Parallel ear decomposition search (EDS) and st-numbering in graphs

Extended abstract
  • Yael Maon
  • Baruch Schieber
  • Uzi Vishkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 227)


The linear time serial algorithm for planarity testing of [LEC-67] uses the linear time serial algorithm of [ET-76] for st-numbering. This st-numbering algorithm is based on depth-first search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is not amenable to poly-log time parallelism using "around linearly" (or even polynomially) many processors. The first contribution of this paper is a general method for searching efficiently in parallel undirected graphs, called ear-decomposition search (EDS).

The second contribution demonstrates the applicability of this search method. We present an efficient parallel algorithm for st-numbering in a biconnected graph. The algorithm is quite subtle and runs in logarithmic time using a linear number of processors on a concurrent-read concurrent-write (CRCW) PRAM. An efficient parallel algorithm for the problem did not exist before. It was not even known to be in NC.


Parallel Algorithm Internal Vertex Numbering Algorithm Adjacency List Serial Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Yael Maon
    • 1
    • 2
  • Baruch Schieber
    • 1
    • 2
  • Uzi Vishkin
    • 1
    • 2
  1. 1.Department of Computer Science School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Computer Science Courant Institute of Mathematical SciencesNew York UniversityNew York

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