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Tarjan's strongly connected components algorithm : ウィキペディア英語版 | Tarjan's strongly connected components algorithm
Tarjan's Algorithm is an algorithm in graph theory for finding the strongly connected components of a graph. Although proposed earlier, it can be seen as an improved version of Kosaraju's algorithm, and is comparable in efficiency to the path-based strong component algorithm. Tarjan's Algorithm is named for its discoverer, Robert Tarjan. == Overview ==
The algorithm takes a directed graph as input, and produces a partition of the graph's vertices into the graph's strongly connected components. Each vertex of the graph appears in exactly one of the strongly connected components. Any vertex that is not on a directed cycle forms a strongly connected component all by itself: for example, a vertex whose in-degree or out-degree is 0, or any vertex of an acyclic graph. The basic idea of the algorithm is this: a depth-first search begins from an arbitrary start node (and subsequent depth-first searches are conducted on any nodes that have not yet been found). As usual with depth-first search, the search visits every node of the graph exactly once, declining to revisit any node that has already been explored. Thus, the collection of search trees is a spanning forest of the graph. The strongly connected components will be recovered as certain subtrees of this forest. The roots of these subtrees are called the "roots" of the strongly connected components. Any node of a strongly connected component might serve as the root, if it happens to be the first node of the component that is discovered by the search.
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