A transitive closure algorithm

@article{Purdom1970ATC,
  title={A transitive closure algorithm},
  author={Paul Walton Purdom},
  journal={BIT Numerical Mathematics},
  year={1970},
  volume={10},
  pages={76-94}
}
  • P. Purdom
  • Published 1 March 1970
  • Mathematics, Computer Science
  • BIT Numerical Mathematics
An algorithm is given for computing the transitive closure of a directed graph in a time no greater thana1N1n+a2n2 for largen wherea1 anda2 are constants depending on the computer used to execute the algorithm,n is the number of nodes in the graph andN1 is the number of arcs (not counting those arcs which are part of a cycle and not counting those arcs which can be removed without changing the transitive closure). For graphs where each arc is selected at random with probabilityp, the average… 
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