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An Approach for Mixed Upward Planarization

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Algorithms and Data Structures (WADS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2125))

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Abstract

In this paper, we consider the problem of finding a mixed upward planarization of a mixed graph, i.e., a graph with directed and undirected edges. The problem is a generalization of the planarization problem for undirected graphs and is motivated by several applications in graph drawing. We present a heuristical approach for this problem which provides good quality and reasonable running time in practice, even for large graphs. This planarization method combined with a graph drawing algorithm for upward planar graphs can be seen as a real alternative to the wellknown Sugiyama algorithm.

Partially supported by DFG-Grant Ka812/8-1

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References

  1. T. Asano, H. Imai, and A. Mukaiyama, Finding a Maximum Weight Independent Set of a Circle Graph. IEICE Transactions, E74, 1991, pp. 681–683.

    Google Scholar 

  2. C. Batini, E. Nardelli, and R. Tamassia, A Layout Algorithm for Data-Flow Diagrams. IEEE Trans. Softw. Eng., SE-12(4), 1986, pp. 538–546

    Google Scholar 

  3. P. Bertolazzi, G. Di Battista, G. Liotta, and C. Mannino, Upward drawings of triconnected digraphs, Algorithmica, 6(12), 1996, p. 476–497.

    Google Scholar 

  4. G. Booch, J. Rumbaugh, I. Jacobson, The Unified Modeling Language, Addison-Weslay, 1999.

    Google Scholar 

  5. Cimikowski, R., An analysis of heuristics for the maximum planar subgraph problem, in Proceedings of the 6th ACM-SIAM Symposium of Discrete Algorithms, 1995, pp. 322–331.

    Google Scholar 

  6. R. Dial, Algorithm 360: Shortest path forest with topological ordering, Communications of ACM, 12, 1969, pp. 632–633

    Article  Google Scholar 

  7. G. Di Battista and P. Eades and R. Tamassia and I. G. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, 1999.

    Google Scholar 

  8. Eiglsperger, M., Foessmeier, U., Kaufmann, M., Orthogonal Graph Drawing with Constraints, Proc. 11th Symposium on Discrete Algorithms (SODA’00), pp. 3–11, ACM-SIAM, 2000.

    Google Scholar 

  9. F. Eppinger, Kombinatorische Einbettung teilgerichteter Graphen, Diplomarbeit, Universität Tübingen, 2001.

    Google Scholar 

  10. A. Garg and R. Tamassia. On the computational complexity of upward and rectiliniar planarity testing. In R. Tamassia and I. G. Tollis, editors, Graph Drawing (Proc. GD’94), LNCS 894, pages 286–297. Springer Verlag, 1995.

    Google Scholar 

  11. Goldschmidt, O., Takvorian, A., An efficient graph planarization two-phase heuristic, Networks, 24 (1994), pp. 69–73.

    Article  MATH  MathSciNet  Google Scholar 

  12. R. Jayakumar, K. Thulasiraman, and M.N.S. Swamy, O(n 2) Algorithms for graph planarization, IEEE Trans. on CAD 8(3), 257–267, 1989

    Google Scholar 

  13. M. Jünger, S. Leipert and P. Mutzel, Level Planarity Testing in Linear Time, In S.H. Whiteside, editor, Graph Drawing (Proc. GD’98), LNCS 1547, pages 224–237. Springer Verlag, 1999.

    Chapter  Google Scholar 

  14. M. Jünger and S. Leipert, Level Planar Embedding in Linear Time, In J. Kra-tochvil, editor, Graph Drawing (Proc. GD’99), volume 1547 of Lecture Notes Comput. Sci., pages 72–81. Springer Verlag, 2000.

    Google Scholar 

  15. M. Jünger and P. Mutzel, Solving the maximum weight planar subgraph problem by Branch & Cut, In Proc. of the 3rd conference on integer programming and combinatorial optimization (IPCO), pp. 479–492, 1993

    Google Scholar 

  16. G. Kant, An O(n 2) maximal planarization algorithm based on PQ-trees. Tech. Rep. RUU-CS-92-03, CS Dept., Univ. Utrecht, Netherlands, Jan., 1992

    Google Scholar 

  17. M. Resende and C. Ribeiro, A GRASP for graph planarization, Networks, 29 (1997), pp. 173–189

    Article  MATH  Google Scholar 

  18. J. Seemann, Extending the Sugiyama Algorithm for Drawing UML Class Diagrams, In G. Di Battista, editor, Graph Drawing (Proc. GD’97), volume 1353 of Lecture Notes Comput. Sci., pages 415–424. Springer Verlag, 1998.

    Google Scholar 

  19. Sugiyama, K., Tagawa, S. and Toda, M. 1981. Methods for Visual Understanding of Hierarchical Systems, IEEE Trans. Syst. Man Cybern., SMC-11, no. 2, pp. 109–125.

    Article  MathSciNet  Google Scholar 

  20. R. Tamassia, On Embedding a Graph in the Grid with the Minimum Number of Bends, SIAM J. Comput., 16(3), 1987, pp. 421–444.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany

    Markus Eiglsperger & Michael Kaufmann

Authors
  1. Markus Eiglsperger
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  2. Michael Kaufmann
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Candada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. Center for Geometric Computing, Brown University, Providence, RI, 02912-1910, USA

    Roberto Tamassia

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© 2001 Springer-Verlag Berlin Heidelberg

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Eiglsperger, M., Kaufmann, M. (2001). An Approach for Mixed Upward Planarization. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_33

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  • DOI: https://doi.org/10.1007/3-540-44634-6_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42423-9

  • Online ISBN: 978-3-540-44634-7

  • eBook Packages: Springer Book Archive

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