Abstract
Representing a graph in the 3-dimensional space is one of the most recent and challenging research issues for the graph drawing community. We deal with 3-dimensional proximity drawings of trees. We provide combinatorial characterizations of the classes of representable graphs and present several drawing algorithms.
Research supported in part by Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo of the Italian National Research Council (CNR).
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References
Advanced Visual Interfaces, Proccedings of the Workshop AVI'92, edited by T. Catarci, M.F. Costabile, and S. Levialdi, World Scientific series in Computer Science, Vol. 36, 1992.
P. Bose, G. Di Battista, W. Lenhart, and G. Liotta. Proximity Constraints and Representable Trees. Proc. Graph Drawing'94, LNCS, pp. 340–351, Princeton, NJ, 1994.
P. Bose, W. Lenhart, and G. Liotta. Characterizing Proximity Trees. To appear in Algorithmica: Special Issue on Graph Drawing.
R. Cohen, P. Eades, T. Lin, and F. Ruskey. Three-Dimensional Graph Drawing. Proc. Graph Drawing'94, LNCS, pp. 1–1, Princeton, NJ, 1994.
J.H. Conway, N.J.A. Sloane. Sphere Packings, Lattices, and Groups, Springer Verlag, 1993.
G. Di Battista, P. Eades, R. Tamassia and I.G. Tollis. Algorithms for Automatic Graph Drawing: An Annotated Bibliography. Computational Geometry: Theory and Applications, 4, 5, 1994, pp. 235–282.
G. Di Battista, W. Lenhart, and G. Liotta. Proximity Drawability: a Survey. Proc. Graph Drawing'94, LNCS, pp. 328–339, Princeton, NJ, 1994.
P. Eades and S. Whitesides. The Realization Problem for Euclidean Minimum Spanning Trees is NP-hard. Proc. ACM Symposium on Computational Geometry, 1994, pp. 49–56.
H. ElGindy, G. Liotta, A. Lubiw, H. Meijer, and S.H. Whitesides. Recognizing Rectangle of Influence Drawable Graphs. Proc. Graph Drawing'94, LNCS, pp. 352–363, Princeton, NJ, 1994.
J. W. Jaromczyk and G. T. Toussaint. Relative Neighborhood Graphs and Their Relatives. Proceedings of the IEEE, 80, 1992, pp. 1502–1517.
D. G. Kirkpatrick and J. D. Radke. A Framework for Computational Morphology. Computational Geometry, G. T. Toussaint, Elsevier, Amsterdam, 1985, pp. 217–248.
E. L. Lawler. Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976.
J. Leech. The Problem of the Thirteen Spheres. The Mathematical Gazette, 40, 1956, pp. 22–23.
G. Liotta. Computing Proximity Drawings of Graphs. Ph.D Thesis, University of Rome “La Sapienza”, 1995.
A. Lubiw, and N. Sleumer, All Maximal Outerplanar Graphs are Relative Neighborhood Graphs. Proc. CCCG '93, 1993, pp. 198–203.
C. Monma and S. Suri. Transitions in Geometric Minimum Spanning Trees. Proc. ACM Symposium on Computational Geometry, 1991, pp. 239–249.
S. P. Reiss. 3-D Visualization of Program Information. Proc. Graph Drawing'94, LNCS, pp. 12–24, Princeton, NJ, 1994
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Liotta, G., Di Battista, G. (1995). Computing proximity drawings of trees in the 3-dimensional space. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_66
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DOI: https://doi.org/10.1007/3-540-60220-8_66
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