REACH’s 2.49× search gain comes from one index—not one index per geographic filter

What the benchmark actually tests

REACH targets a narrower problem than ordinary approximate nearest-neighbor search: retrieve the nearest vectors only among objects inside a query-centered geographic disk. The paper evaluates that geo-filtered ANN task on four datasets, with the largest containing 10 million objects, and sweeps six mean selectivities from roughly 0.00001 to 1. Its headline comparison fixes quality at 0.95 Recall@10 and reports throughput in queries per second.

On the selective-query portion of that evaluation, REACH delivers 2.49× higher geometric-mean QPS than the strongest baseline selected separately for each setting. It is fastest in 14 of 16 selective dataset/selectivity cells. Against two named spatial-graph baselines, the reported throughput multipliers are 6.33× over CubeGraph and 3.56× over Geo-Partition. These are evaluation results from the paper, not independent reproductions.

Why the single-index detail matters

The comparison is not merely another graph-search tuning result. Geographic disks can produce many different active subsets, while a normal proximity graph loses routes when out-of-disk vertices are removed. Some alternatives compensate by scanning all eligible objects, over-fetching global candidates or maintaining partition-specific graph structures.

REACH instead stores one fixed-width, vector-distance-sorted neighbor row per object. At query time it skips inactive neighbors and evaluates only the first requested number of active entries. The paper’s claim is therefore that one static graph can retain useful navigation across changing disk filters, rather than requiring a separate index for every geographic region or selectivity regime.

That design also changes the infrastructure comparison. Relative to CubeGraph, the paper reports 3.8× to 11.9× faster index construction. On three of the four datasets, REACH uses 37% to 45% less index space. Those figures are separate from query throughput and should not be folded into the 2.49× number.

The caveat hidden in the headline

The 2.49× result is a geometric mean over selective queries at a fixed 0.95 Recall@10 target. It is not an all-query average, not a latency claim at perfect recall and not evidence that REACH accelerates unfiltered ANN by the same factor. The paper says performance remains comparable on non-selective settings; its strongest advantage is where disk filtering removes enough graph vertices to damage conventional routing.

That is still a useful benchmark result. It isolates a real failure mode in location-aware vector retrieval and measures quality, throughput, build time and index size separately. The next evidentiary step is an artifact release or independent rerun that can test whether the 14-of-16 selective-cell advantage survives different hardware, implementations and geographic distributions.