An optimal algorithm for one-separation of a set of isothetic polygons

Extended abstract
  • Amitava Datta
  • Kamala Krithivasan
  • Thomas Ottmann
Regular Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1203)


We consider the problem of separating a collection of isothetic polygons in the plane by translating one polygon at a time to infinity. The directions of translation are the four isothetic (parallel to the axes) directions, but a particular polygon can be translated only in one of these four directions. Our algorithm detects whether a set is separable in this sense and computes a translational ordering of the polygons. The time and space complexities of our algorithm is Θ(n log n) and Θ(n) respectively, where n is the total number of edges of the polygons in the set. The best previous algorithm in the plane for this problem had complexities of O(n log2n) time and O(n log n) space.


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  1. [1]
    P. K. Agarwal, M. de Berg, D. Halperin and M. Sharir. ”Efficient generation of k-directional assembly sequences”, Proc. 7th ACM-SIAM Symp. Discrete Algorithms, (1996), pp. 122–131.Google Scholar
  2. [2]
    M. de Berg, H. Everett and H. Wagener. ”Translation queries for sets of polygons”, Internat. J. Comput. Geom. Appl., Vol. 5, (1995), pp. 221–242.Google Scholar
  3. [3]
    B. Chazelle, Th. Ottmann, E. Soisalon-Soininen and D. Wood. ”The complexity and decidability of SEPARATION TM”, Proc. International Colloquium on Automata, Languages and Programming, (1984), LNCS 172, pp. 119–127.Google Scholar
  4. [4]
    F. Dehne and J.-R. Sack. ”Translation separability of sets of polygons”, The Visual Computer, 3, (1987), pp. 227–235.Google Scholar
  5. [5]
    M. Devine and D. Wood. ”SEPARATIONTM in d dimensions or strip mining in asteroid fields”, Comput. and Graphics, Vol. 13, No. 3, (1989), pp. 329–336.Google Scholar
  6. [6]
    L. J. Guibas and F. F. Yao. ”On translating a set of rectangles”, in Advances in Computing Research, Volume I: Computational Geometry, Ed. F. P. Preparata, JAI Press Inc., (1983), pp. 61–77.Google Scholar
  7. [7]
    D. Nussbaum and J.-R. Sack. ”Disassembling two-dimensional composite parts via translation”, International Journal of Computational Geometry & Applications, Vol. 3, No. 1, (1993), pp. 71–84.Google Scholar
  8. [8]
    Th. Ottmann and P. Widmayer, ”On translating a set of line segments”, Computer Vision, Graphics and Image Processing, Vol. 24, (1983), pp. 382–389.Google Scholar
  9. [9]
    F. P. Preparata and M. I. Shamos. Computational Geometry: an Introduction, Springer-Verlag, 1985.Google Scholar
  10. [10]
    J. Reif. ”Complexity of the mover's problem and generalizations”, Proc. 20th IEEE Symposium on Foundations of Computer Science, (1979), pp. 560–570.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Amitava Datta
    • 1
  • Kamala Krithivasan
    • 2
  • Thomas Ottmann
    • 3
  1. 1.Department of Mathematics, Statistics and Computing ScienceUniversity of New EnglandArmidaleAustralia
  2. 2.Department of Computer Science and EngineeringIndian Institute of TechnologyMadrasIndia
  3. 3.Institut für InformatikUniversität FreiburgFreiburgGermany

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