MapSets: Visualizing Embedded and Clustered Graphs

  • Alon Efrat
  • Yifan Hu
  • Stephen G. Kobourov
  • Sergey Pupyrev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)


We describe MapSets, a method for visualizing embedded and clustered graphs. The proposed method relies on a theoretically sound geometric algorithm, which guarantees the contiguity and disjointness of the regions representing the clusters, and also optimizes the convexity of the regions. A fully functional implementation is available online and is used in a comparison with related earlier methods.


Span Tree Minimum Span Tree Steiner Tree Contiguous Region Euler Diagram 
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.
    Agarwal, P.K., Edelsbrunner, H., Schwarzkopf, O., Welzl, E.: Euclidean minimum spanning trees and bichromatic closest pairs. Discrete & Comput. Geom. 6(1), 407–422 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Alper, B., Riche, N.H., Ramos, G., Czerwinski, M.: Design study of LineSets, a novel set visualization technique. IEEE Trans. Vis. Comput. Graphics 17(12), 2259–2267 (2011)CrossRefGoogle Scholar
  3. 3.
    Arora, S., Chang, K.: Approximation schemes for degree-restricted MST and red–blue separation problems. Algorithmica 40(3), 189–210 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Boyack, K.W., Klavans, R., Börner, K.: Mapping the backbone of science. Scientometrics 64, 351–374 (2005)CrossRefGoogle Scholar
  5. 5.
    Chung, F., Graham, R.: A new bound for Euclidean Steiner minimal trees. Annals of the New York Academy of Sciences 440(1), 328–346 (1985)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Collins, C., Penn, G., Carpendale, S.: Bubble sets: Revealing set relations with isocontours over existing visualizations. IEEE Trans. Vis. Comput. Graphics 15(6), 1009–1016 (2009)CrossRefGoogle Scholar
  7. 7.
    Dinkla, K., van Kreveld, M.J., Speckmann, B., Westenberg, M.A.: Kelp diagrams: Point set membership visualization. Comput. Graph. Forum 31(3, pt1), 875–884 (2012)CrossRefGoogle Scholar
  8. 8.
    Dwyer, T., Nachmanson, L.: Fast edge-routing for large graphs. In: Eppstein, D., Gansner, E.R. (eds.) GD 2009. LNCS, vol. 5849, pp. 147–158. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Hu, Y., Gansner, E.R., Kobourov, S.G.: Visualizing graphs and clusters as maps. IEEE Comput. Graphics and Appl. 30(6), 54–66 (2010)CrossRefGoogle Scholar
  10. 10.
    Hurtado, F., Korman, M., van Kreveld, M., Löffler, M., Sacristán, V., Silveira, R.I., Speckmann, B.: Colored spanning graphs for set visualization. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 280–291. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Jianu, R., Rusu, A., Hu, Y., Taggart, D.: How to display group information on node-link diagrams: An evaluation. IEEE Trans. Vis. Comput. Graphics 20(11), 1530–1541 (2014)CrossRefGoogle Scholar
  12. 12.
    Kanizsa, G., Gerbino, W.: Convexity and symmetry in figure-ground organization. Vision and Artifact, 25–32 (1976)Google Scholar
  13. 13.
    Kobourov, S.G., Pupyrev, S., Simonetto, P.: Visualizing graphs as maps with contiguous regions. Comput. Graph. Forum (2014)Google Scholar
  14. 14.
    Kratochvíl, J., Nešetřil, J.: Independent set and clique problems in intersection-defined classes of graphs. Commentationes Math. Univ. Carolinae 31(1), 85–93 (1990)zbMATHGoogle Scholar
  15. 15.
    Meulemans, W., Riche, N., Speckmann, B., Alper, B., Dwyer, T.: KelpFusion: A hybrid set visualization technique. IEEE Trans. Vis. Comput. Graphics 19(11), 1846–1858 (2013)CrossRefGoogle Scholar
  16. 16.
    Mitchell, J.S.: Geometric shortest paths and network optimization. Handbook of Computational Geometry 334, 633–702 (2000)CrossRefGoogle Scholar
  17. 17.
    Novembre, et al.: Genes mirror geography within Europe. Nature 456(7218), 98–101 (2008)Google Scholar
  18. 18.
    Pupyrev, S., Nachmanson, L., Bereg, S., Holroyd, A.E.: Edge routing with ordered bundles. In: van Kreveld, M., Speckmann, B. (eds.) GD 2011. LNCS, vol. 7034, pp. 136–147. Springer, Heidelberg (2011)Google Scholar
  19. 19.
    Purves, D., Lotto, R.B.: Why we see what we do: An empirical theory of vision. Sinauer Associates (2003)Google Scholar
  20. 20.
    Riche, N.H., Dwyer, T.: Untangling Euler diagrams. IEEE Trans. Vis. Comput. Graphics 16(6), 1090–1099 (2010)CrossRefGoogle Scholar
  21. 21.
    Simonetto, P., Auber, D., Archambault, D.: Fully automatic visualisation of overlapping sets. Comput. Graph. Forum 28(3), 967–974 (2009)CrossRefGoogle Scholar
  22. 22.
    Skupin, A., Fabrikant, S.I.: Spatialization methods: a cartographic research agenda for non-geographic information visualization. Cartogr. Geogr. Inform. 30, 95–119 (2003)CrossRefGoogle Scholar
  23. 23.
    Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis, and Machine Vision. Thomson-Engineering (2007)Google Scholar
  24. 24.
    Zunic, J., Rosin, P.L.: A convexity measurement for polygons. IEEE Trans. Pattern Anal. Mach. Intell. 26, 173–182 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alon Efrat
    • 1
  • Yifan Hu
    • 2
  • Stephen G. Kobourov
    • 1
  • Sergey Pupyrev
    • 1
    • 3
  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA
  2. 2.Yahoo LabsNew YorkUSA
  3. 3.Institute of Mathematics and Computer ScienceUral Federal UniversityRussia

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