arXiv subjects

Achilleas Michalopoulos

Publications and source records attributed to Achilleas Michalopoulos.

3 recordsLinked to original sources

arXiv2026

In-memory Multidimensional Indexing Using the skd-tree

In this paper, we revisit the problem of indexing multi-dimensional data in memory for the efficient support of multi-dimensional range queries and nearest neighbor queries. This is a classic problem in main-memory databases, where there is a need for indexing multiple columns simultaneously. Established data structures include the R-tree, kd-tree, quad-tree, and grid-based partitioning. More recently, multi-dimensional learned indexes have also been proposed to address this problem. We propose slicing kd-tree (skd-tree), a variant of the kd-tree, where each node partitions the space of its subtree into multiple slices across a single splitting dimension. By compressing the splitters of the partitions and with the help of data-parallelism, we (i) radically reduce the number of levels of the tree and (ii) limit the number of computations required for multi-dimensional range and proximity queries. The nodes of the skd-tree resemble the nodes of a main-memory B+-tree, however, a different dimension is used at each level. Our novel range and kNN algorithms on the skd-tree apply only a small constant number of SIMD instructions at each node during tree traversal. Our contributions also include a novel top-down construction algorithm, different types of inner and leaf nodes that warrant tree balancing, and a novel update algorithm. Our skd-tree achieves strong performance compared to existing methods, according to our experimental evaluation on real and synthetic datasets.

cs.DB↗

arXiv2026

CRISP: Correlation-Resilient Indexing via Subspace Partitioning

As the dimensionality of modern learned representations increases to thousands of dimensions, the state-of-the-art Approximate Nearest Neighbor (ANN) indices exhibit severe limitations. Graph-based methods (e.g., HNSW) suffer from prohibitive memory consumption and routing degradation, while recent randomized quantization and learned rotation approaches (e.g., RaBitQ, OPQ) impose significant preprocessing overheads. We introduce CRISP, a novel framework designed for ANN search in very-high-dimensional spaces. Unlike rigid pipelines that apply expensive orthogonal rotations indiscriminately, CRISP employs a lightweight, correlation- aware adaptive strategy that redistributes variance only when necessary, effectively reducing the preprocessing complexity. We couple this adaptive mechanism with a cache-coherent Compressed Sparse Row (CSR) index structure. Furthermore, CRISP incorporates a multi-stage dual-mode query engine: a Guaranteed Mode that preserves rigorous theoretical lower bounds on recall, and an Optimized Mode that leverages rank-based weighted scoring and early termination to reduce query latency. Extensive evaluation on datasets of very high dimensionality (up to 4096) demonstrates that CRISP achieves state-of-the-art query throughput, low construction costs, and peak memory efficiency.

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arXiv2025

BS-tree: A gapped data-parallel B-tree

We propose BS-tree, an in-memory implementation of the B+-tree that adopts the structure of the disk-based index (i.e., a balanced, multiway tree), setting the node size to a memory block that can be processed fast and in parallel using SIMD instructions. A novel feature of the BS-tree is that it enables gaps (unused positions) within nodes by duplicating key values. This allows (i) branchless SIMD search within each node, and (ii) branchless update operations in nodes without key shifting. We implement a frame of reference (FOR) compression mechanism, which allows nodes to have varying capacities, and can greatly decrease the memory footprint of BS-tree. We compare our approach to existing main-memory indices and learned indices under different workloads of queries and updates and demonstrate its robustness and superiority compared to previous work in single- and multi-threaded processing.

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