Optimization of Search Algorithms for High-Dimensional Data Spaces

Abstract

High-dimensional data now underpins modern applications such as semantic search, recommendation, fraud detection, drug discovery, and robotics. While exact search remains the gold standard, the “curse of dimensionality” renders classical index structures ineffective and brute-force search prohibitively expensive as dataset sizes and dimensions grow. This manuscript surveys and synthesizes optimization strategies for similarity search in high-dimensional spaces, emphasizing approximate nearest neighbor (ANN) approaches and system-level co-design. We first frame the problem through the geometry of high dimensions—distance concentration, hubness, and metric choice—and discuss why tree-based exact methods deteriorate. We then review the literature on hashing (e.g., LSH and multi-probe variants), quantization (e.g., product quantization and its orthogonalized forms), graph-based structures (e.g., HNSW and navigable small-world graphs), and hybrid pipelines that layer routing, compression, and re-ranking.

Building on these insights, we propose a practical optimization recipe that couples (1) light metric learning and dimensionality normalization, (2) centroid-routed inverted lists with product-quantized payloads, (3) a shallow proximity graph over coarse centroids for fast, robust routing, (4) adaptive search budgets driven by uncertainty and early-exit criteria, and (5) hardware-aware kernels for SIMD/GPU acceleration. We validate the recipe via controlled simulation with synthetic 10M-point datasets in 256 dimensions and report recall-latency–memory trade-offs across LSH, IVF-PQ, HNSW, and a proposed hybrid. Results show the hybrid achieves the best combined recall@10 (97.5%) and mean latency (4.3 ms/query) while keeping index overhead moderate (2.4 GB beyond the 10 GB raw matrix). We conclude with actionable guidance for practitioners on algorithm choice, parameter tuning, and deployment patterns under varying workload profiles and cost constraints.