Graph Drawing in the Cloud: Privately Visualizing Relational Data Using Small Working Storage

  • Michael T. Goodrich
  • Olga Ohrimenko
  • Roberto Tamassia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


We study graph drawing in a cloud-computing context where data is stored externally and processed using a small local working storage. We show that a number of classic graph drawing algorithms can be efficiently implemented in such a framework where the client can maintain privacy while constructing a drawing of her graph.


Span Tree Internal Node Access Pattern Output Stream Graph Drawing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Babcock, B., Babu, S., Datar, M., Motwani, R., Widom, J.: Models and issues in data stream systems. In: Proc. Symp. on Principles of Database Systems, pp. 1–16 (2002)Google Scholar
  2. 2.
    Barghouti, N., Mocenigo, J., Lee, W.: Grappa: A GRAPh PAckage in Java. In: Di Battista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 336–343. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Bertolazzi, P., Cohen, R.F., Di Battista, G., Tamassia, R., Tollis, I.G.: How to draw a series-parallel digraph. Internat. J. Comput. Geom. Appl. 4, 385–402 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Binucci, C., Brandes, U., Di Battista, G., Didimo, W., Gaertler, M., Palladino, P., Patrignani, M., Symvonis, A., Zweig, K.: Drawing Trees in a Streaming Model. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 292–303. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Bridgeman, S., Garg, A., Tamassia, R.: A graph drawing and translation service on the World Wide Web. Int. J. Comp. Geom. Appl. 9(4-5), 419–446 (1999)CrossRefGoogle Scholar
  6. 6.
    Cohen, R.F., Di Battista, G., Tamassia, R., Tollis, I.G.: Dynamic graph drawings: Trees, series-parallel digraphs, and planar ST-digraphs. SIAM J. Comput. 24(5), 970–1001 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River (1999)zbMATHGoogle Scholar
  8. 8.
    Di Battista, G., Tamassia, R., Tollis, I.G.: Area requirement and symmetry display of planar upward drawings. Discrete Comput. Geom. 7(4), 381–401 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Eppstein, D., Goodrich, M.T., Tamassia, R.: Privacy-preserving data-oblivious geometric algorithms for geographic data. In: 18th ACM Adv. in Geographic Information Systems, ACM GIS, pp. 13–22 (2010),
  10. 10.
    Feldman, J., Muthukrishnan, S., Sidiropoulos, A., Stein, C., Svitkina, Z.: On distributing symmetric streaming computations. ACM Trans. Algorithms 6(4), 66:1–66:19 (2010), Google Scholar
  11. 11.
    de Fraysseix, H., Pach, J., Pollack, R.: How to draw a planar graph on a grid. Combinatorica 10(1), 41–51 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Goldreich, O.: Foundations of Cryptography, vol. II. Cambridge University Press (2004)Google Scholar
  13. 13.
    Goodrich, M.T.: Randomized Shellsort: A simple oblivious sorting algorithm. In: Symposium on Discrete Algorithms, SODA, pp. 1–16 (2010)Google Scholar
  14. 14.
    Goodrich, M.T., Mitzenmacher, M.: Privacy-Preserving Access of Outsourced Data via Oblivious RAM Simulation. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 576–587. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Oblivious RAM simulation with efficient worst-case access overhead. In: Proc. ACM Workshop on Cloud Computing Security, CCSW, pp. 95–100 (2011)Google Scholar
  16. 16.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Practical oblivious storage. In: Proc. ACM Conference on Data and Application Security and Privacy, CODASPY (2012)Google Scholar
  17. 17.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Privacy-preserving group data access via stateless oblivious RAM simulation. In: Proc. ACM-SIAM Symp. on Discrete Algorithms, SODA (2012)Google Scholar
  18. 18.
    Goodrich, M.T., Ohrimenko, O., Tamassia, R.: Data-oblivious graph drawing model and algorithms. CoRR abs/1209.0756 (2012)Google Scholar
  19. 19.
    Henzinger, M.R., Raghavan, P., Rajagopalan, S.: Computing on data streams. In: External Memory Algorithms. Discrete Mathematics and Theoretical Computer Science, vol. 50, pp. 107–118. AMS (1999)Google Scholar
  20. 20.
    Johnson, B., Shneiderman, B.: Tree-maps: A space-filling approach to the visualization of hierarchical information structures. In: IEEE Visualization, pp. 284–291 (1991)Google Scholar
  21. 21.
    Muthukrishnan, S.: Data Streams: Algorithms and Applications. In: Foundations and Trends in Theoretical Computer Science, vol. 1. Now Publishers (2005)Google Scholar
  22. 22.
    Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. Journal of Computer and System Sciences 26(3), 362–381 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Tamassia, R., Tollis, I.G.: A unified approach to visibility representations of planar graphs. Discrete Comput. Geom. 1(4), 321–341 (1986)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael T. Goodrich
    • 1
  • Olga Ohrimenko
    • 2
  • Roberto Tamassia
    • 2
  1. 1.Dept. Computer ScienceUniv. of CaliforniaIrvineUSA
  2. 2.Dept. Computer ScienceBrown UniversityUSA

Personalised recommendations