Abstract
We present an algorithm for external memory planar point location that is both effective and easy to implement. The base algorithm is an external memory variant of the bucket method by Edahiro, Kokubo and Asano that is combined with Lee and Yang’s batched internal memory algorithm for planar point location. Although our algorithm is not optimal in terms of its worst-case behavior, we show its efficiency for both batched and single-shot queries by experiments with real-world data. The experiments show that the algorithm benefits from its mainly sequential disk access pattern and significantly outperforms the fastest algorithm for internal memory.
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U. Adamy and R. Seidel. On the exact worst case query complexity of planar point location. Proc. 9th Annual ACM-SIAM Symp. Discrete Algorithms, 609–618. 1998.
P. Agarwal, L. Arge, G. Brodal, and J. Vitter. I/O-effcient dynamic point location in monotone planar subdivisions. Proc. 10th Annual ACM-SIAM Symp. Discrete Algorithms, 11–20. 1999.
A. Aggarwal and J. Vitter. The input/output complexity of sorting and related problems. Comm. ACM, 31(9):1116–1127, 1988.
L. Arge, R. Barve, O. Procopiuc, L. Toma, D. Vengro., and R. Wickremesinghe. TPIE user manual and reference, edition 0.9.01a. Duke University, North Carolina, <http://www.cs.duke.edu/TPIE/>, 1999. (accessed 12 Jul. 1999).
L. Arge, O. Procopiuc, S. Ramaswamy, T. Suel, J. Vahrenhold, and J. Vitter. A unified approach for indexed and non-indexed spatial join. Proc. 7th Intl. Conf. Extending Databases Technology, LNCS 1777, 413–429. 2000.
L. Arge and J. Vahrenhold. I/O-effcient dynamic planar point location. Proc. 16th Annual ACM Symp. Computational Geometry, 191–200. 2000.
L. Arge, D. Vengro., and J. Vitter. External-memory algorithms for processing line segments in geographic information systems. Proc. 3rd Annual European Symp. Algorithms, LNCS 979, 295–310. 1995.
K. Baumann. Implementation and comparison of five algorithms for point-location in trapezoidal decompositions. Master’s thesis, Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität Münster, Germany, 1996. (in German).
B. Chazelle and L. Guibas. Fractional cascading: I. A data structuring technique. Algorithmica, 1:133–162, 1986.
Y.-J. Chiang. Experiments on the practical I/O efficiency of geometric algorithms: Distribution sweep vs. plane sweep. Computational Geometry: Theory and Applications, 9(4):211–236, March 1998.
A. Crauser, P. Ferragina, K. Mehlhorn, U. Meyer, and E. Ramos. Randomized external-memory algorithms for some geometric problems. Proc. 14th Annual ACM Symp. Computational Geometry, 259-268. 1998.
D. Dobkin and R. Lipton. Multidimensional searching problems. SIAM J. Comput., 5:181–186, 1976.
M. Edahiro, I. Kokubo, and T. Asano. A new point-location algorithm and its practical efficiency: Comparison with existing algorithms. ACM Trans. Graphics, 3(2):86–109, 1984.
H. Edelsbrunner, L. Guibas, and J. Stol.. Optimal point location in a monotone subdivision. SIAM J. Comput., 15(2):317–340, 1986.
W. R. Franklin. Adaptive grids for geometric operations. Proc. 6th Intl. Symp. Automated Cartography (Auto-Carto Six), vol. 2, 230–239. 1983.
M. Goodrich, J.-J. Tsay, D. Vengro., and J. Vitter. External-memory computational geometry. Proc. 34th Annual IEEE Symp. Found. Computer Science, 714–723. 1993.
K. Kim and S. Cha. Sibling clustering of tree-based spatial indexes for efficient spatial query processing. Proc. 1998 ACM CIKM Intl. Conf. Information and Knowledge Management, 398–405. 1998.
D. Kirkpatrick. Optimal search in planar subdivisions. SIAM J. Comput., 12(1):28–35, 1983.
D.-T. Lee and C. Yang. Location of multiple points in a planar subdivision. Inf. Proc. Letters, 9(4):190–193, 1979.
K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, 1994.
D. Musser and A. Saini. STL Tutorial and Reference Guide: C++ Programming with the Standard Template Library. Addison-Wesley, 1996.
F. Preparata and M. Shamos. Computational Geometry: An Introduction. Springer, 2nd edition, 1988.
N. Sarnak and R. Tarjan. Planar point location using persistent search trees. Comm. ACM, 29:669–679, 1986.
J. Snoeyink. Point location. Handbook of Discrete and Computational Geometry, Discrete Mathematics and its Applications, chapter 30, 559–574. CRC Press, 1997.
U.S. Geological Survey. 1:100,000-scale digital line graphs (DLG). http://edcwww.cr.usgs.gov/doc/edchome/ndcdb/ndcdb.html (accessed 26 May 1999).
J. Vahrenhold. External Memory Algorithms for Geographic Information Systems. PhD thesis, Fachbereich Mathematik und Informatik,Westfälische Wilhelms-Universität Münster, Germany, 1999.
D. Vengro. A transparent parallel I/O environment. In Proc. DAGS Symp., 1994.
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Vahrenhold, J., Hinrichs, K.H. (2001). Planar Point Location for Large Data Sets: To Seek or Not to Seek. In: Näher, S., Wagner, D. (eds) Algorithm Engineering. WAE 2000. Lecture Notes in Computer Science, vol 1982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44691-5_16
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DOI: https://doi.org/10.1007/3-540-44691-5_16
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