Skip to main content
SpringerLink
Log in

On Generating Strong Elimination Orderings of Strongly Chordal Graphs

  • Conference paper
Book cover Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1530))

Abstract

We present a conceptually simple algorithm to generate an ordering of the vertices of an undirected graph. The ordering generated turns out to be a strong elimination ordering if and only if the given graph is a strongly chordal graph. This algorithm makes use of maximum cardinality search and lexicographic breadth first search algorithms which are used to generate perfect elimination orderings of a chordal graph. Our algorithm takes O(k 2 n) time where k is the size of the largest minimal vertex separator and n denotes the number vertices in the graph. The algorithm provides a new insight into the structure of strongly chordal graphs and also gives rise to a new algorithm of the same time complexity for recognition of strongly chordal graphs.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. Jl. of ACM 30, 479–513 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fagin, R.: Degrees of Acyclicity for hypergraph and relational database schemes. Jl. of ACM 30, 514–550 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  3. Farber, M.: Characterization of Strongly Chordal Graphs. Discrete Math. 43, 173–189 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Farber, M., Anstee, R.P.: Characterization of Totally Balanced Matrices. Jl. of Algorithms 5, 215–230 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  5. Farber, M.: Domination, Independent Domination and Duality in Strongly Chordal Graphs. Discrete Applied Mathematics 7, 115–130 (1884)

    Article  MathSciNet  Google Scholar 

  6. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)

    MATH  Google Scholar 

  7. Lehel, J.: A characterization of totally balanced matrices. Discrete Mathematics 57, 59–65 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lubiw, A.: Double Lexical Ordering of matrices. SIAM Jl. of Computing 16(5), 854–879 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  9. Peng, S.-L., Chang, M.-S.: A simple linear-time algorithm for the domatic prtition problem on strongly chordal graphs. Information processing Letters 43, 297–300 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Rose, D.J.: A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations. In: Reed, R.C. (ed.) Graph Theory and Computing, pp. 183–217. Academic Press, London (1972)

    Google Scholar 

  11. Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic Aspects of Vertex Elimination on Graphs. SIAM Jl. of Computing 5, 266–283 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  12. Spinrad, J.P.: Doubly Lexical Ordering of Dense 0-1 Matrices. Information Processing Letters 45, 229–235 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sreenivasa Kumar, P., Veni Madhavan, C.E.: 2-Separator Chordal Graphs. In: Proceedings of National Seminar on Theoretical Computer Science, Kharagpur, India, pp. 37–52 (1993)

    Google Scholar 

  14. Tarjan, R.E., Paige, R.: Three Partition Refinement Algorithm. SIAM Jl. Computing 16, 973–989 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Yannakakis, M., Tarjan, R.E.: Simple Linear-time Algorithms to Test Chordality of Graphs, Test acyclicity of Hypergraphs and Selectively Reduce Acyclic Hypergraphs. SIAM Jl. Computing 13(3), 565–579 (1984)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science & Engineering, Indian Institute of Technology, Madras, 600 036, India

    N. Kalyana Rama Prasad & P. Sreenivasa Kumar

Authors
  1. N. Kalyana Rama Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Sreenivasa Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Institute of Mathematical Sciences, 600 113, Chennai, India

    Vikraman Arvind

  2. National Institute of Advanced Studies, Indian Institute of Science Campus, 560012, Bangalore, India

    Sundar Ramanujam

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kalyana Rama Prasad, N., Sreenivasa Kumar, P. (1998). On Generating Strong Elimination Orderings of Strongly Chordal Graphs. In: Arvind, V., Ramanujam, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1998. Lecture Notes in Computer Science, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49382-2_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-49382-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65384-4

  • Online ISBN: 978-3-540-49382-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation