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  1. Is Topological sort's method BFS or DFS, Which is right?
    (I think BFS is right but some site said DFS and some said BFS. I'm confused...)

  2. Is Kahn's algorithm same to the BFS(or DFS)? or BFS(or DFS) is just tool for Kahn's algorithm?

ywbird
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  • Topological Sort can be done either way, but it's probably better/simpler/more efficient to do it like a BFS. IIRC, Kahn's algorithm is effectively a BFS. – RBarryYoung Oct 11 '21 at 11:27
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    Kahn's algorithm has nothing to do with BFS. – Matt Timmermans Oct 11 '21 at 14:15
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    @RBarryYoung, if I am interpreting the [Wikipedia article](https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm) correctly, then it says, "the structure S can be simply a set or a queue or a stack"; so I think Kahn's algorithm can also be implemented as DFS (by using a stack). Do you agree? Am I missing something? – Someone Mar 09 '22 at 04:00

1 Answers1

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Kahn's algorithm and DFS are both used to topological sorting in practice. Which to choose depends on your graph and its representation:

  • If you don't have easy access to the list of all vertices (like when you only get a reference to the root of the graph), then would have to do a search to find them all before implementing Kahn's algorithm, so you might as well use DFS and do your topological sort at the same time.

  • If your graph might have a long path, then it would be inappropriate to use a recursive search. A DFS implementation should use an explicit stack, and that makes it more complicated than Kahn's algorithm. If you do have a list of all vertices, then you probably want to use Kahn's algorithm instead.

If neither or both of the above apply, then it's pretty much a wash and you should use whichever you prefer. I would normally use Kahn's algorithm in this case, because detecting cycles in the input graph is easier to make fast and robust.

Matt Timmermans
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