Tarjan's strongly connected components algorithm: Difference between revisions

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The Root Property: v'.dfs should read v'.index in the v.lowlink property
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== The Root Property ==
 
The crux of the algorithm comes in determining whether a node is the root of a strongly connected component. To do this, each node is given a depth search index <tt>v.index</tt>, which numbers the nodes consecutively in the order in which they are discovered. In addition, each node is assigned a value <tt>v.lowlink</tt> that satisfies <tt>v.lowlink := min {v'.dfsindex: v' is reachable from v}</tt>. Therefore <tt>v</tt> is the root of a strongly connected component if and only if <tt>v.lowlink = v.index</tt>. The value <tt>v.lowlink</tt> is computed during the depth first search such that it is always known when needed.
 
== The Algorithm in [[pseudocode]] ==