An algorithm for transitive closure with linear expected time

  • C. -P. Schnorr
Vorträge In Der Reihenfolge Des Programms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 48)


An algorithm for transitive closure is described with expected time O(n+m*) where n is the number of nodes and m* is the expected number of edges in the transitive closure.


Independent Random Variable Expected Number Transitive Closure Input Graph Edge Reversal 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Arlazarov, V.L., Dinic, E.A., Kronod, M.A., Faradzev, I.A.: On economical construction of the transitive closure of an oriented graph. Dokl. Acad.Nauk,SSSR, 11 (1970), 1209–1210Google Scholar
  2. [2]
    Bloniarz, Fischer, Meyer: A note on the average time to compute transitive closures. In: Automata Languages and Programming. Ed.: Michaelson and Milner, Edinburgh University Press 1976Google Scholar
  3. [3]
    Erdös, Spencer: Probabilistic methods in combinatorics. New York: Academic Press (1974)Google Scholar
  4. [4]
    Fischer, Meyer: Boolean matrix multiplication and transitive closure. Twelfth Annual IEEE. Symposium on Switching and Automata Theory, East Lansing, Michigan, 1971, 129–131Google Scholar
  5. [5]
    Kolmogorov, Uspenskij: On the definition of an algorithm. Uspecki mat. Nauk 13,4 3–28 (1958), English translation in: Amer.math.Soc. Transl.II Ser.29, 217–245 (1963)Google Scholar
  6. [6]
    Schnorr, C.P.: Rekursive Funktionen und ihre Komplexität. Teubner, Stuttgart 1974Google Scholar
  7. [7]
    Schönhage, A.: Universelle Turingspeicherung. In: Automatentheorie und formale Sprachen. Ed.: Dörr, Hotz. B.I. Mannheim Wien Zürich, 1970Google Scholar
  8. [8]
    Warshall, S.: A theorem on Boolean matrices. J. ACM 9 (1962), 11–12CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • C. -P. Schnorr

There are no affiliations available

Personalised recommendations