When the map gets built: paying later, or paying less
How can the cost of building an index be deferred or shrunk?
So far every index was built up front and paid for in full. Three ideas relax that.
Sparse indexing (Index anatomy): index every Nth key and pay a bounded scan inside the block. Quantization (Key domains): index a lossy copy of the data and accept some recall loss. Two more ideas change when the map is built rather than what it maps.
Cracking (adaptive indexing). The index is built as a side effect of querying. The first query that filters a column splits the data into "below the boundary" and "above the boundary". Each later query splits the pieces further. Frequently queried regions become finely ordered, and untouched regions stay unordered. You pay nothing up front, and the index follows the workload.
Learned indexes. An index is a function from key to position. A sorted array's position function is the cumulative distribution of the keys, so one can fit a model to it (a line, a small neural network) and keep a small error bound for a final local search. The idea is worth understanding because it reframes what an index is. But it is research, not current engineering practice: the update problem (what happens to the fit when keys are inserted) is unsolved enough that no major production system relies on one. Treat it as an interesting direction, not as a live option.
The common point: the data's own distribution is information. Sparse indexes, zone maps, cracking and learned indexes all exploit it; the difference is when and how the exploitation is paid for.