Abstract
We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separators for planar graphs, discovered by Lipton and Tarjan [2], in order to divide the graph into smaller subgraphs. For a planar graph with n nodes, the algorithmic variant considered uses O(n(log n)3/ε) preprocessing time and O(n(log n)2/ε) space to answer factor (1 + ε) distance queries in O(n(log n)2/ε) time. By performing experiments on randomly generated planar graphs and on planar graphs derived from real world road networks, we investigate some key characteristics of the oracle, such as preprocessing time, query time, precision, and characteristics related to the underlying data structure, including space consumption. For graphs with one million nodes, the average query time is less than 20μs.
This is a preview of subscription content, log in via an institution to check access.
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
Thorup, M.: Compact Oracles for Reachability and Approximate Distances in Planar Digraphs. Journal of the ACM 51, 993–1024 (2004)
Lipton, R.J., Tarjan, R.E.: A Separator Theorem for Planar Graphs. SIAM Journal on Applied Mathematics 36, 177–189 (1979)
Thorup, M., Zwick, U.: Approximate Distance Oracles. Journal of the ACM 52, 1–24 (2005)
Goldberg, A.V., Harrelson, C.: Computing the Shortest Path: A * Meets Graph Theory. In: Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 156–165. ACM Press, New York (2005)
Gutman, R.: Reach-Based Routing: A New Approach to Shortest Path Algorithms Optimized for Road Networks. In: Proceedings 6th Workshop on Algorithm Engineering and Experiments (ALENEX), pp. 100–111 (2004)
Goldberg, A.V., Kaplan, H., Werneck, R.: Reach for A *: Efficient Point-to-Point Shortest Path Algorithms. In: Workshop on Algorithm Engineering and Experiments (2006)
Sanders, P., Schultes, D.: Highway Hierachies Hasten Exact Shortest Path Queries. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 568–579. Springer, Heidelberg (2005)
Sanders, P., Schultes, D.: Engineering Highway Hierachies. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 804–816. Springer, Heidelberg (2006)
Bast, H., Funke, S., Sanders, P., Schultes, D.: Fast Routing in Road Networks with Transit Nodes. Science 316, 566 (2007)
Bast, H., Funke, S., Matijevic, D., Sanders, P., Schultes, D.: In Transit to Constant Time Shortest-Path Queries in Road Networks. In: Proc. 9th Workshop on Algorithm Engineering and Experimentation (ALENEX) (2007)
Fakcharoenphol, J., Rao, S.: Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time. In: Proceedings of 42nd IEEE Symposium on Foundations of Computer Science, pp. 232–241. IEEE Computer Society Press, Los Alamitos (2001)
Gavoille, C., Peleg, D., Pérennes, S., Raz, R.: Distance Labeling in Graphs. Journal of Algorithms 53, 85–112 (2004)
Klein, P.: Preprocessing an Undirected Planar Network to Enable Fast Approximate Distance Queries. In: Proceedings of the thirteenth annual ACM-SIAM Symposium on Discrete Algorithms, pp. 820–827. ACM Press, New York (2002)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT Press, Cambridge (2001)
Demetrescu, C., Goldberg, A.V., Johnson, D.: 9th DIMACS Implementation Challenge (2006), http://www.dis.uniroma1.it/~challenge9/
GMBH, A.S.S.: LEDA 5.2 (2007), http://www.algorithmic-solutions.com/
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Muller, L.F., Zachariasen, M. (2007). Fast and Compact Oracles for Approximate Distances in Planar Graphs. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_58
Download citation
DOI: https://doi.org/10.1007/978-3-540-75520-3_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75519-7
Online ISBN: 978-3-540-75520-3
eBook Packages: Computer ScienceComputer Science (R0)