I'd recommend Text::CSV_XS for reading the CSV file, though the structure seems reliable enough to simply use split if you wish.

I'd start by storing the data in a hash of hashes, but perhaps hash of arrays will be needed if multiple children nodes are possible.

There might be some useful tools in List::Utils, but if not, I'd probably store a sister element with depth as I walked through the tree (more efficient to build that whilst assembling the master tree, I should think).

From there it is likely to be straight subtraction of the depth values and select the smallest one(s). Would likely expect a tree walk for that part.

Probably build a reverse path hash on the way in, report on it on the way out.

For more details, post some code and show what isn't working as expected.