems ion connection with graphs. Numer. Math. 1, 269–271 (1959)
Bauer, R., Delling, D., Wagner, D.: Experimental study of speed-up techniques for timetable information systems. J. Netw. 57, 38–52 (2011)
Hart, P.E., Nilsson, N., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4, 100–107 (1968)
Goldberg, A., Harelson, C.: Computing the shortest path: A* search meets graph theory. In: Proceedings of 16th Annual ACM-SIAM Symposium Discrete Algorithms (SODA’05), pp. 156–165 (2005)
Delling, D., Wagner, D.: Landmark-based routing in dynamic graphs. In: Proceedings of 6th Workshop of Experimental Algorithms, Lecture Notes in Computer Science, vol. 4525, pp. 52–65. Springer, June 2007
Möhring, R.H., Schilling, H., Schiltz, B., Wagner, D., Willhalm, T.: Partitioning graphs to speed up Dijkstra’s algorithm. In: Proceedings of 4th Workshop on Experimental Algorithms (WEA’05), Lecture Notes in Computer Science, vol. 3503, pp. 189–202. Springer, 2005
Bauer, R., Delling, D.: SHARC: fast and robust unidirectional routing. In: Proceedings of 10th Workshop of Algorithms and Engineering Experiments (ALENEX’08), SIAM, pp. 13–26 April 2008
Sanders, P., Schultes, D.: Engineering highway hierarchies. In: Proceedings of 14th Annual European Symposium Algorithms (ESA’06), Lecture Notes in Computer Science, vol. 4168, pp. 804–816. Springer, 2006
Geisberger, R., Sanders, P., Schultes, D., Delling, D.: Contraction hierarchies: faster and simpler hierarchical routing in road networks. In: Proceedings of 7th Workshop Experimental Algorithms, pp. 319–333 (2008)
Goldberg, A., Kaplan, H., Werneck, R.F.: Reach for A*: efficient point-to-point shortest path algorithms. In: Proceedings of the 8th Workshop on Algorithms Engineering and Experiments (ALENEX’06), SIAM, pp. 129–143 (2006)
Gutman, R.J.: Reach-based routing: a new approach to shortest path algorithm optimized for road networks. In: Proceedings of 6th Workshop Algorithm Engineering and Experiments (ALENEX’04), SIAM, pp. 100–111 (2004)
Bast, H., Funke, S., Matijevic, S., Sanders, P., Schultes, D.: Intransit to constant time shortest path queries in road networks. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments and the 4th Workshop on Analytic Algorithmics and Combinatorics, pp. 46–59 (2007)
Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast routing in road networks with transit nodes. Science 316, 566 (2007)
Schultes, D., Sanders, P.: Dynamic highway-node routing. In: Proceedings of 6th Workshop on Experimental Algorithms (WEA’07), Lecture Notes in Computer Science, vol. 4525, pp. 66–79. Springer, June 2007
Chlamtac, I., Conti, M., Liu, J.: Mobile ad-hoc networking: imperatives and challenges, pp. 13–64. Ad-Hoc Networks I, Elsevier (2003)
Acknowledgments
This work was supported by the Bilateral Cooperation Research Project between Bulgaria-Romania (2010–2012) entitled “Electronic Health Records for the Next Generation Medical Decision Support in Romanian and Bulgarian National Healthcare Systems”, NextGenElectroMedSupport.
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Cozac, I. (2014). Large Graphs: Fast Cost Update and Query Algorithms. Application for Emergency Vehicles. In: Iantovics, B., Kountchev, R. (eds) Advanced Intelligent Computational Technologies and Decision Support Systems. Studies in Computational Intelligence, vol 486. Springer, Cham. https://doi.org/10.1007/978-3-319-00467-9_19
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DOI: https://doi.org/10.1007/978-3-319-00467-9_19
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