Quadtree vs Alternatives: R-tree, Geohash, and Hexagonal Grids

Quadtree Characteristics
Quadtrees adapt to data distribution, creating fine subdivisions where points cluster. Tree structure enables efficient pruning during queries. Good for point data with non-uniform distribution. In-memory implementation is straightforward. Supports dynamic inserts and deletes.
Limitations: square cells are poor approximations of circles, causing over-fetch at cell boundaries. Deep trees in dense regions can cause traversal overhead. Not inherently designed for disk storage; requires serialization strategy.
R-tree Comparison
R-trees group nearby points into bounding rectangles. Rectangles can overlap, allowing flexible grouping. Optimized for disk access: each node fills a disk page. Standard in spatial databases like PostGIS.
R-trees excel at range queries and nearest neighbor searches. They handle rectangles and polygons natively, not just points. The trade-off is complexity: insertion requires choosing which rectangle to expand, potentially triggering splits and rebalancing.
Geohash and H3 Comparison
Geohash and H3 are grid-based: fixed cell structure independent of data. No tree traversal needed; cells are computed directly from coordinates. Work well with standard databases using prefix or equality queries.
Grids waste space in empty regions and lack detail in dense regions. Quadtrees adapt; grids do not. But grids are simpler to implement, shard, and cache. For billion-point datasets, grid simplicity often beats quadtree adaptivity.
🎯 When To Use: Quadtrees for in-memory indexes with non-uniform data and dynamic updates. R-trees for disk-based spatial databases with complex shapes. Geohash/H3 for distributed systems needing simple, shardable cell IDs.

💡 Key Takeaways

✓Quadtrees adapt to density; good for in-memory with non-uniform data

✓R-trees use bounding rectangles, optimized for disk, handle complex shapes

✓Geohash/H3 are fixed grids: simpler, shardable, but waste space in empty regions

✓Quadtrees excel at dynamic updates; grids excel at distributed queries

✓Choose based on data distribution, storage system, and query patterns

📌 Interview Tips

1Compare adaptation: quadtree creates fine cells only where data exists; geohash allocates cells regardless of content

2For PostGIS or spatial database, recommend R-tree: built-in, disk-optimized, handles polygons

3For distributed key-value store, recommend geohash: simple cell IDs work as keys without tree traversal

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