Computing a Minimum-Width Square or Rectangular Annulus with Outliers

[Extended Abstract]
  • Sang Won BaeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


A square or rectangular annulus is the closed region between a square or rectangle and its offset. In this paper, we address the problem of computing a minimum-width square or rectangular annulus that contains at least \(n-k\) points out of n given points in the plane. The k excluded points are considered as outliers of the n input points. We present several first algorithms to the problem.


  1. 1.
    Abellanas, M., Hurtado, F., Icking, C., Ma, L., Palop, B., Ramos, P.: Best fitting rectangles. In: Proceedings of the European Workshop on Computational Geometry (EuroCG 2003) (2003)Google Scholar
  2. 2.
    Aggarwal, A., Imai, H., Katoh, N., Suri, S.: Finding \(k\) points with minimum diameter and related problems. J. Algorithms 12, 38–56 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ahn, H.K., Bae, S.W., Demaine, E.D., Demaine, M.L., Kim, S.S., Korman, M., Reinbacher, I., Son, W.: Covering points by disjoint boxes with outliers. Comput. Geom. Theor. Appl. 44(3), 178–190 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov, R., Bose, P., Couture, M., Maheshwari, A., Morin, P., Paquette, M., Smid, M., Wuhrer, S.: Algorithms for optimal outlier removal. J. Discrete Alg. 7(2), 239–248 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bae, S.W.: Computing a minimum-width square annulus in arbitrary orientation [extended abstract]. In: Proceedings of the 10th International Workshop on Algorithms and Computation (WALCOM 2016), vol. 9627, pp. 131–142 (2016)Google Scholar
  6. 6.
    de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computationsl Geometry: Alogorithms and Applications, 2nd edn. Springer, Heidelberg (2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    Chan, T.M.: Geometric applications of a randomized optimization technique. Discrete Comput. Geom. 22(4), 547–567 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chan, T.M.: Remarks on \(k\)-level algorithms in the plane (1999). ManuscriptGoogle Scholar
  9. 9.
    Dey, T.K.: Improved bounds on planar \(k\)-sets and related problems. Discrete Comput. Geom. 19, 373–382 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Everett, H., Robert, J.M., van Kreveld, M.: An optimal algorithm for computing \((\le k)\)-levels, with applications. Int. J. Comput. Geom. Appl. 6(3), 247–261 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gluchshenko, O.N., Hamacher, H.W., Tamir, A.: An optimal \(O(n \log n)\) algorithm for finding an enclosing planar rectilinear annulus of minimum width. Oper. Res. Lett. 37(3), 168–170 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Hershberger, J.: Finding the upper envelope of \(n\) line segments in \(O(n\log n)\) time. Inform. Proc. Lett. 33, 169–174 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Matoušek, J.: On geometric optimization with few violated constraints. Discrete Comput. Geom. 14, 365–384 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Mukherjee, J., Mahapatra, P., Karmakar, A., Das, S.: Minimum-width rectangular annulus. Theor. Comput. Sci. 508, 74–80 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Segal, M., Kedem, K.: Enclosing \(k\) points in the smallest axis parallel rectangle. Inform. Process. Lett. 65, 95–99 (1998)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceKyonggi UniversitySuwonSouth Korea

Personalised recommendations