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To demonstrate the computational value of depth-first search for developing linear-time graph algorithms.

Depth-First Search and Linear Graph Algorithms

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To demonstrate the computational value of depth-first search for developing linear-time graph algorithms.
Formulated an improved depth-first search algorithm to identify strongly connected components in directed graphs.
Constructed a depth-first search algorithm to detect biconnected components in undirected graphs.
Evaluated asymptotic space and time requirements as linear functions of graph vertices and edges.
The strongly connected components algorithm operates within space and time bounds of k1*V + k2*E + k3 for constants k1, k2, and k3.
The biconnected components algorithm achieves equivalent linear space and time complexity proportional to total vertices (V) and edges (E).

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Algorithmic analysis demonstrates linear-time computation for graph components, indicating depth-first search yields optimal processing bounds.

Robert E. Tarjan (1972) studied this question.

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Algorithmic analysis demonstrates linear-time computation for graph components, indicating depth-first search yields optimal processing bounds.