Why do separate B-tree indexes on latitude and longitude fail for proximity search?

Why do separate B-tree indexes on latitude and longitude fail for proximity search?

• A. They treat two dimensions independently, creating broad rectangles requiring distance filtering.
• B. They perform too many in-place updates.
• C. They cannot handle any queries beyond exact matches.
• D. They can't support ordering by distance.

Answer: (A)

Proximity search in two dimensions needs to consider latitude and longitude together. A B-tree on latitude orders points by one dimension, and a separate B-tree on longitude orders points by the other. To find nearby points, you’d have to pull points from a latitude window and a longitude window and then intersect those results. That creates a large set of candidate points arranged as broad rectangles in the plane, many of which are far from the query location. You then must compute the actual distance for each candidate to filter out the far ones, which is very inefficient. In contrast, a spatial index (like an R-tree, kd-tree, or a grid/geohash-based index) organizes data with the two dimensions in mind, so proximity queries can directly prune candidates that are outside the radius without enumerating a huge cross-section. That’s why separate 1D indexes fail for proximity search: they don’t capture the joint spatial relationship between latitude and longitude, forcing heavy post-filtering.

Proximity search in two dimensions needs to consider latitude and longitude together. A B-tree on latitude orders points by one dimension, and a separate B-tree on longitude orders points by the other. To find nearby points, you’d have to pull points from a latitude window and a longitude window and then intersect those results. That creates a large set of candidate points arranged as broad rectangles in the plane, many of which are far from the query location. You then must compute the actual distance for each candidate to filter out the far ones, which is very inefficient.

In contrast, a spatial index (like an R-tree, kd-tree, or a grid/geohash-based index) organizes data with the two dimensions in mind, so proximity queries can directly prune candidates that are outside the radius without enumerating a huge cross-section. That’s why separate 1D indexes fail for proximity search: they don’t capture the joint spatial relationship between latitude and longitude, forcing heavy post-filtering.