Advertisement

Approximation Algorithm for the Largest Area Convex Hull of Same Size Non-overlapping Axis-Aligned Squares

  • Wenqi Ju
  • Jun Luo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6213)

Abstract

Given a set of n equal size and non-overlapping axis-aligned squares, we need to choose exactly one point in each square to make the area of a convex hull of the resulting point set as large as possible. Previous algorithm [10] on this problem gives an optimal algorithm with O(n 3) running time. In this paper, we propose an approximation algorithm which runs in O(nlogn) time and gives a convex hull with area larger than the area of the optimal convex hull minus the area of one square.

Keywords

Convex Hull Imprecise Data Computational Geometry 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akl, S.G., Toussaint, G.T.: Efficient convex hull algorithms for pattern recognition applications. In: Int. Joint Conf. on Pattern Recognition, Kyoto, Japan, pp. 483–487 (1978)Google Scholar
  2. 2.
    Beresford, A.R., Stajano, F.: Location Privacy in pervasive Computing. IEEE Pervasive Computing 2(1) (2003)Google Scholar
  3. 3.
    Bhattacharya, B.K., E. Gindy, H.: A new linear convex hull algorithm for simple polygons. IEEE Trans. Inform. Theory 30, 85–88 (1984)CrossRefzbMATHGoogle Scholar
  4. 4.
    Böhm, C., Kriegel, H.: Determing the convex hull in large multidimensional databases. In: Kambayashi, Y., Winiwarter, W., Arikawa, M. (eds.) DaWaK 2001. LNCS, vol. 2114, pp. 294–306. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Gedik, B., Liu, L.: A customizable k-anonymity model for protecting location privacy. In: ICDCS (2005)Google Scholar
  6. 6.
    Graham, R.L.: An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters 26, 132–133 (1972)CrossRefzbMATHGoogle Scholar
  7. 7.
    Graham, R.L., Yao, F.F.: Finding the convex hull of a simple polygon. J. Algorithms 4, 324–331 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lee, D.T.: On finding the convex huff of a simple polygon. Internat. J. Comput. Inform. Sci. 12, 87–98 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Melkman, A.: On-Line Construction of the Convex Hull of a Simple Polyline. Information Processing Letters 25, 11–12 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Loffler, M., van Kreveld, M.: Largest and Smallest Convex Hulls for Imprecise Points. Algorithmica 56(2), 235–269 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Wenqi Ju
    • 1
    • 2
  • Jun Luo
    • 1
  1. 1.Shenzhen Institutes of Advanced TechnologyChinese Academy of SciencesChina
  2. 2.Institute of Computing TechnologyChinese Academy of SciencesChina

Personalised recommendations