How does memory consumption grow with dataset size for different index types, and what methods can be used to estimate or control memory usage when scaling up?

Memory consumption for indexes generally grows linearly with dataset size, but the rate varies by index type and implementation. Hash-based indexes (like hash tables) typically use O(n) space, storing a fixed overhead per entry, but collisions or load factors can increase memory use. Tree-based indexes (e.g., B-trees) also scale linearly but have higher constants due to node structures (e.g., pointers, keys per node). Inverted indexes, common in search engines, grow with the number of unique terms and their document associations, which can be superlinear in edge cases (e.g., many unique terms). For example, a hash index storing 1 million 64-bit keys with 8-byte values might use ~16 MB (24 bytes per entry), while a B-tree with 50 keys per node might require ~20% more due to internal node overhead. Sparse or compressed indexes (e.g., bitmap indexes) can reduce growth rates by exploiting data patterns, but this depends on the data’s compressibility.

To estimate memory usage, calculate the per-entry overhead of the index structure. For a hash index, this includes the key, value, and any collision handling (e.g., linked list pointers). For a B-tree, estimate node size (keys + child pointers) multiplied by tree height. Tools like sizeof() in C++ or memory profilers (e.g., Valgrind) can measure real-world usage. Sampling helps: index a subset (e.g., 10% of data), measure memory, and extrapolate. For example, if indexing 100k entries uses 16 MB, scaling to 10 million might require ~1.6 GB, adjusted for data distribution (e.g., larger keys increase memory). Database systems like PostgreSQL provide pg_relation_size to monitor index size, while in-memory stores like Redis offer INFO memory metrics.

To control memory, consider trade-offs between speed and space. Use compressed indexes (e.g., prefix compression in B-trees) or probabilistic structures (Bloom filters) for approximate membership checks. Shard large datasets across multiple indexes or machines to limit per-instance growth. Tune parameters: adjust hash table load factors to balance collision rates and memory, or limit B-tree node sizes. For example, decreasing a hash table’s load factor from 0.75 to 0.5 reduces collisions but increases memory by ~33%. Disk-based indexing (e.g., using LMDB) offloads parts of the index from RAM but sacrifices latency. Prioritize memory-efficient data types—using 32-bit integers instead of strings for document IDs in an inverted index can save 50% of space. Regularly monitor and prune unused entries (e.g., TTL in Redis) to prevent unbounded growth.