## Depth-first search is inherently sequential.(English)Zbl 0572.68051

This paper concerns the computational complexity of depth-first search. Suppose we are given a rooted graph G with fixed adjacency lists and vertices u,v. We wish to test if u is first visited before v in depth- first search order of G. We show that this problem, for undirected and directed graphs, is complete in deterministic polynomial time with respect to deterministic log-space reductions. This gives strong evidence that depth-first search ordering can be done neither in deterministic space (log n)$${}^ c$$ nor in parallel time (log n)$${}^ c$$, for any constant $$c>0$$.

### MSC:

 68R10 Graph theory (including graph drawing) in computer science
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### References:

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