Dynamic Approximate Neighbours

• Dynamic ANN is a paradigm that extends classical approximate nearest neighbour search to support real-time data updates, ensuring efficient query speed and adaptable indexing.
• Techniques such as retroactive data structures, online vector quantization, and graph-based indexes optimize update costs while maintaining high recall in mutable, high-dimensional spaces.
• This approach is pivotal for practical deployments in vector databases, computer vision, and real-time recommendation systems by balancing speed, accuracy, and memory efficiency.

Dynamic Approximate Nearest Neighbours (Dynamic ANN) encompasses a broad range of algorithmic and data structural techniques that enable efficient, high-quality nearest neighbour queries over datasets that evolve over time through insertions, deletions, and updates. These dynamic scenarios arise in modern AI workloads, vector databases, spatiotemporal systems, and a variety of sensor-driven or streaming data applications, in contrast to traditional static settings where the dataset is fixed post-construction. Dynamic ANN research targets the core challenge of maintaining query speed, approximation quality, and index efficiency in highly mutable environments, often under strict computational and memory constraints.

1. Fundamental Concepts and Evolution of Dynamic ANN

Dynamic ANN generalizes the classical approximate nearest neighbour problem to face online modifications: points may be inserted, deleted, or altered, and queries must remain efficient and accurate even as the dataset structure changes. Early research primarily tackled static datasets, utilizing spatial partitioning trees (e.g., k-d trees) or quantized codes (e.g., Product Quantization). Dynamic scenarios introduce additional complexity, particularly in high-dimensional settings where partitioning-based or quantisation-based indexes may require expensive global restructuring for each update.

Different paradigms have developed in response:

• Retroactive Data Structures: Handling insertions and deletions at arbitrary timeline points, not just in real-time, to support queries with historical semantics (Goodrich et al., 2011).
• Online and Streaming Quantisation: Mechanisms such as Dictionary Annealing and HCLAE adapt vector quantization codebooks with each batch of new arrivals, supporting both online feature learning and continuous ingestion (Liu et al., 2015, Liu et al., 2015).
• Incremental Graph-Based Indexes: Dynamic proximity graphs such as HNSW, DEG, and CleANN maintain neighbour relationships via local or global rewiring upon updates, targeting minimization of search path inflation and degradation (Doshi et al., 2020, Hezel et al., 2023, Zhang et al., 26 Jul 2025).
• Adaptive, Data-Aware Operations: Methods like DADE achieve efficiency by reducing the dimensionality of distance comparisons adaptively per candidate, tightly controlling recall/speed/accuracy trade-offs as the underlying data distribution evolves (Deng et al., 26 Nov 2024).

2. Data Structures and Algorithms for Dynamic ANN

A wide spectrum of data structures has been proposed to handle the demands of dynamic updates:

Index Type	Update Support	Query Speed	Scaling
Retroactive Segment Trees	Full (any time)	O(log n)	O(n log n/log log n) (Goodrich et al., 2011)
Online Vector Quantization	Batches [insert]	O(1) encode	GPU-ready (Liu et al., 2015, Liu et al., 2015)
Dynamic Graphs (DEG, CleANN, HNSW)	Local/global	O(log n)–sublinear	Web-scale, multi-thread (Hezel et al., 2023, Zhang et al., 26 Jul 2025)
LSH with Dynamic Encoding	Insert/Delete	O(log n)	High-dim. (Wei et al., 16 Jun 2024)
Adaptive Estimation	Any	Data-dependent	High-dim., plug-in (Deng et al., 26 Nov 2024, LeJeune et al., 2019)

• Segment Trees with Multidimensional Structures: A retroactive segment tree indexes temporal intervals, with each node augmented by a spatial ANN structure (quadtree, skip-quadtree, or skip-list in z-order). Fractional cascading using space-filling curves enables efficient O(log n) retroactive queries. Update amortization and approximation factors are explicit, e.g., c = √d(4d+4)+1 (Goodrich et al., 2011).
• Graph-Based Indexes: Structures such as DEG (Hezel et al., 2023) or CleANN (Zhang et al., 26 Jul 2025) maintain even-regular or workload-aware graphs, enabling incremental or concurrent insert/delete operations. The core innovation lies in separating local (neighbourhood) update cost from global index maintenance, employing edge optimization, consolidation, and semi-lazy cleaning to ensure scalability and stable recall under dynamism.
• Dual-Index and Tiered Approaches: DQF maintains both a “hot” index for high-frequency (popular) queries and a full index for completeness. A decision tree dynamically determines whether a query’s answer can terminate early (reducing full index accesses), optimizing for practical query distributions (Zipfian, non-uniform) (Gao et al., 10 Aug 2025).
• Dynamic Encoding Trees: DET-LSH eschews classic multi-dimensional space partitioning, using dynamically determined per-dimension encodings (iSAX-like) and multiple independent DE-Trees to support range and k-ANN queries with efficient independent updates. Query accuracy is maintained probabilistically via tailored search radius adjustments (Wei et al., 16 Jun 2024).

3. Analytical Guarantees, Complexity, and Limitations

Dynamic ANN methods quantify their performance through explicit bounds and empirical results. Common metrics include worst-case and amortized update complexity, query time, space consumption, and recall (ratio of correct neighbours returned). Core theoretical guarantees include:

• Retroactive Structures: O(log n) amortized update, O(log n) query time, and O(n log n / log log n) space for (1+ε)-ANN/range queries for fixed d, with constants growing exponentially with d (Goodrich et al., 2011).
• Dynamic Graphs: Throughput improvements of 7–1200× for CleANN over previous dynamic methods are attributed to (i) concurrent operation support, (ii) workload-aware linking, and (iii) memory cleaning techniques. Theoretical and empirical evidence demonstrate nearly static-level recall (Zhang et al., 26 Jul 2025).
• DADE Adaptive Estimation: Distance estimation uses PCA-computed orthogonal projections, combining dimensional reduction with hypothesis testing so that the expected value of the approximation remains unbiased:

$$E[\|X_1 - X_2\|^2] = \frac{\sum_{k=1}^D \lambda_k}{\sum_{k=1}^d \lambda_k}E[\|W_d^T X_1 - W_d^T X_2\|^2]$$

Incremental dimensionality is selected until the hypothesis test supports a confident decision (Deng et al., 26 Nov 2024).

• LSH with Dynamic Trees: Success probability for correct ANN retrieval is at least $1/2 - 1/e$, with indexing and query speedups up to 6× and 2×, respectively, over previous LSH-based approaches, in high-dimensional dynamic regimes (Wei et al., 16 Jun 2024).

Limiting factors noted in the literature include:

• High constants due to complicated secondary structures (e.g., CDFC, skip-quadtrees) or space-filling curve orderings (retroactive and high-dim encodings).
• Exponential dependence on intrinsic or ambient dimension for methods where the underlying assumption is fixed d.
• Amortized bounds may hide infrequent but costly rebuild or rebalancing stages in practice, especially under highly non-uniform updates.
• Sensitivity to memory overheads in quantization or graph-based approaches under large-scale, streaming ingestion (Harwood et al., 30 Apr 2024).
• Sparse data or rapidly changing query distributions can degrade certain data-dependent indexes (e.g., k-d trees under high update rates (Harwood et al., 30 Apr 2024)).

4. Adaptation to Dynamic Workloads and Data Distributions

Adaptivity is a recurring theme in contemporary dynamic ANN design:

• Index Structures: LANNS partitions web-scale data via sharding and segmentation, enabling parallel HNSW index construction and query processing with minimal recall loss, even under distributed or changing workloads (Doshi et al., 2020).
• Query Preference Awareness: DQF and GATE introduce learning-based mechanisms to prioritize hot entries or optimal entry points for non-uniform, time-evolving query distributions. DQF uses a small “hot” index that can be quickly rebuilt as query popularity drifts, maintaining high throughput and recall while limiting maintenance cost (Gao et al., 10 Aug 2025). GATE leverages contrastive learning on topological and semantic node features to adapt entry point selection in proximity graphs, reducing traversal redundancy and path length (Ruan et al., 19 Jun 2025).
• Online and Streaming Quantization: Dictionary Annealing and HCLAE support online updates, allowing codebooks and encoding trees to be refined incrementally as new data streams in, thus retaining compression efficiency and search accuracy in streaming or batch-incremental scenarios (Liu et al., 2015, Liu et al., 2015).
• Adaptive Estimation: DADE determines, for each query-candidate pair, the minimum number of dimensions necessary for a confident distance estimation under a specified error probability, thus automatically balancing per-query compute cost and accuracy (Deng et al., 26 Nov 2024). Dynamic Continuous Indexing also adapts retrieval effort to local data density, retrieving more candidates in dense regions (Li et al., 2015).

5. Hardware-Conscious and Large-Scale Dynamic ANN

At web and data-center scale, hardware-aware methods and hybrid storage architectures emerge as crucial:

• In-Storage and DRAM-PIM Accelerators: NDSearch applies near-data processing (NDP), embedding graph traversal and distance computation kernels directly into SSDs (SEARSSD), thereby circumventing PCIe and memory bottlenecks for massive graphs (Wang et al., 2023). DRIM-ANN aligns ANNS algorithms with DRAM-PIM hardware characteristics via multiplier-less look-up table (LUT) distance computations and two-tiered load balancing—dynamically partitioning and scheduling queries across thousands of memory-bound DPUs (Chen et al., 21 Oct 2024).
• Load Balancing and Scheduling: Both NDSearch and DRIM-ANN implement offline and online data locality optimizations, dynamically assigning requests and data partitions to minimize hot spots, data movement, and energy consumption at scale. DRIM-ANN, in particular, reports average speedups of 2.92× over high-end CPUs, with further gains as hardware improves.

6. Empirical Evaluation: Benchmarks and Practical Guidance

Modern dynamic ANN research stresses the importance of evaluating not only recall and latency on static data but also update efficiency and query throughput under continuous data ingestion. The CANDY benchmark exemplifies this trend, providing systematic evaluation across diverse datasets and optimization techniques (Zeng et al., 28 Jun 2024). Key empirical findings include:

• Simpler AKNN baselines often surpass highly complex algorithms in continuous ingestion scenarios, especially in terms of recall and latency.
• Dynamic adaptability—in indexing, search strategy, or candidate pruning—is paramount for maintaining quality as data patterns evolve.
• Trade-offs are dataset- and application-dependent, with batch size (update/search), event processing rates, and index scaling strategies significantly impacting overall system performance (Harwood et al., 30 Apr 2024).

7. Applications, Extensions, and Future Research Directions

Dynamic ANN underpins critical applications in:

• Vector and spatiotemporal databases (requiring retroactive or streaming query support)
• Computer vision and retrieval systems (dealing with streaming image/video embeddings)
• Real-time recommendation, fraud detection, and online learning systems

Recent work opens several directions:

• Integration of learning-driven adaptive mechanisms (as in GATE and DQF) to handle non-stationary query/user distributions.
• Hardware-aware and distributed system design for multi-modal, web-scale deployment (NDSearch, DRIM-ANN).
• Rigorous empirical benchmarks that expose update latency and index maintenance costs alongside recall and speed.
• Extensions to non-Euclidean geometry, such as dynamic hyperbolic space ANN with quadtrees and spanner structures (Kisfaludi-Bak et al., 2023).
• Data-aware pruning and estimation (DADE), suggesting even tightly coupled operations can be adaptively accelerated without recall loss.

In summary, dynamic approximate nearest neighbour search is a mature and rapidly evolving field, with a taxonomy of solutions that balance algorithmic, statistical, and hardware/engineering considerations. The spectrum of methods reflects a shared aim: robust, efficient, and high-quality search in environments where both the data and the queries are in perpetual flux.