Quadtree is a spatial index that subdivides a region into four quadrants. Which statement about quadtrees is correct?

Quadtree is a spatial index that subdivides a region into four quadrants. Which statement about quadtrees is correct?

• A. A data structure used only for integer keys in memory.
• B. A tree-based spatial index that subdivides a region into four quadrants, foundational for R-trees and used in Google Maps tiling.
• C. The primary indexing structure for relational databases today.
• D. A 2D expansion of B-tree used for numeric keys.

Answer: (B)

The main idea being tested is hierarchical spatial partitioning using four-way subdivision. A quadtree represents space as square regions, and when more detail is needed, each region is split into four equal quadrants (typically labeled for reference as NW, NE, SW, SE). This creates a tree where leaves correspond to areas that either hold data or meet some capacity threshold, and internal nodes represent larger areas that encompass their children. The power of this structure is that queries—like finding all objects within a region or nearby points—can skip entire branches of the tree that don’t intersect the query area, making spatial searches efficient. This is why the statement is correct: a quadtree is a tree-based spatial index designed around four-quadrant subdivision, and it naturally supports hierarchical tiling schemes used in maps. Map services, including Google Maps tiling, use a quadtree-like subdivision to represent the world at multiple zoom levels, producing tiles that cover progressively smaller areas as you zoom in. The other descriptions don’t fit because quadtrees are not restricted to integer keys in memory, they aren’t the primary indexing structure for relational databases (that role is typically B-trees and their variants), and they are not simply a 2D expansion of B-trees.

The main idea being tested is hierarchical spatial partitioning using four-way subdivision. A quadtree represents space as square regions, and when more detail is needed, each region is split into four equal quadrants (typically labeled for reference as NW, NE, SW, SE). This creates a tree where leaves correspond to areas that either hold data or meet some capacity threshold, and internal nodes represent larger areas that encompass their children. The power of this structure is that queries—like finding all objects within a region or nearby points—can skip entire branches of the tree that don’t intersect the query area, making spatial searches efficient.

This is why the statement is correct: a quadtree is a tree-based spatial index designed around four-quadrant subdivision, and it naturally supports hierarchical tiling schemes used in maps. Map services, including Google Maps tiling, use a quadtree-like subdivision to represent the world at multiple zoom levels, producing tiles that cover progressively smaller areas as you zoom in. The other descriptions don’t fit because quadtrees are not restricted to integer keys in memory, they aren’t the primary indexing structure for relational databases (that role is typically B-trees and their variants), and they are not simply a 2D expansion of B-trees.