Abstract
With the recent development of a rich variety of parallel computer architectures, much attention has been paid to the study of parallel computational geometry. In this paper we put the focus on systolic computational geometry algorithms among those algorithms being developed rapidly in recent years for the various kinds of parallel processors. Our paper gives a survey of recent studies on systolic computational geometry algorithms We show that most of the fundamental geometrical problems can be solved in linear-time by conventional one-dimensional systolic arrays proposed by Kung et al. This paper also includes many new results and some open problems for which we have no linear-time systolic algorithms.
Zusammenfassung
Die neueren Entwicklungen, die zu parallelen Rechnerarchitekturen führen, haben die Aufmerksamkeit auf das Gebiet der parallelen “Computational Geometry” gelenkt. In diesem Artikel wird das Hauptaugenmerk auf systolische Algorithmen für diesen Themenkreis gerichtet. Es wird ein Überblick über derartige Algorithmen gegeben. Es zeigt sich, daß die meisten grundlegenden geometrischen Probleme mit eindimensionalen systolischen Arrays, wie sie von Kung et al. eingeführt wurden, in Linearzeit gelöst werden können. Eine Reihe neuer Ergebnisse wird vorgestellt, und offene Probleme werden angesprochen.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Preparata, F. P., Shamos, M. I.: Computational geometry, an introduction, p. 390. New York: Springer-Verlag 1985.
Lee, D. T., Preparata, F. P.: Computational geometry — a survey. IEEE Trans. on Computers. Vol. C-33, No. 12, pp. 1072–1101 (1984).
Leiserson, C. E.: Systolic priority queues. Proc. of the Caltech Conf. on VLSI (Deitz, C. E., ed.), pp. 199–214 (1979).
Kung, H. T.: Let's design algorithms for VLSI systems. Proc. of the Caltech Conf. on VLSI (Deitz, C. E., ed.), pp. 55–90 (1979).
Kung, H. T., Leiserson, C. E.: Algorithms for VLSI processor arrays, in Chapter 8 of Mead, C. A. and Coway, L. A. Introduction to VLSI Systems. Reading, Massachusetts: Addison-Wesley 1980.
Savage, C.: A systolic data structure chip for connectivity problems, in VLSI systems and computations (Kung, H. T., Sproull, R. F., Steele, G. L., Jr., eds.), pp. 269–300 (1981).
Chazelle, B.: Computational geometry on a systolic chip. IEEE Trans. on Computers, Vol. C-33, No. 9, pp. 774–785 (1984).
Kane, R., Sahni, S.: A systolic design rule checker. Proc. of the IEEE 21 st Design Automation Conf., pp. 243–250 (1984).
Kane, R., Sahni, S.: Hardware algorithm for net extraction. Proc. of the IEEE ISCAS85, pp. 51–54 (1985).
Kane, R., Sahni, S.: Systolic algorithms for rectilinear polygons. Proc. of the IEEE Intern. Conf. on Computer Design: VLSI in Computers ICCD'84, pp. 831–836 (1984).
Asano, T., Umeo, H.: Systolic algorithms for computing the visivility polygon and triangulation of a polygonal region. Parallel Computing6, 209–216 (1988).
Shih, Z. C., Chen, G. H., Lee, R. C. T.: Systolic algorithms to examine all pairs of elements. Commun. ACM, Vol. 30, No. 2, pp. 161–167 (1987).
IEEE Computer: Special issue on Systolic Arrays (Fortes, J. A. B., Wah, B. W., eds.) Vol. 20, No. 7 (1987).
Lodi, E., Pagli, L: A VLSI algorithm for a visibility problem, in VLSI: Algorithms and Architectures (Bertolazzi, P., Luccio, F., eds.), pp. 125–134. North-Holland: Elsevier Science Publisher, B. V., 1985.
Tarjan, R. E., Van Wyk, C. J.: AnO(nloglogn)-time algorithm for triangulating a simple polygon. SIAM J. on Computing 17, 1 (1988), to appear.
Yap, C. K.: What can be paralleilized in computational geometry? Parallel Algorithms and Architectures (Albrecht, A., Jung, H., Mehlhorn, K. eds.), pp. 184–195. Berlin: Akademie-Verlag (1987).
Toussaint, G. T.: Pattern recognition and geometrical complexity. Proc. of the 5th Intern. Conf. on Pattern Recognition, pp. 1324–1347 (1980).
Miller, R., Stout, Q. F.: Mesh computer algorithms for computational geometry. Tech. Rep. of State University of New York, 86-18, p. 44 (1986).
Dyer, C. R.: Parallel image processing by memory augmented cellular automata. IEEE Trans. on PAMI, Vol. PAMI-3, pp. 29–41 (1981).
Miller, R., Stout, Q. F.: Pyramid computer algorithms for determining geometric properties of images. Proc. of the Symp. on Computational Geometry, pp. 263–271 (1985).
Perez, A., Abidi, M. A., Bouldin, D. W.: The use of a VLSI sorter coprocessor to find the convex hull. Proc. of Comp Euro 87, pp. 66–69 (1987).
Lu, M., Varman, P.: Solving geometric problems on a two-dimensional systolic array. Proc. of Comp Euro 87, pp. 699–702 (1987).
Dehne, F.: Computational geometry and VLSI. Proc. of Comp Euro 87, pp. 870–875 (1987).
Lu, M.: Constructing the Voronoi diagram on a mesh-connected computer. Proc. of the 1986 Intern. Conf. on Parallel Processing, pp. 806–811 (1986).
Sato, M., Tachibana, M., Torii, S., Ohotsuki, T.: An algorithm for partitioning a set of points on the plane by a rectilinear region. Trans. IECE of Japan, Vol. L 66-D No. 2, pp. 214–219 (1983).
Asano, T.: Geometric searching algorithms and their applications. Proc. of the Mathematical Programming Symposium, pp. 205–220 (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Umeo, H., Asano, T. Systolic algorithms for computational geometry problems — A survey. Computing 41, 19–40 (1989). https://doi.org/10.1007/BF02238727
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02238727