Skip to main content

Minimal elimination of planar graphs

  • Conference paper
  • First Online:
Algorithm Theory — SWAT'98 (SWAT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1432))

Included in the following conference series:

Abstract

We prove that the problem to get an inclusion minimal elimination ordering can be solved in linear time for planar graphs. An essential tool is the use of breadth-first search.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Agrawal, P. Klein, R. Ravi, Cutting Down on Fill-in Using Nested Dissection, in Sparse Matrix Computations: Graph Theory Issues and Algorithms, A. George, J. Gilbert, J.W.-H. Liu ed., IMA Volumes in Mathematics and its Applications, Vol. 56, Springer Verlag, 1993, pp. 31–55.

    Google Scholar 

  2. J. Blair, P. Heggernes, J.A. Telle, Making an Arbitrary Filled Graph Minimal by Removing Fill Edges, Algorithm Theory-SWAT '96, R. Karlsson, A. Lingas ed., LLNCS 1097, pp. 173–184.

    Google Scholar 

  3. P. Bunemann, A Characterization of Rigid Circuit Graphs, Discrete Mathematics 9 (1974), pp. 205–212.

    Article  MathSciNet  Google Scholar 

  4. E. Dahlhaus, Minimal Elimination Ordering inside a Given Chordal Graph, WG 97 (R. Möhring ed.), LLNCS 1335, pp. 132–143.

    Google Scholar 

  5. Elias Dahlhaus, Marek Karpinski, An Efficient Parallel Algorithm for the Minimal Elimination Ordering (MEO) of an Arbitrary Graph, Theoretical Computer Science 134 (1994), pp. 493–528.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Eiermann, O. Ernst, W. Queck, Finite Element Tutorial, TU-Bergakademie Freiberg.

    Google Scholar 

  7. M. Farber, Characterizations of Strongly Chordal Graphs, Discrete Mathematics 43 (1983), pp. 173–189.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Gavril, The Intersection Graphs of Subtrees in Trees Are Exactly the Chordal Graphs, Journal of Combinatorial Theory Series B, vol. 16 (1974), pp. 47–56.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Gilbert, R. Tarjan, The Analysis of a Nested Dissection Algorithm, Numerische Mathematik 50 (1987), pp. 427–449.

    MathSciNet  Google Scholar 

  10. R. Lipton, R. Tarjan, A Separator Theorem for Planar Graphs, SIAM Journal on Applied Mathematics 36 (1979) pp. 177–189.

    Article  MathSciNet  MATH  Google Scholar 

  11. Parra, A., Scheffler, P., How to use minimal separators for its chordal triangulation, Proceedings of the 20 th International Symposium on Automata, Languages and Programming (ICALP'95), Springer-Verlag Lecture Notes in Computer Science 944, (1995), pp. 123–134.

    MathSciNet  Google Scholar 

  12. D. Rose, Triangulated Graphs and the Elimination Process, Journal of Mathematical Analysis and Applications 32 (1970), pp. 597–609.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Rose, R. Tarjan, G. Lueker, Algorithmic Aspects on Vertex Elimination on Graphs, SIAM Journal on Computing 5 (1976), pp. 266–283.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Tarjan, M. Yannakakis, Simple Linear Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs, SIAM Journal on Computing 13 (1984), pp. 566–579. Addendum: SIAM Journal on Computing 14 (1985), pp. 254–255.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Yannakakis, Computing the Minimum Fill-in is NP-complete, SIAM Journal on Algebraic and Discrete Methods 2 (1981), pp. 77–79.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Stefan Arnborg Lars Ivansson

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dahlhaus, E. (1998). Minimal elimination of planar graphs. In: Arnborg, S., Ivansson, L. (eds) Algorithm Theory — SWAT'98. SWAT 1998. Lecture Notes in Computer Science, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054369

Download citation

  • DOI: https://doi.org/10.1007/BFb0054369

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64682-2

  • Online ISBN: 978-3-540-69106-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics