In-memory Multidimensional Indexing Using the skd-tree
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918484637646848 |
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| author | Michalopoulos, Achilleas Tsitsigkos, Dimitrios Mamoulis, Nikos |
| author_facet | Michalopoulos, Achilleas Tsitsigkos, Dimitrios Mamoulis, Nikos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | In-memory Multidimensional Indexing Using the skd-tree Michalopoulos, Achilleas Tsitsigkos, Dimitrios Mamoulis, Nikos Databases 97P30 H.2.2 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. |
| title | In-memory Multidimensional Indexing Using the skd-tree |
| topic | Databases 97P30 H.2.2 |
| url | https://arxiv.org/abs/2605.03640 |