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Choosing Colors for Geometric Graphs Via Color Space Embeddings

  • Michael B. Dillencourt
  • David Eppstein
  • Michael T. Goodrich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

Abstract

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored: assigning display colors to the graph’s vertices. We study the additional aesthetic criterion of assigning distinct colors to vertices of a geometric graph so that the colors assigned to adjacent vertices are as different from one another as possible. We formulate this as a problem involving perceptual metrics in color space and we develop algorithms for solving this problem by embedding the graph in color space. We also present an application of this work to a distributed load-balancing visualization problem.

Keywords

graph drawing graph coloring color space color perception 

References

  1. 1.
    Alon, N., Erdős, P.: Disjoint edges in geometric graphs. Discrete Comput. Geom. 4, 287–290 (1989)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Bern, M.W., Eppstein, D., Hutchings, B.: Algorithms for coloring quadtrees. Algorithmica 32(1), 87–94 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan, London (1976)Google Scholar
  4. 4.
    Brewer, C.A.: Color use guidelines for data representation. In: Proc. Section on Statistical Graphics, pp. 55–60. American Statistical Association (1999)Google Scholar
  5. 5.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice-Hall, Upper Saddle River (1999)CrossRefzbMATHGoogle Scholar
  6. 6.
    Eppstein, D.: Testing bipartiteness of geometric intersection graphs. In: Proc. 15th Symp. Discrete Algorithms, ACM/SIAM, pp. 853–861. ACM Press, New York (2004)Google Scholar
  7. 7.
    Felsner, S., Hurtado, F., Noy, M., Streinu, I.: Hamiltonicity and colorings of arrangement graphs. In: Proc. 11th Symp. Discrete Algorithms, ACM/SIAM, pp. 155–164. ACM Press, New York (2000)Google Scholar
  8. 8.
    Healey, C.G.: Choosing effective colours for data visualization. In: Yagel, R., Nielson, G.M. (eds.) IEEE Visualization ’96, pp. 263–270. IEEE Computer Society Press, Los Alamitos (1996)Google Scholar
  9. 9.
    Jünger, M., Mutzel, P.: Graph Drawing Software. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  10. 10.
    Kaufmann, M., Wagner, D. (eds.): Drawing Graphs. LNCS, vol. 2025. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  11. 11.
    Lee, P., Kedem, Z.M.: Automatic data and computation decomposition on distributed memory parallel computers. ACM Trans. Programming Languages and Systems 24(1), 1–50 (2002)CrossRefGoogle Scholar
  12. 12.
    Levkowitz, H., Herman, G.T.: Color scales for image data. IEEE Computer Graphics and Applications 12(1), 72–80 (1992)CrossRefGoogle Scholar
  13. 13.
    Nishizeki, T.: Planar Graph Drawing. LNSC, vol. 12. World Scientific, Singapore (2004)zbMATHGoogle Scholar
  14. 14.
    Pan, L., Lai, M.K., Noguchi, K., Huseynov, J.J., Bic, L.F., Dillencourt, M.B.: Distributed parallel computing using Navigational Programming. Int. J. Parallel Programming 32(1), 1–37 (2004)CrossRefzbMATHGoogle Scholar
  15. 15.
    Pan, L., Xue, J., Lai, M.K., Bic, L., Dillencourt, M.B., Bic, L.: Toward automatic data distributions for migrating computations (Submitted for publication, 2006)Google Scholar
  16. 16.
    Rheingans, P., Tebbs, B.: A tool for dynamic explorations of color mappings. Computer Graphics 24(2), 145–146 (1990)CrossRefGoogle Scholar
  17. 17.
    Robertson, P.K.: Visualizing color gamuts: A user interface for the effective use of perceptual color spaces in data displays. IEEE Computer Graphics and Applications 8(5), 50–64 (1988)CrossRefGoogle Scholar
  18. 18.
    Rubner, Y., Puzicha, J., Tomasi, C., Buhmann, J.M.: Empirical evaluation of dissimilarity measures for color and texture. Computer Vision and Image Understanding 84, 25–43 (2001)CrossRefzbMATHGoogle Scholar
  19. 19.
    Stokes, M., Anderson, M., Chandrasekar, S., Motta, R.: A Standard Default Color Space for the Internet – sRGB (1996), Available online at, http://www.w3.org/pub/
  20. 20.
    Stone, M.: A Field Guide to Digital Color, 2nd edn. Morgan Kaufmann, San Francisco (2003)Google Scholar
  21. 21.
    Tufte, E.R.: The Visual Display of Quantative Information. Graphics Press, Cheshire (1983)Google Scholar
  22. 22.
    Tufte, E.R.: Envisioning Information. Graphics Press, Cheshire (1990)Google Scholar
  23. 23.
    Ware, C.: Color sequences for univariate maps: Theory, experiments, and principles. IEEE Computer Graphics and Applications 8(5), 41–49 (1988)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Michael B. Dillencourt
    • 1
  • David Eppstein
    • 1
  • Michael T. Goodrich
    • 1
  1. 1.Dept. of Computer Science, Univ. of California, Irvine, CA 92697-3425USA

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