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Fast Exact Computation of Isochrones in Road Networks

  • Moritz Baum
  • Valentin Buchhold
  • Julian Dibbelt
  • Dorothea Wagner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9685)

Abstract

We study the problem of computing isochrones in static and dynamic road networks, where the objective is to identify the boundary of the region in range from a given source within a certain amount of time. While there is a wide range of practical applications for this problem (e. g., urban planning, geomarketing, visualizing the cruising range of a vehicle), there has been little research on fast algorithms for large, realistic inputs, and existing approaches tend to compute more information than necessary. Our contribution is twofold: (1) We propose a more compact but sufficient definition of isochrones, based on which, (2) we provide several easy-to-parallelize, scalable algorithmic approaches for faster computation. By extensive experimental analysis, we demonstrate that our techniques enable fast isochrone computation within milliseconds even on continental networks, significantly faster than the state-of-the-art.

Keywords

Query Time Linear Sweep Internal Vertex Boundary Vertex Incoming Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abraham, I., Delling, D., Fiat, A., Goldberg, A.V., Werneck, R.F.: HLDB: location-based services in databases. In: Proceedings of the 20th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems (GIS 2012), pp. 339–348. ACM Press, New York (2012)Google Scholar
  2. 2.
    Bast, H., Delling, D., Goldberg, A.V., Müller-Hannemann, M., Pajor, T., Sanders, P., Wagner, D., Werneck, R.F.: Route Planning in Transportation Networks. Technical report abs/1504.05140, ArXiv e-prints (2015)Google Scholar
  3. 3.
    Bauer, V., Gamper, J., Loperfido, R., Profanter, S., Putzer, S., Timko, I.: Computing isochrones in multi-modal, schedule-based transport networks. In: Proceedings of the 16th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (GIS 2008), pp. 78:1–78:2. ACM Press, New York (2008)Google Scholar
  4. 4.
    Baum, M., Bläsius, T., Gemsa, A., Rutter, I., Wegner, F.: Scalable Isocontour Visualization in Road Networks via Minimum-Link Paths. Technical report abs/1602.01777, ArXiv e-prints (2016)Google Scholar
  5. 5.
    Delling, D., Goldberg, A.V., Nowatzyk, A., Werneck, R.F.: PHAST: hardware-accelerated shortest path trees. J. Parallel Distrib. Comput. 73(7), 940–952 (2013)CrossRefGoogle Scholar
  6. 6.
    Delling, D., Goldberg, A.V., Pajor, T., Werneck, R.F.: Customizable route planning. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 376–387. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Delling, D., Goldberg, A.V., Pajor, T., Werneck, R.F.: Customizable route planning in road networks. Transportation Science (2015)Google Scholar
  8. 8.
    Delling, D., Goldberg, A.V., Razenshteyn, I., Werneck, R.F.: Graph partitioning with natural cuts. In: Proceedings of the 25th International Parallel and Distributed Processing Symposium (IPDPS 2011), pp. 1135–1146. IEEE Computer Society (2011)Google Scholar
  9. 9.
    Delling, D., Goldberg, A.V., Werneck, R.F.: Faster batched shortest paths inroad networks. In: Proceedings of the 11th Workshop on Algorithmic Approachesfor Transportation Modeling, Optimization, and Systems (ATMOS 2011). OpenAccessSeries in Informatics, vol. 20, pp. 52–63. OASIcs (2011)Google Scholar
  10. 10.
    Delling, D., Holzer, M., Müller, K., Schulz, F., Wagner, D.: High-performance multi-level routing. In: The Shortest Path Problem: Ninth DIMACS Implementation Challenge, DIMACS Book, vol. 74, pp. 73–92. American Mathematical Society (2009)Google Scholar
  11. 11.
    Delling, D., Werneck, R.F.: Faster customization of road networks. In: Bonifaci, V., Demetrescu, C., Marchetti-Spaccamela, A. (eds.) SEA 2013. LNCS, vol. 7933, pp. 30–42. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Delling, D., Werneck, R.F.: Customizable point-of-interest queries in road networks. IEEE Trans. Knowl. Data Eng. 27(3), 686–698 (2015)CrossRefGoogle Scholar
  13. 13.
    Demetrescu, C., Goldberg, A.V., Johnson, D.S. (eds.): The Shortest Path Problem: Ninth DIMACS Implementation Challenge, DIMACS Book, vol. 74. American Mathematical Society (2009)Google Scholar
  14. 14.
    Dibbelt, J., Strasser, B., Wagner, D.: Customizable contraction hierarchies. In: Gudmundsson, J., Katajainen, J. (eds.) SEA 2014. LNCS, vol. 8504, pp. 271–282. Springer, Heidelberg (2014)Google Scholar
  15. 15.
    Dibbelt, J., Strasser, B., Wagner, D.: Customizable contraction hierarchies. ACM J. Exp. Algorithmics 21(1), 108–122 (2016)Google Scholar
  16. 16.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Efentakis, A., Grivas, N., Lamprianidis, G., Magenschab, G., Pfoser, D.: Isochrones, traffic and DEMOgraphics. In: Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (GIS 2013), pp. 548–551. ACM Press, New York (2013)Google Scholar
  18. 18.
    Efentakis, A., Pfoser, D.: GRASP. Extending graph separators for the single-source shortest-path problem. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 358–370. Springer, Heidelberg (2014)Google Scholar
  19. 19.
    Efentakis, A., Pfoser, D., Vassiliou, Y.: SALT. A unified framework for all shortest-path query variants on road networks. In: Bampis, E. (ed.) SEA 2015. LNCS, vol. 9125, pp. 298–311. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  20. 20.
    Efentakis, A., Theodorakis, D., Pfoser, D.: Crowdsourcing computing resources for shortest-path computation. In: Proceedings of the 20th ACM SIGSPATIAL International Symposium on Advances in Geographic Information Systems (GIS 2012), pp. 434–437. ACM Press, New York (2012)Google Scholar
  21. 21.
    Erwig, M.: The graph voronoi diagram with applications. Networks 36(3), 156–163 (2000)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Foti, F., Waddell, P., Luxen, D.: A generalized computational framework for accessibility: from the pedestrian to the metropolitan scale. In: Proceedings of the 4th TRB Conference on Innovations in Travel Modeling. Transportation Research Board (2012)Google Scholar
  23. 23.
    Gamper, J., Böhlen, M., Cometti, W., Innerebner, M.: Defining isochrones in multimodal spatial networks. In: Proceedings of the 20th ACM International Conference on Information and Knowledge Management (CIKM 2011), pp. 2381–2384. ACM Press, New York (2011)Google Scholar
  24. 24.
    Gamper, J., Böhlen, M., Innerebner, M.: Scalable computation of isochrones with network expiration. In: Ailamaki, A., Bowers, S. (eds.) SSDBM 2012. LNCS, vol. 7338, pp. 526–543. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  25. 25.
    Geisberger, R.: Advanced Route Planning in Transportation Networks. Ph.D. thesis, Karlsruhe Institute of Technology (2011)Google Scholar
  26. 26.
    Geisberger, R., Luxen, D., Sanders, P., Neubauer, S., Volker, L.: Fast detour computation for ride sharing. In: Proceedings of the 10th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS 2010). OpenAccess Series in Informatics, vol. 14, pp. 88–99. OASIcs (2010)Google Scholar
  27. 27.
    Geisberger, R., Sanders, P., Schultes, D., Vetter, C.: Exact routing in large road networks using contraction hierarchies. Transp. Sci. 46(3), 388–404 (2012)CrossRefGoogle Scholar
  28. 28.
    Grubwinkler, S., Brunner, T., Lienkamp, M.: Range prediction for EVs via crowd-sourcing. In: Proceedings of the 10th IEEE International Vehicle Power and Propulsion Conference (VPPC 2014), pp. 1–6. IEEE (2014)Google Scholar
  29. 29.
    Holzer, M., Schulz, F., Wagner, D.: Engineering multilevel overlay graphs for shortest-path queries. ACM J. Exp. Algorithmics 13, 1–26 (2008)MathSciNetMATHGoogle Scholar
  30. 30.
    Innerebner, M., Böhlen, M., Gamper, J.: ISOGA: a system for geographical reachability analysis. In: Liang, S.H.L., Wang, X., Claramunt, C. (eds.) W2GIS 2013. LNCS, vol. 7820, pp. 180–189. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  31. 31.
    Jung, S., Pramanik, S.: An efficient path computation model for hierarchically structured topographical road maps. IEEE Trans. Knowl. Data Eng. 14(5), 1029–1046 (2002)CrossRefGoogle Scholar
  32. 32.
    Knopp, S., Sanders, P., Schultes, D., Schulz, F., Wagner, D.: Computing many-to-many shortest paths using highway hierarchies. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments (ALENEX 2007), pp. 36–45. SIAM (2007)Google Scholar
  33. 33.
    Marciuska, S., Gamper, J.: Determining objects within isochrones in spatial network databases. In: Catania, B., Ivanović, M., Thalheim, B. (eds.) ADBIS 2010. LNCS, vol. 6295, pp. 392–405. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  34. 34.
    Okabe, A., Satoh, T., Furuta, T., Suzuki, A., Okano, K.: Generalized network voronoi diagrams: concepts, computational methods, and applications. Int. J. Geogr. Inf. Sci. 22(9), 965–994 (2008)CrossRefGoogle Scholar
  35. 35.
    O’Sullivan, D., Morrison, A., Shearer, J.: Using desktop GIS for the investigation of accessibility by public transport: an isochrone approach. Int. J. Geogr. Inf. Sci. 14(1), 85–104 (2000)CrossRefGoogle Scholar
  36. 36.
    Pothen, A., Simon, H.D., Liou, K.P.: Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11, 430–452 (1990)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Sanders, P., Schulz, C.: Distributed evolutionary graph partitioning. In: Proceedings of the 14th Meeting on Algorithm Engineering and Experiments (ALENEX 2012), pp. 16–29. SIAM (2012)Google Scholar
  38. 38.
    Schulz, C.: High Quality Graph Partitioning. Ph.D. thesis, Karlsruhe Institute of Technology (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Moritz Baum
    • 1
  • Valentin Buchhold
    • 1
  • Julian Dibbelt
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany

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