Question: What is generally the fastest algorithm to recursively make a directory (similar to UNIX mkdir -p) using the FTP protocol?

I have considered one approach:

1. MKDIR node
2. if error and nodes left go to 1 with next node
3. end

But this might have bad performance if part of the directory most likely exists. For example, with some amortization the "/a/b/c/d" part of "/a/b/c/d/e/f/g" path exists %99 of the time.

Answer: 
Considering that sending a command and receiving the response is taking most of the time, the fastest way to create a directory path is using as few commands as possible. 

As there is no way other than to try to create or cd into a directory to check for its existence, just using mkdir a; mkdir a/b; ..., mkdir a/b/c/d/e/f would be the generally fastest way (do not cd into the subdirectories to create the next as this would prolong the process).

If you create multiple directories this way, you could of course keep track of which top-level directories you already created. Also, depending on the length of your paths and the likelihood that the upper directories already exist, you could try to start with e.g. mkdir a/b/c (for a/b/c/d/e/f) and then backtrack if it did not succeed. However if it's more likely that directories do not exist this will actually be slower in the long run.
If the existing directory hierarchy is equally likely to end at any given depth, then **binary searching** for the start position will be the fastest way. But as [dseifert points out](https://stackoverflow.com/questions/901979/the-fastest-way-to-implement-mktree-in-ftp/903540#903540), if most of the time the directories already exist down to say level k, then it will be faster to start binary searching at level k rather than level n/2.

BTW, you'd have to be creating *a lot* of *very deep* directories for this sort of optimisation to be worth your time. Are you sure you're not optimising prematurely?