A Time-Space Trade-Off for Triangulations of Points in the Plane

  • Hee-Kap Ahn
  • Nicola Baraldo
  • Eunjin Oh
  • Francesco Silvestri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10392)

Abstract

In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm.

References

  1. 1.
    Agarwal, P.K., Krishnan, S., Mustafa, N.H., Venkatasubramanian, S.: Streaming geometric optimization using graphics hardware. In: Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 544–555. Springer, Heidelberg (2003). doi:10.1007/978-3-540-39658-1_50 CrossRefGoogle Scholar
  2. 2.
    Aronov, B., Korman, M., Pratt, S., van Ressen, A., Roeloffzen, M.: Time-space trade-offs for triangulating a simple polygon. In: Proceedings of the 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016), vol. 53, pp. 30:1–30:12 (2016)Google Scholar
  3. 3.
    Asano, T., Kirkpatrick, D.: Time-space tradeoffs for all-nearest-larger-neighbors problems. In: Dehne, F., Solis-Oba, R., Sack, J.-R. (eds.) WADS 2013. LNCS, vol. 8037, pp. 61–72. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40104-6_6 CrossRefGoogle Scholar
  4. 4.
    Banyassady, B., Korman, M., Mulzer, W., van Renssen, A., Roeloffzen, M., Seiferth, P., Stein, Y.: Improved time-space trade-offs for computing Voronoi diagrams. In: Proceedings of the 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017), vol. 66, pp. 9:1–9:14 (2017)Google Scholar
  5. 5.
    Barba, L., Korman, M., Langerman, S., Sadakane, K., Silveira, R.I.: Space-time trade-offs for stack-based algorithms. Algorithmica 72(4), 1097–1129 (2015)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Borodin, A., Cook, S.: A time-space tradeoff for sorting on a general sequential model of computation. SIAM J. Comput. 11(2), 287–297 (1982)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Chan, T.M., Chen, E.Y.: Multi-pass geometric algorithms. Discret. Comput. Geom. 37(1), 79–102 (2007)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Darwish, O., Elmasry, A.: Optimal time-space tradeoff for the 2D convex-hull problem. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 284–295. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44777-2_24 Google Scholar
  9. 9.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: On graph problems in a semi-streaming model. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 531–543. Springer, Heidelberg (2004). doi:10.1007/978-3-540-27836-8_46 CrossRefGoogle Scholar
  10. 10.
    Feigenbaum, J., Kannan, S., McGregor, A., Suri, S., Zhang, J.: Graph distances in the data-stream model. SIAM J. Comput. 38(5), 1709–1727 (2009)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Frederickson, G.N.: Upper bounds for time-space trade-offs in sorting and selection. J. Comput. Syst. 34(1), 19–26 (1987)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Korman, M., Mulzer, W., Renssen, A., Roeloffzen, M., Seiferth, P., Stein, Y.: Time-space trade-offs for triangulations and Voronoi diagrams. In: Dehne, F., Sack, J.-R., Stege, U. (eds.) WADS 2015. LNCS, vol. 9214, pp. 482–494. Springer, Cham (2015). doi:10.1007/978-3-319-21840-3_40 CrossRefGoogle Scholar
  13. 13.
    Munro, J., Paterson, M.: Selection and sorting with limited storage. Theoret. Comput. Sci. 12(3), 315–323 (1980)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Pagter, J., Rauhe, T.: Optimal time-space trade-offs for sorting. In: Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS 1998), pp. 264–268 (1998)Google Scholar
  15. 15.
    Suri, S., Toth, C.D., Zhou, Y.: Range counting over multidimensional data streams. Discret. Comput. Geom. 36(4), 633–655 (2006)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Nicola Baraldo
    • 2
  • Eunjin Oh
    • 1
  • Francesco Silvestri
    • 2
  1. 1.Pohang University of Science and TechnologyPohangKorea
  2. 2.University of PadovaPadovaItaly

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