Assigning to $#array is preferrable, I just didn't think of that off of the top of my head.
The two-level index should work. The overhead of accessing it indirectly may lose the benefits of avoiding reallocations.
When it comes to strings, I was thinking something simpler. Use 4 bytes per offset. Pack each offset into those 4 bytes. Sure, you can save more memory, but see if the simple approach is a big enough win. (It certainly should take less code, and makes it easy to access the 432343rd offset - depending on what you do this could be a big win.)
Personally I'd avoid all of these approachs unless I knew that the naive approach had serious problems for my dataset. (Yes, you've indicated why you think that it may for you. This is a reminder for anyone else who might be reading this thread.)
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