Design a custom algorithm for Approximate Nearest Neighbor (ANN) search in a high-dimensional vector space (e.g., 1024 dimensions) that optimizes for memory efficiency over query speed. Compare your approach against Hierarchical Navigable Small World (HNSW) graphs and IVF (Inverted File) indexes. Explain the mathematical trade-offs involved in your distance metric selection (e.g., Euclidean vs. Cosine similarity) and provide pseudo-code for the indexing and retrieval processes.