SymphonyQG: Towards Symphonious Integration of Quantization and Graph for Approximate Nearest Neighbor Search

Approximate nearest neighbor (ANN) search in high-dimensional Euclidean space has a broad range of applications. Among existing ANN algorithms, graph-based methods have shown superior performance in terms of the time-accuracy trade-off. However, they face performance bottlenecks due to the random memory accesses caused by the searching process on the graph indices and the costs of computing exact distances to guide the searching process. To relieve the bottlenecks, a recent method named NGT-QG makes an attempt by integrating quantization and graph. It (1) replicates and stores the quantization codes of a vertex's neighbors compactly so that they can be accessed sequentially, and (2) uses a SIMD-based implementation named FastScan to efficiently estimate distances based on the quantization codes in batch for guiding the searching process. While NGT-QG achieves promising improvements over the vanilla graph-based methods, it has not fully unleashed the potential of integrating quantization and graph. For instance, it entails a re-ranking step to compute exact distances at the end, which introduces extra random memory accesses; its graph structure is not jointly designed considering the in-batch nature of FastScan, which causes wastes of computation in searching. In this work, following NGT-QG, we present a new method named SymphonyQG, which achieves more symphonious integration of quantization and graph (e.g., it avoids the explicit re-ranking step and refines the graph structure to be more aligned with FastScan). Based on extensive experiments on real-world datasets, SymphonyQG establishes the new state-of-the-art in terms of the time-accuracy trade-off.

Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search

Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory consumption. Recently, a method called RaBitQ achieves the state-of-the-art performance among these methods. It produces better empirical performance in both accuracy and efficiency when using the same compression rate and provides rigorous theoretical guarantees. However, the method is only designed for compressing vectors at high compression rates (32x) and lacks support for achieving higher accuracy by using more space. In this paper, we introduce a new quantization method to address this limitation by extending RaBitQ. The new method inherits the theoretical guarantees of RaBitQ and achieves the asymptotic optimality in terms of the trade-off between space and error bounds as to be proven in this study. Additionally, we present efficient implementations of the method, enabling its application to ANN queries to reduce both space and time consumption. Extensive experiments on real-world datasets confirm that our method consistently outperforms the state-of-the-art baselines in both accuracy and efficiency when using the same amount of memory.

iRangeGraph: Improvising Range-dedicated Graphs for Range-filtering Nearest Neighbor Search

Range-filtering approximate nearest neighbor (RFANN) search is attracting increasing attention in academia and industry. Given a set of data objects, each being a pair of a high-dimensional vector and a numeric value, an RFANN query with a vector and a numeric range as parameters returns the data object whose numeric value is in the query range and whose vector is nearest to the query vector. To process this query, a recent study proposes to build $O(n^2)$ dedicated graph-based indexes for all possible query ranges to enable efficient processing on a database of $n$ objects. As storing all these indexes is prohibitively expensive, the study constructs compressed indexes instead, which reduces the memory consumption considerably. However, this incurs suboptimal performance because the compression is lossy. In this study, instead of materializing a compressed index for every possible query range in preparation for querying, we materialize graph-based indexes, called elemental graphs, for a moderate number of ranges. We then provide an effective and efficient algorithm that during querying can construct an index for any query range using the elemental graphs. We prove that the time needed to construct such an index is low. We also cover an experimental study on real-world datasets that provides evidence that the materialized elemental graphs only consume moderate space and that the proposed method is capable of superior and stable query performance across different query workloads.

RaBitQ: Quantizing High-Dimensional Vectors with a Theoretical Error Bound for Approximate Nearest Neighbor Search

Searching for approximate nearest neighbors (ANN) in the high-dimensional Euclidean space is a pivotal problem. Recently, with the help of fast SIMD-based implementations, Product Quantization (PQ) and its variants can often efficiently and accurately estimate the distances between the vectors and have achieved great success in the in-memory ANN search. Despite their empirical success, we note that these methods do not have a theoretical error bound and are observed to fail disastrously on some real-world datasets. Motivated by this, we propose a new randomized quantization method named RaBitQ, which quantizes $D$-dimensional vectors into $D$-bit strings. RaBitQ guarantees a sharp theoretical error bound and provides good empirical accuracy at the same time. In addition, we introduce efficient implementations of RaBitQ, supporting to estimate the distances with bitwise operations or SIMD-based operations. Extensive experiments on real-world datasets confirm that (1) our method outperforms PQ and its variants in terms of accuracy-efficiency trade-off by a clear margin and (2) its empirical performance is well-aligned with our theoretical analysis.

High-Dimensional Approximate Nearest Neighbor Search: with Reliable and Efficient Distance Comparison Operations

Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations (DCOs). For each operation, it scans full dimensions of an object and thus, runs in linear time wrt the dimensionality. To speed it up, we propose a randomized algorithm named ADSampling which runs in logarithmic time wrt to the dimensionality for the majority of DCOs and succeeds with high probability. In addition, based on ADSampling we develop one general and two algorithm-specific techniques as plugins to enhance existing AKNN algorithms. Both theoretical and empirical studies confirm that: (1) our techniques introduce nearly no accuracy loss and (2) they consistently improve the efficiency.