Abstract
In orthogonal graph drawing, edges are represented by sequences of horizontal and vertical straight line segments. For graphs of degree at most four, this can be achieved by embedding the graph in a grid. The number of bends displayed is an important criterion for layout quality. A well-known algorith of Tamassia efficiently embeds a planar graph with fixed combinatorial embedding and vertex degree at most four in the grid such that the nu ber of bends is minimum 23.
When given a dynamic graph, i.e.a graph that changes over time, one has to take into accounFt not only the static criteria of layout quality, but also the effort users spent to regain familiarity with the layout. Therefore, consecutive layouts should compromize between quality and stability. We here extend Tamassia’s layout model to dynamic graphs in a way that allows to specify the relative importance of the nu ber of bends vs. the number of changes between consecutive layouts. We also show that optimal layouts in the dynamic odel can be computed efficiently by means that are very similar to the static model, namely by solving a minimum cost flow proble in a suitably defined network.
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References
Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin. Network flows Prentice Hall, 1993.
Therese C. Biedl. New lower bounds for orthogonal graph drawings. In Proc. Graph Drawing’ 95, pages 28–39. Springer, LNCS vol. 1027, 1996.
Stina S. Bridgeman, Jody Fanto, Ashim Garg, Roberto Tamassia, and Luca Vismara. InteractiveGiotto An algorith for interactive orthogonal graph drawing. In Proc. Graph Drawing’97, pages 303–308. Springer, LNCS vol. 1353, 1997.
Therese C. Biedl and Goos Kant. A better heuristic for orthogonal graph drawing. In Proc. 2nd European Symposium on Algorithms, pages 24–33. Springer, LNCS vol. 855, 1994.
Therese C. Biedl and Michael Kaufmann. Area-efficient static and incremental graph drawings. In Proc. 5th European Symposium on Algorithms pages 37–52. Springer, LNCS vol. 1284, 1997.
Therese C. Biedl, Brendan P. Madden, and Ioannis G. Tollis. The three-phase method: A unified approach to orthogonal graph drawing. In Proc. Graph Drawing pages 391–402. Springer, LNCS vol. 1353, 1997.
Karl-Friedrich Böhringer and Frances Newbery Paulisch. Using constraints to achieve stability in automatic graph layout algorithms. In CHI’90 pages 43–51. ACM, The Association for Computing Machinery, 1990.
Ulrik Brandes and Dorothea Wagner. A Bayesian paradigm for dynamic graph layout. In Proc. Graph Drawing’ 97, pages 237–247. Springer, LNCS vol. 1353, 1997.
Ulrik Brandes and Dorothea Wagner. Randofield odels for graph layout. Konstanzer Schriften in Mathematik und Informatik 33, Universität Konstanz, 1997.
Robert F. Cohen, Giuseppe Di Battista, Roberto Tamassia, Ioannis G. Tollis, and P. Bertolazzi. A framework for dynamic graph drawing. In Proc. 8th Symposium on Computational geometry, pages 261–270. ACM, The Association for Computing Machinery, 1992
Giuseppe Di Battista, Peter Eades, Roberto Tamassia, and Ioannis G. Tollis. Algorithms for drawing graphs: An annotated bibliography. Computational Geometry, 4:235–282, 1994.
Giuseppe Di Battista and Luca Vismara. Angles of planar triangular graphs. SIAM J. Discrete Math., 9(3):349–359, 1996.
Peter Eades, Wei Lai, Kazuo Misue, and Kozo Sugiyama. Preserving the mental map of a diagram. Proc. Compugraphics’ 91, 9:24–33, 1991.
Ulrich Fößeier and Michael Kaufmann. Drawing High Degree Graphs with Low Bend numbers. In Proc. Graph Drawing’ 95, pages 254–266. Springer, LNCS vol. 1027, 1996.
Ashim Garg. On drawing angle graphs. In Proc. Graph Drawing’ 94, pages 84–95. Springer, LNCS vol. 894, 1995.
Ashim Garg and Roberto Tamassia. On the computational complexity of upward and rectilinear planarity testing. In Proc. Graph Drawing’ 94, pages 286–297. Springer, LNCS vol. 894, 1995.
Ashim Garg and Roberto Tamassia. An new inimu cost flow algorith with applications to graph drawing. In Proc. Graph Drawing’ 96, pages 201–216. Springer, LNCS vol. 1190, 1997.
Seth Malitz and Achilleas Papakostas. On the angular resolution of planar graphs. SIAM J. Discrete Math., 7(2):172–183, 1994.
Stephen North. Incremental layout in DynaDAG. In Proc. Graph Drawing’ 95, pages 409–418. Springer, LNCS vol. 1027, 1996.
Achilleas Papakostas and Ioannis G. Tollis. Improved algorithms and bounds for orthogonal drawings. In Proc. Graph Drawing’ 94, pages 40–51. Springer, LNCS vol. 894, 1995.
Achilleas Papakostas and Ioannis G. Tollis. Issues in interactive orthogonal graph drawing. In Proc. Graph Drawing’ 95, pages 419–430. Springer, LNCS vol. 1027, 1996.
Helen Purchase. Which aesthetic has the greatest effect on human understanding? In Proc. Graph Drawing’ 97, pages 248–261. Springer, LNCS vol. 1353, 1997.
Roberto Tamassia. On embedding a graph in the grid with the minimum number of bends. SIAM J. Comput., 16(3):421–444, 1987.
Roberto Tamassia, Giuseppe DiBattista, and Carlo Batini. Automatic graph drawing and readability of diagrams. IEEE Trans. Syst. Man Cybern., SMC-18(1):61–79, 1988.
Gopalakrishnan Vijayan. Geometry of planar graphs with angles. In Proc. 2nd Symposium on Computational Geometry, pages 116–124. ACM, The Association of Computing Machinery, 1986.
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Brandes, U., Wagner, D. (1998). Dynamic Grid Embedding with Few Bends and Changes. In: Chwa, KY., Ibarra, O.H. (eds) Algorithms and Computation. ISAAC 1998. Lecture Notes in Computer Science, vol 1533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49381-6_11
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DOI: https://doi.org/10.1007/3-540-49381-6_11
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