LMSFC: A Novel Multidimensional Index based on Learned Monotonic Space Filling Curves

Summary: LMSFC learns a monotonic, data- and workload-adaptive space-filling curve to map multidimensional points to 1D, replacing fixed SFCs (e.g., z-order) to improve locality for learned indexes. Provides offline/online SFC optimization and outperforms prior methods. (summarized by gpt-5-mini on Feb 09 2026)

Paper ID: h2b39ef918dd1c59c
Venue: VLDB
Year: 2023
Pagerank: 5.7196547e-05
Overall Rank: 6,604 | 55.74%
DOI: 10.14778/3603581.3603598
PDF: Download (CC BY-NC-ND 4.0)

Incoming Non-self Citations Over Time

Authors

1. Jian Gao (University of New South Wales)
2. Xin Cao (University of New South Wales)
3. Xin Yao (Huawei)
4. Gong Zhang (Huawei)
5. Wei Wang (Hong Kong University of Science and Technology)

BibTeX Citation

@article{gao_vldb23,
        title = {{LMSFC: A Novel Multidimensional Index based on Learned Monotonic Space Filling Curves}},
        author = {Gao, Jian and Cao, Xin and Yao, Xin and Zhang, Gong and Wang, Wei},
        journal = {PVLDB},
        series = {{VLDB} '23},
        volume = {16},
        number = {10},
        pages = {2605--2617},
        doi = {10.14778/3603581.3603598},
        url = {https://doi.org/10.14778/3603581.3603598},
        year = {2023}
}

Incoming Citations (Sorted by Pagerank)

Showing 6 of 6 citing papers.

Rank	Citing Paper	Year	Venue	Pagerank
6,889	Accelerating String-key Learned Index Structures via Memoization-based Incremental Training	2024	VLDB	5.6393954e-05
9,176	One Seed, Two Birds: A Unified Learned Structure for Exact and Approximate Counting	2024	SIGMOD	5.200391e-05
10,822	Toward Drift-Aware Database Benchmarking	2026	VLDB	4.9605343e-05
11,127	A Workload-Aware Encrypted Index for Efficient Privacy-Preserving Range Queries	2026	VLDB	4.9605343e-05
11,183	Optimizing Block Skipping for High-Dimensional Data with Learned Adaptive Curve	2025	SIGMOD	4.9605343e-05
11,712	Efficient Cost Modeling of Space-filling Curves	2024	VLDB	4.9605343e-05

Outgoing Citations (Sorted by Pagerank)

Showing 18 of 18 cited papers.

Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.

Rank	Cited Paper	Year	Venue	Pagerank
2	R-Trees: A Dynamic Index Structure For Spatial Searching	1984	SIGMOD	0.0019892478
4	The R*-tree: An Efficient and Robust Access Method for Points and Rectangles	1990	SIGMOD	0.0011386412
40	The Case for Learned Index Structures	2018	SIGMOD	0.00046249672
44	The R+-Tree: A Dynamic Multi-Dimensional Index for Objects	1987	VLDB	0.00045231517
338	Hilbert R-tree: An Improved R-tree Using Fractals	1994	VLDB	0.0002058961
427	ALEX: An Updatable Adaptive Learned Index	2020	SIGMOD	0.00018429918
461	The PGM-index: a fully-dynamic compressed learned index with provable worst-case bounds	2020	VLDB	0.00017835351
774	FITing-Tree: A Data-aware Index Structure	2019	SIGMOD	0.00014063511
834	Benchmarking Learned Indexes	2021	VLDB	0.00013539098
870	Learning Multi-dimensional Indexes	2020	SIGMOD	0.0001332034
1,064	Are We Ready For Learned Cardinality Estimation?	2021	VLDB	0.00012181459
1,132	Qd-tree: Learning Data Layouts for Big Data Analytics	2020	SIGMOD	0.00011873466
1,190	Tsunami: A Learned Multi-dimensional Index for Correlated Data and Skewed Workloads	2021	VLDB	0.00011564169
1,445	LISA: A Learned Index Structure for Spatial Data	2020	SIGMOD	0.00010607118
1,529	Updatable Learned Index with Precise Positions	2021	VLDB	0.00010320909
1,884	Effectively Learning Spatial Indices	2020	VLDB	9.422145e-05
2,211	Integrating the UB-Tree into a Database System Kernel	2000	VLDB	8.8443254e-05
4,879	The RLR-Tree: A Reinforcement Learning Based R-Tree for Spatial Data	2023	SIGMOD	6.3567479e-05

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