is there a cheap/easy way to get sub O(N) performance, using the out-of-the-box functionality of perl?
No. It is possible to do o(N) queries, but only after ω(N) pre-processing time. That's independent of the language.
Further, I would like to be able to update the array (insert elements in the middle) with minimal cost.
If you mean by "updating", "adding more elements", using a traditional Perl array, it takes linear time.

In reply to Re^3: maintaining a sorted structure by JavaFan
in thread maintaining a sorted structure by Anonymous Monk

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