Talk:Maximal elements algorithms

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As far as I know, Kosaraju's algorithm finds the "strongly connected components" of a directed graph. But the Schwartz set is not identical to the "strongly connected components", but to the "communicating classes" of a directed graph.

A strongly connected component SCC is a set of knots with the following property:

  1. If knot A is in SCC and knot B is in SCC \ {A}, then there is a directed path from knot A to knot B, that consists only of knots in SCC, and a directed path from knot B to knot A, that consists only of knots in SCC.

On the other side, a communicating class CC is a set of knots with the following properties:

  1. If knot A is in CC and knot B is in CC \ {A}, then there is a directed path from knot A to knot B and a directed path from knot B to knot A.
  2. If knot A is in CC and there is a directed path from knot B to knot A, then also knot B is in CC.

Markus Schulze 04:44, 27 October 2006 (PDT)