Fréchet-Distance on Road Networks

  • Chenglin Fan
  • Jun Luo
  • Binhai Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)

Abstract

As a measure for the resemblance of tracks in a network graph, we consider the so-called Fréechet-distance based on network distance. For paths P and Q consisting of p and q consecutive edges, an O((p 2 + q 2)logpq) time algorithm measuring the Fréechet-distance between P and Q is developed. Then some important variants are investigated, namely weak Fréechet distance, discrete Fréechet distance , all based on the network distance.

Keywords

Road Network Network Graph Simple Polygon Network Distance Monotone Path 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alt, H., Buchin, M.: Semi-computability of the fréchet distance between surfaces. In: EuroCG, pp. 45–48 (2005)Google Scholar
  2. 2.
    Alt, H., Efrat, A., Rote, G., Wenk, C.: Matching planar maps. In: SODA, pp. 589–598 (2003)Google Scholar
  3. 3.
    Alt, H., Godau, M.: Computing the fréchet distance between two polygonal curves. Int. J. Comput. Geometry Appl. 5, 75–91 (1995)CrossRefMATHGoogle Scholar
  4. 4.
    Brakatsoulas, S., Pfoser, D., Salas, R., Wenk, C.: On map-matching vehicle tracking data. In: VLDB 2005: Proceedings of the 31st International Conference on Very Large Data Bases, pp. 853–864. VLDB Endowment (2005)Google Scholar
  5. 5.
    Buchin, K., Buchin, M., Wenk, C.: Computing the fréchet distance between simple polygons. Comput. Geom. Theory Appl. 41(1-2), 2–20 (2008)CrossRefMATHGoogle Scholar
  6. 6.
    Cole, R.: Slowing down sorting networks to obtain faster sorting algorithms. J. ACM 34(1), 200–208 (1987)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Eiter, T., Mannila, H.: Computing discrete fréchet distance. Technical report, Technische Universitat Wien (1994)Google Scholar
  8. 8.
    Klein, P., Rao, S., Rauch, M., Subramanian, S.: Faster shortest-path algorithms for planar graphs. In: STOC 1994: Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 27–37. ACM, New York (1994)CrossRefGoogle Scholar
  9. 9.
    Megiddo, N.: Applying parallel computation algorithms in the design of serial algorithms. J. ACM 30(4), 852–865 (1983)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Rote, G.: Computing the fréchet distance between piecewise smooth curves. Comput. Geom. Theory Appl. 37(3), 162–174 (2007)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Chenglin Fan
    • 1
    • 2
  • Jun Luo
    • 1
  • Binhai Zhu
    • 3
  1. 1.Shenzhen Institutes of Advanced TechnologyChinese Academy of SciencesShenzhenChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina
  3. 3.Department of Computer ScienceMontana State UniversityBozemanUSA

Personalised recommendations