Abstract
In the design of algorithms for large-scale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient new external-memory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red-blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems, the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them.
Supported in part by the ESPRIT II Basic Research Actions Program of the EC under contract No. 7141 (Project ALCOM II). This work was done while a Visiting Scholar at Duke University.
Supported in part by the U.S. Army Research Office under grant DAAH04-93-G-0076 and by the National Science Foundation under grant DMR-9217290. This work was done while a Visiting Scholar at Duke University.
Supported in part by the National Science Foundation under grant CCR-9007851 and by the U.S. Army Research Office under grants DAAL03-91-G-0035 and DAAH04-93-G-0076.
Acronym for Basic Research in Computer Science, a Center of the Danish National Research Foundation.
Preview
Unable to display preview. Download preview PDF.
References
A. Aggarwal and J. S. Vitter. The input/output complexity of sorting and related problems. Communications of the ACM, 31(9):1116–1127, Sept. 1988.
D. S. Andrews, J. Snoeyink, J. Boritz, T. Chan, G. Denham, J. Harrison, and C. Zhu. Further comparisons of algorithms for geometric intersection problems. In Proc. 6th Int'l. Symp. on Spatial Data Handling, 1994.
ARC/INFO. Understanding GIS—the ARC/INFO method. ARC/INFO, 1993. Rev. 6 for workstations.
L. Arge. The buffer tree: A new technique for optimal I/O-algorithms. In Proc. of 4th Workshop on Algorithms and Data Structures, 1995.
L. Arge, M. Knudsen, and K. Larsen. A general lower bound on the I/O-complexity of comparison-based algorithms. In Proc. of 3rd Workshop on Algorithms and Data Structures, LNCS 709, pages 83–94, 1993.
T. M. Chan. A simple trapezoid sweep algorithm for reporting red/blue segment intersections. In Proc. 6th Can. Conf. Comp. Geom., 1994.
B. Chazelle. Triangulating a simple polygon in linear time. In Proc. IEEE Foundation of Comp. Sci., 1990.
B. Chazelle and H. Edelsbrunner. An optimal algorithm for intersecting line segments in the plane. JACM, 39:1–54, 1992.
B. Chazelle, H. Edelsbrunner, L. J. Guibas, and M. Sharir. Algorithms for bichromatic line-segment problems and polyhedral terrains. Algorithmica, 11:116–132, 1994.
B. Chazelle and L. J. 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. In Proc of 4th Workshop on Algorithms and Data Structures, 1995.
Y.-J. Chiang, M. T. Goodrich, E. F. Grove, R. Tamassia, D. E. Vengroff, and J. S. Vitter. External-memory graph algorithms. In Proc. ACM-SIAM Symp. on Discrete Alg., pages 139–149, Jan. 1995.
R. F. Cromp. An intellegent information fusion system for handling the archiving and querying of terabyte-sized spatial databases. In S. R. Tate ed., Report on the Workshop on Data and Image Compression Needs and Uses in the Scientific Community, CESDIS Technical Report Series, TR-93-99, pages 75–84, 1993.
H. Edelsbrunner and M. H. Overmars. Batched dynamic solutions to decomposable searching problems. Journal of Algorithms, 6:515–542, 1985.
A. Fournier and D. Y. Montuno. Triangulating simple polygons and equivalent problems. ACM Trans. on Graphics, 3(2):153–174, 1984.
M. T. Goodrich, J.-J. Tsay, D. E. Vengroff, and J. S. Vitter. External-memory computational geometry. In Proc. of IEEE Foundations of Comp. Sci., pages 714–723, Nov. 1993.
L. M. Haas and W. F. Cody. Exploiting extensible dbms in integrated geographic information systems. In Proc. of Advances in Spatial Databases, LNCS 525, 1991.
R. Laurini and A. D. Thompson. Fundamentals of Spatial Information Systems. A.P.I.C. Series, Academic Press, New York, NY, 1992.
H. G. Mairson and J. Stolfi. Reporting and counting intersections between two sets of line segments. In R. Earnshaw (ed.), Theoretical Foundation of Computer Graphics and CAD, NATO ASI Series, Vol. F40, pages 307–326, 1988.
M. H. Nodine and J. S. Vitter. Large-scale sorting in parallel memories. In Proc. of 3rd Annual ACM Symp. on Parallel Algorithms and Architectures, pages 29–39, July 1991.
M. H. Nodine and J. S. Vitter. Deterministic distribution sort in shared and distributed memory multiprocessors. In Proc. 5th ACM Symp. on Parallel Algorithms and Architectures, pages 120–129, June–July 1993.
L. Palazzi and J. Snoeyink. Counting and reporting red/blue segment intersections. In Proc. of 3th Workshop on Algorithms and Data Structures, LNCS 709, pages 530–540, 1993.
Y. N. Patt. The I/O subsystem—a candidate for improvement. Guest Editor's Introduction in IEEE Comp., 27(3):15–16, 1994.
C. Ruemmler and J. Wilkes. An introduction to disk drive modeling. IEEE Comp., 27(3): 17–28, Mar. 1994.
H. Samet. Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison Wesley, MA, 1989.
V. K. Vaishnavi and D. Wood. Rectilinear line segment intersection, layered segment trees, and dynamization. Journal of Algorithms, 3:160–176, 1982.
M. J. van Kreveld. Geographic information systems. Technical Report INF/DOC-95-01, Utrecht University, 1995.
J. S. Vitter and E. A. M. Shriver. Algorithms for parallel memory, I: Two-level memories. Algorithmica, 12(2–3):110–147, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arge, L., Vengroff, D.E., Vitter, J.S. (1995). External-memory algorithms for processing line segments in geographic information systems. In: Spirakis, P. (eds) Algorithms — ESA '95. ESA 1995. Lecture Notes in Computer Science, vol 979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60313-1_151
Download citation
DOI: https://doi.org/10.1007/3-540-60313-1_151
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60313-9
Online ISBN: 978-3-540-44913-3
eBook Packages: Springer Book Archive