Eager st-Ordering

  • Ulrik Brandes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2461)


Given a biconnected graph G = (V,E) with edge s, tE, an st-ordering is an ordering v1, . . . , vn of V such that s = v1, t = vn, and every other vertex has both a higher-numbered and a lower-numbered neighbor. Previous linear-time st-ordering algorithms are based on a preprocessing step in which depth-first search is used to compute lowpoints. The actual ordering is determined only in a second pass over the graph. We present a new, incremental algorithm that does not require lowpoint information and, throughout a single depth-first traversal, maintains an st-ordering of the biconnected component of s, t in the traversed subgraph.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Ebert. st-ordering the vertices of biconnected graphs. Computing, 30(1):19–33, 1983.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    S. Even and R. E. Tarjan. Computing an st-numbering. Theoretical Computer Science, 2(3):339–344, 1976.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    S. Even and R. E. Tarjan. Corrigendum: Computing an st-numbering. Theoretical Computer Science, 4(1):123, 1977.CrossRefMathSciNetGoogle Scholar
  4. [4]
    H. N. Gabow. Path-based depth-first search for strong and biconnected components. Information Processing Letters, 74:107–114, 2000.CrossRefMathSciNetGoogle Scholar
  5. [5]
    A. Lempel, S. Even, and I. Cederbaum. An algorithm for planarity testing of graphs. In P. Rosenstiehl, editor, Proceedings of the International Symposium on the Theory of Graphs (Rome, July 1966), pages 215–232. Gordon and Breach, 1967.Google Scholar
  6. [6]
    R. E. Tarjan. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1:146–160, 1973.CrossRefMathSciNetGoogle Scholar
  7. [7]
    R. E. Tarjan. Two streamlined depth-first search algorithms. Fundamenta Informaticae, 9:85–94, 1986.MATHMathSciNetGoogle Scholar
  8. [8]
    H. Whitney. Non-separable and planar graphs. Transactions of the American Mathematical Society, 34:339–362, 1932.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ulrik Brandes
    • 1
  1. 1.Department of Computer & Information ScienceUniversity of KonstanzUSA

Personalised recommendations