A fast sequential and parallel algorithm for the computation of the k-closure of a graph

  • Ingo Schiermeyer
Algorithmic Graph Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 411)


In 1976 Bondy and Chvátal introduced the k-closure Ck(G) of a graph and described an algorithm which constructs it in O(n4) time. We present an algorithm which requires O(n3) time. However, in the average case, Ck(G) is computed by this algorithm for almost all integers k (in the asymptotic sense) with O ≦ k ≦ 2n − 2 in O(n2) time. We next present a parallel algorithm which requires O(n2 log n) time. In the average case, this algorithm computes Ck(G) for almost all integers k in O(log n) parallel time.

Key Words

sequential and parallel graph algorithms graph properties hamiltonian graphs computational complexity polylog parallel algorithm random graphs 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Ingo Schiermeyer
    • 1
  1. 1.Lehrstuhl C für MathematikTechnische Hochschule AachenAachenWest-Germany

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