Pitfalls of using PQ-trees in automatic graph drawing

  • Michael Jünger
  • Sebastian Leipert
  • Petra Mutzel
Crossings and Planarity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

A number of erroneous attempts involving PQ-trees in the context of automatic graph drawing algorithms have been presented in the literature in recent years. In order to prevent future research from constructing algorithms with similar errors we point out some of the major mistakes.

In particular, we examine erroneous usage of the PQ-tree data structure in algorithms for computing maximal planar subgraphs and an algorithm for testing leveled planarity of leveled directed acyclic graphs with several sources and sinks.

References

  1. Booth, K. and Lueker, G. (1976). Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13, 335–379.Google Scholar
  2. Chiba, N., Nishizeki, T., Abe, S., and Ozawa, T. (1985). A linear algorithm for embedding planar graphs using PQ-trees. Journal of Computer and System Sciences, 30, 54–76.CrossRefGoogle Scholar
  3. Di Battista, G. and Nardelli, E. (1988). Hierarchies and planarity theory. IEEE Transactions on systems, man, and cybernetics, 18(6), 1035–1046.Google Scholar
  4. Even, S. (1979). Graph Algorithms. Computer Science Press, Potomac, Maryland.Google Scholar
  5. Even, S. and Tarjan, R. E. (1976). Computing an st-numbering. Theoretical Computer Science, 2, 339–344.CrossRefGoogle Scholar
  6. Heath, L. and Pemmaraju, S. (1996a). Recognizing leveled-planar dags in linear time. In F. J. Brandenburg, editor, Proc. Graph Drawing '95, volume 1027 of Lecture Notes in Computer Science, pages 300–311. Springer Verlag.Google Scholar
  7. Heath, L. and Pemmaraju, S. (1996b). Stack and queue layouts of directed acyclic graphs: Part II. Technical report, Department of Computer Science, Virginia Polytechnic Institute & State University.Google Scholar
  8. Jayakumar, R., Thulasiraman, K., and Swamy, M. (1986). On maximal planarization of non-planar graphs. IEEE Transactions on Circuits Systems, 33(8), 843–844.CrossRefGoogle Scholar
  9. Jayakumar, R., Thulasiraman, K., and Swamy, M. (1989). On O(n 2) algorithms for graph planarization. IEEE Transactions on Computer-Aided Design, 8(3), 257–267.CrossRefGoogle Scholar
  10. Jünger, M., Leipert, S., and Mutzel, P. (1996). On computing a maximal planar subgraph using PQ-trees. Technical Report 96.227, Institut für Informatik der Universität zu Köln.Google Scholar
  11. Kant, G. (1992). An O(n 2) maximal planarization algorithm based on PQ-trees. Technical Report RUU-CS-92-03, Department of Computer Science, Utrecht University.Google Scholar
  12. Lempel, A., Even, S., and Cederbaum, I. (1967). An algorithm for planarity testing of graphs. In Theory of Graphs: International Symposium: Rome, July 1966, pages 215–232. Gordon and Breach, New York.Google Scholar
  13. Ozawa, T. and Takahashi, H. (1981). A graph-planarization algorithm and its application to random graphs. In Graph Theory and Algorithms, volume 108 of Lecture Notes in Computer Science, pages 95–107. Springer Verlag.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Michael Jünger
    • 1
  • Sebastian Leipert
    • 2
  • Petra Mutzel
    • 3
  1. 1.Institut für InformatikUniversität zu KölnKöln
  2. 2.Institut für InformatikUniversität zu KölnKöln
  3. 3.Max-Planck-Institut für InformatikSaarbrücken

Personalised recommendations