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International Symposium on Algorithms and Computation

ISAAC 1995: Algorithms and Computations pp 352–361Cite as

A linear time algorithm for finding maximal planar subgraphs

  • Session 10
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1004))

Abstract

Given an undirected graph G, the maximal planar subgraph problem is to determine a planar subgraph H of G such that no edge of G-H can be added to H without destroying planarity. Polynomial algorithms have been obtained by Jakayumar, Thulasiraman and Swamy [6] and Wu [9], O(mlogn) algorithms were previously given by Di Battista and Tamassia [3] and Cai, Han and Tarjan [2]. A recent O(mα(n)) algorithm was obtained by La Poute [7], Our algorithm is based on a simple planarity test [5] developed by the author, which is a vertex addition algorithm based on a depth-first-search ordering. The planarity test [5] uses no complicated data structure and is conceptually simpler than Hopcroft anf Tarjan's path addition and Lempel, Even and Cederbaum's vertex addition approaches.

The research of this author was supported in part by the National Science Council of the Republic of China.

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References

  1. K. S. Booth and G. S. Lueker, Testing the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. Syst. Sci. 13(1976), 335–379.

    Google Scholar 

  2. J. Cai, X. Han and R. T. Tarjan, An O(mlogn)-time algorithm for the maximal planar subgraph problem, SIAM J. Comput. 22(1994), 1142–1162.

    Google Scholar 

  3. G. Di Battista and R. Tamassia [1989], Incremental planarity testing, in Proc. 30th Annual IEEE Symposium on Foundation of Computer Science, 436–411.

    Google Scholar 

  4. J. E. Hopcroft and R. E. Tarjan, Efficient planarity testing, J. Assoc. Comput. Mach. 21(1994), 549–568.

    Google Scholar 

  5. W. K. Shih and W. L. Hsu, A simple test for planar graphs, 1993, submitted.

    Google Scholar 

  6. R. Jakayumar, K. Thulasiraman and M. N. S. Swamy, An O(n 2) algorithms for graph planarization, IEEE Trans. CAD 8(1989), 257–267.

    Google Scholar 

  7. J. A. La Poute, Alpha-Algorithms for incremental planarity testing, STOC 1994, 706–715.

    Google Scholar 

  8. A. Lempel, S. Even and I. Cederbaum, An algorithm for planarity testing of graphs, Theory of Graphs, ed., P. Rosenstiehl, Gordon and Breach, New York, 1967, 215–232.

    Google Scholar 

  9. W. Wu, On the planar imbedding of linear graphs, J. Systems Sci. Math. Sci. 5, 290–302, 1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan, ROC

    Wen-Lian Hsu

Authors
  1. Wen-Lian Hsu
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Editor information

John Staples Peter Eades Naoki Katoh Alistair Moffat

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© 1995 Springer-Verlag Berlin Heidelberg

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Hsu, WL. (1995). A linear time algorithm for finding maximal planar subgraphs. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015441

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  • DOI: https://doi.org/10.1007/BFb0015441

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60573-7

  • Online ISBN: 978-3-540-47766-2

  • eBook Packages: Springer Book Archive

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