What key domains forbid

What this article forbids

You cannot range-query a hash.
You cannot get one contiguous run in two dimensions.
You cannot have uniform adjacency and exact hierarchical nesting in the same cell system.
You cannot guarantee exact nearest-neighbor results in high dimension without examining effectively everything.
You cannot update a posting list or an ANN graph in place at reasonable cost, which is why both grow the same tombstone-and-merge apparatus.

Escapes and prices

Linearization escapes dimensionality, priced in perimeter-many seeks plus false positives.
Partitioning escapes fragmentation, priced in overlap or imbalance.
Inversion escapes the wrong-key problem, priced in immutable segments and a merge policy.
Quantization escapes the memory cliff, priced in recall.
Graph navigation escapes partition scanning, priced in build cost and unsolved deletion.
Correlated layout escapes the index entirely: the only free one in the list, and only while the correlation holds.

Case, resolvedConstructed case · Priya at Parcelo

A depot finder that reads half the table

A depot finder on (latitude, longitude) read much of the table, a LIKE '%bicycle%' support search took minutes, nearest-neighbor search over 100 million item embeddings was hopeless, and a batch of late offline scans made recent time-range queries read far more. Where it started: Key domains →

Depot finder. A plain B-tree on (latitude, longitude) gives one run only for latitude; the longitude filter is applied entry by entry. She keys the index with a cell id from a space-filling-curve scheme (a geohash-like cell at about 1 km resolution). A 2 km radius query becomes a covering of a few cells (the number of runs grows with the perimeter of the search circle), one range seek per cell, then an exact distance check on the candidates to remove false positives.
Support search. She replaces LIKE '%bicycle%' with an inverted index. Queries intersect posting lists starting from the rarest word, and results are ranked with top-k early termination. The query that took minutes returns in tens of milliseconds. She also notes that a query made only of very common words gets no pruning, so the search form requires at least one non-common term.
Similar items. Exact search over 100 million 768-dimensional vectors has nothing to prune. She counts memory first: 100 million × 3,072 B is about 300 GB, which does not fit on one machine. Product quantization to 96 bytes per vector (about 10 GB) crosses the memory cliff, and a graph or inverted-file index on top gives millisecond answers at the price of some missed neighbors. She measures recall against exact results on a sample before agreeing to it.
Late events. The offline batch broke the correlation between timestamp and arrival order, so block min/max ranges now overlap. She sorts the late batch into a separate, correctly time-ordered load (or rewrites the affected blocks) so each block has a narrow range again.