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Quasi-Upward Planar Drawings of Mixed Graphs with Few Bends: Heuristics and Exact Methods

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Algorithms and Computation (WALCOM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8344))

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Abstract

A mixed graph has both directed and undirected edges. We study how to compute a crossing-free drawing of a planar embedded mixed graph, such that it is upward “as much as possible”. Roughly speaking, in an upward drawing of a mixed graph all edges are monotone in the vertical direction and directed edges flow monotonically from bottom to top according to their orientation. We study quasi-upward drawings of mixed graphs, that is, upward drawings where edges can break the vertical monotonicity in a finite number of edge points, called bends. We describe both efficient heuristics and exact methods for computing quasi-upward planar drawings of planar embedded mixed graphs with few bends, and we extensively compare them experimentally: the results show the effectiveness of our algorithms in many cases.

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References

  1. Auer, C., Bachmaier, C., Brandenburg, F.J., Gleißner, A.: Classification of planar upward embedding. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 415–426. Springer, Heidelberg (2011)

    Google Scholar 

  2. Auer, C., Bachmaier, C., Brandenburg, F.J., Gleißner, A., Hanauer, K.: The duals of upward planar graphs on cylinders. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds.) WG 2012. LNCS, vol. 7551, pp. 103–113. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Bang-Jensen, J., Gutin, G.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer (2009)

    Google Scholar 

  4. Bertolazzi, P., Di Battista, G., Didimo, W.: Quasi-upward planarity. Algorithmica 32(3), 474–506 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bertolazzi, P., Di Battista, G., Liotta, G., Mannino, C.: Upward drawings of triconnected digraphs. Algorithmica 6(12), 476–497 (1994)

    Article  Google Scholar 

  6. Bertolazzi, P., Di Battista, G., Mannino, C., Tamassia, R.: Optimal upward planarity testing of single-source digraphs. SIAM J. on Computing 27, 132–169 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Binucci, C., Di Giacomo, E., Didimo, W., Rextin, A.: Switch-regular upward planar embeddings of directed trees. J. of Graph Algorithms and Applications 15(5), 587–629 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Binucci, C., Didimo, W.: Upward planarity testing of embedded mixed graphs. In: Speckmann, B. (ed.) GD 2011. LNCS, vol. 7034, pp. 427–432. Springer, Heidelberg (2011)

    Google Scholar 

  9. Binucci, C., Didimo, W., Giordano, F.: Maximum upward planar subgraphs of embedded planar digraphs. Computational Geometry: Theory and Applications 41(3), 230–246 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Binucci, C., Didimo, W., Patrignani, M.: Upward and quasi-upward planarity testing of embedded mixed graphs. Technical report, RT-001-12, DIEI - University of Perugia (2012)

    Google Scholar 

  11. Boesch, F., Tindell, R.: Robbins’s theorem for mixed multigraphs. American Mathematical Monthly 87(9), 716–719 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  12. Chan, H.: A parameterized algorithm for upward planarity testing. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 157–168. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Chimani, M., Gutwenger, C., Mutzel, P., Wong, H.-M.: Layer-free upward crossing minimization. ACM J. of Experimental Algorithmics 15 (2010)

    Google Scholar 

  14. Chimani, M., Gutwenger, C., Mutzel, P., Wong, H.-M.: Upward planarization layout. J. of Graph Algorithms and Applications 15(1), 127–155 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chimani, M., Zeranski, R.: Upward planarity testing via SAT. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 248–259. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  16. Chimani, M., Zeranski, R.: Upward planarity testing: A computational study. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 13–24. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Cornelsen, S., Karrenbauer, A.: Accelerated bend minimization. J. of Graph Algorithms and Applications 16(3), 635–650 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  18. Di Battista, G., Didimo, W.: Gdtoolkit. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization. Chapman and Hall/CRC (2013)

    Google Scholar 

  19. Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  20. Didimo, W.: Upward planar drawings and switch-regularity heuristics. J. of Graph Algorithms and Applications 10(2), 259–285 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. Didimo, W., Giordano, F., Liotta, G.: Upward spirality and upward planarity testing. SIAM J. on Discrete Mathematics 23(4), 1842–1899 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  22. Didimo, W., Pizzonia, M.: Upward embeddings and orientations of undirected planar graphs. J. of Graph Algorithms and Applications 7(2), 221–241 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Eades, P., Lin, X., Smyth, W.F.: A fast effective heuristic for the feedback arc set problem. Information Processing Letters 47, 319–323 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  24. Eiglsperger, M., Eppinger, F., Kaufmann, M.: An approach for mixed upward planarization. J. of Graph Algorithms and Applications 7(2), 203–220 (2003)

    Article  MathSciNet  Google Scholar 

  25. Farzad, B., Mahdian, M., Mahmoudian, E., Saberi, A., Sadri, B.: Forced orientation of graphs. Bulletin of Iranian Mathematical Society 32(1), 78–89 (2006)

    Google Scholar 

  26. Frati, F., Kaufmann, M., Pach, J., Tóth, C.D., Wood, D.R.: On the upward planarity of mixed plane graphs. In: Wismath, S., Wolff, A. (eds.) GD 2013. LNCS, vol. 8242, pp. 1–12. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  27. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co. (1979)

    Google Scholar 

  28. Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM J. on Computing 31(2), 601–625 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  29. Healy, P., Lynch, K.: Fixed-parameter tractable algorithms for testing upward planarity. International Journal of Foundations of Computer Science 17(5), 1095–1114 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  30. Hutton, M.D., Lubiw, A.: Upward planarity testing of single-source acyclic digraphs. SIAM J. on Computing 25(2), 291–311 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  31. Lucchesi, C.L., Younger, D.H.: A minimax theorem for directed graphs. J. London Math. Soc. 17, 369–374 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  32. Mchedlidze, T., Symvonis, A.: Unilateral orientation of mixed graphs. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds.) SOFSEM 2010. LNCS, vol. 5901, pp. 588–599. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  33. Papakostas, A.: Upward planarity testing of outerplanar dags. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 298–306. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  34. Stamm, H.: On feedback problems in planar digraphs. In: Möhring, R.H. (ed.) WG 1990. LNCS, vol. 484, pp. 79–89. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Elettronica e dell’Informazione, Università degli Studi di Perugia, Italy

    Carla Binucci & Walter Didimo

Authors
  1. Carla Binucci
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  2. Walter Didimo
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    Sudebkumar Prasant Pal

  2. National Institute of Informatics, 2-1-2 Hitotsubashi, 101-8430, Chiyoda-ku, Tokyo, Japan

    Kunihiko Sadakane

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Binucci, C., Didimo, W. (2014). Quasi-Upward Planar Drawings of Mixed Graphs with Few Bends: Heuristics and Exact Methods. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_28

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  • DOI: https://doi.org/10.1007/978-3-319-04657-0_28

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04656-3

  • Online ISBN: 978-3-319-04657-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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