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Geometric Speed-Up Techniques for Finding Shortest Paths in Large Sparse Graphs

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Algorithms - ESA 2003 (ESA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2832))

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Abstract

In this paper, we consider Dijkstra’s algorithm for the single source single target shortest paths problem in large sparse graphs. The goal is to reduce the response time for online queries by using precomputed information. For the result of the preprocessing, we admit at most linear space. We assume that a layout of the graph is given. From this layout, in the preprocessing, we determine for each edge a geometric object containing all nodes that can be reached on a shortest path starting with that edge. Based on these geometric objects, the search space for online computation can be reduced significantly. We present an extensive experimental study comparing the impact of different types of objects. The test data we use are traffic networks, the typical field of application for this scenario.

This work was partially supported by the Human Potential Programme of the European Union under contract no. HPRN-CT-1999-00104 (AMORE) and and by the DFG under grant WA 654/12-1.

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References

  1. Schulz, F., Wagner, D., Weihe, K.: Dijkstra’s algorithm on-line: An empirical case study from public railroad transport. Journal of Experimental Algorithmics 5 (2000)

    Google Scholar 

  2. Schulz, F., Wagner, D., Zaroliagis, C.: Using multi-level graphs for timetable information. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, pp. 43–59. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM (JACM) 34, 596–615 (1987)

    Article  MathSciNet  Google Scholar 

  5. Thorup, M.: Undirected single source shortest path in linear time. In: IEEE Symposium on Foundations of Computer Science, pp. 12–21 (1997)

    Google Scholar 

  6. Meyer, U.: Single-source shortest-paths on arbitrary directed graphs in linear average-case time. In: Symposium on Discrete Algorithms, pp. 797–806 (2001)

    Google Scholar 

  7. Goldberg, A.V.: A simple shortest path algorithm with linear average time. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 230–241. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Pettie, S., Ramachandran, V., Sridhar, S.: Experimental evaluation of a new shortest path algorithm. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, pp. 126–142. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Zahn, F.B., Noon, C.E.: Shortest path algorithms: An evaluation using real road networks. Transportation Science 32, 65–73 (1998)

    Article  Google Scholar 

  10. Zahn, F.B., Noon, C.E.: A comparison between label-setting and label-correcting algorithms for computing one-to-one shortest paths. Journal of Geographic Information and Decision Analysis 4 (2000)

    Google Scholar 

  11. Barrett, C., Bisset, K., Jacob, R., Konjevod, G., Marathe, M.: Classical and contemporary shortest path problems in road networks: Implementation and experimental analysis of the transims router. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 126–138. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Siklóssy, L., Tulp, E.: Trains, an active time-table searcher. In: Proc. 8th European Conf. Artificial Intelligence, pp. 170–175 (1988)

    Google Scholar 

  13. Nachtigall, K.: Time depending shortest-path problems with applications to railway networks. European Journal of Operational Research 83, 154–166 (1995)

    Article  MATH  Google Scholar 

  14. Müller-Hannemann, M., Weihe, K.: Pareto shortest paths is often feasible in practice. In: Brodal, G.S., Frigioni, D., Marchetti-Spaccamela, A. (eds.) WAE 2001. LNCS, vol. 2141, pp. 185–197. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Preuss, T., Syrbe, J.H.: An integrated traffic information system. In: Proc. 6th Int. Conf. Appl. Computer Networking in Architecture, Construction, Design, Civil Eng., and Urban Planning (europIA 1997) (1997)

    Google Scholar 

  16. Johnson, D.B.: Efficient algorithms for shortest paths in sparse networks. Journal of the ACM (JACM) 24, 1–13 (1977)

    Article  MATH  Google Scholar 

  17. Fabri, A., Giezeman, G.J., Kettner, L., Schirra, S., Schönherr, S.: On the design of CGAL a computational geometry algorithms library. Softw. – Pract. Exp. 30, 1167–1202 (2000)

    Article  MATH  Google Scholar 

  18. Welzl, E.: Smallest enclosing disks (balls and ellipsoids). In: Maurer, H.A. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  19. Toussaint, G.: Solving geometric problems with the rotating calipers. In: Protonotarios, E.N. (ed.) MELECON 1983, NY. IEEE, Los Alamitos (1983); A10.02/1–4

    Google Scholar 

  20. Schwarz, C., Teich, J., Vainshtein, A., Welzl, E., Evans, B.L.: Minimal enclosing parallelogram with application. In: Proceedings of the eleventh annual symposium on Computational geometry, pp. 434–435. ACM Press, New York (1995)

    Chapter  Google Scholar 

  21. Mehlhorn, K., Näher, S.: LEDA, A platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  22. Brandes, U., Eiglsperger, M., Herman, I., Himsolt, M., Scott, M.: GraphML progress report. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 501–512. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  23. Sedgewick, R., Vitter, J.S.: Shortest paths in euclidean space. Algorithmica 1, 31–48 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  24. Shekhar, S., Kohli, A., Coyle, M.: Path computation algorithms for advanced traveler information system (atis). In: Proc. 9th IEEE Intl. Conf. Data Eng., pp. 31–39 (1993)

    Google Scholar 

  25. Jacob, R., Marathe, M., Nagel, K.: A computational study of routing algorithms for realistic transportation networks. In: Mehlhorn, K., ed.: In: WAE 1998 (1998)

    Google Scholar 

  26. Pohl, I.: Bi-directional search. In: Meltzer, B., Michie, D. (eds.) Sixth Annual Machine Intelligence Workshop. Machine Intelligence, vol. 6, pp. 137–140. Edinburgh University Press, Edinburgh (1971)

    Google Scholar 

  27. Jung, S., Pramanik, S.: Hiti graph model of topographical road maps in navigation systems. In: Proc. 12th IEEE Int. Conf. Data Eng., pp. 76–84 (1996)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Logik, Universität Karlsruhe, Komplexität und Deduktionssysteme, D-76128, Karlsruhe

    Dorothea Wagner & Thomas Willhalm

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  1. Dorothea Wagner
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  2. Thomas Willhalm
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Editors and Affiliations

  1. Dipartimento di Informatica e Automazione, Università degli Studi “Roma Tre”, via della Vasca Navale 79, 00146, Rome, Italy

    Giuseppe Di Battista

  2. School of Computer Science, Tel Aviv University, 69978, Tel Aviv, Israel

    Uri Zwick

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Wagner, D., Willhalm, T. (2003). Geometric Speed-Up Techniques for Finding Shortest Paths in Large Sparse Graphs. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_69

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  • DOI: https://doi.org/10.1007/978-3-540-39658-1_69

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20064-2

  • Online ISBN: 978-3-540-39658-1

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