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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, H., Buchin, M.: Semi-computability of the fréchet distance between surfaces. In: EuroCG, pp. 45–48 (2005)
Alt, H., Efrat, A., Rote, G., Wenk, C.: Matching planar maps. In: SODA, pp. 589–598 (2003)
Alt, H., Godau, M.: Computing the fréchet distance between two polygonal curves. Int. J. Comput. Geometry Appl. 5, 75–91 (1995)
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)
Buchin, K., Buchin, M., Wenk, C.: Computing the fréchet distance between simple polygons. Comput. Geom. Theory Appl. 41(1-2), 2–20 (2008)
Cole, R.: Slowing down sorting networks to obtain faster sorting algorithms. J. ACM 34(1), 200–208 (1987)
Eiter, T., Mannila, H.: Computing discrete fréchet distance. Technical report, Technische Universitat Wien (1994)
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)
Megiddo, N.: Applying parallel computation algorithms in the design of serial algorithms. J. ACM 30(4), 852–865 (1983)
Rote, G.: Computing the fréchet distance between piecewise smooth curves. Comput. Geom. Theory Appl. 37(3), 162–174 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fan, C., Luo, J., Zhu, B. (2011). Fréchet-Distance on Road Networks. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-24983-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24982-2
Online ISBN: 978-3-642-24983-9
eBook Packages: Computer ScienceComputer Science (R0)