Learning Multi-dimensional Indexes

Abstract: Scanning and filtering over multi-dimensional tables are key operations in modern analytical database engines. To optimize the performance of these operations, databases often create clustered indexes over a single dimension or multi-dimensional indexes such as R-trees, or use complex sort orders (e.g., Z-ordering). However, these schemes are often hard to tune and their performance is inconsistent across different datasets and queries. In this paper, we introduce Flood, a multi-dimensional in-memory index that automatically adapts itself to a particular dataset and workload by jointly optimizing the index structure and data storage. Flood achieves up to three orders of magnitude faster performance for range scans with predicates than state-of-the-art multi-dimensional indexes or sort orders on real-world datasets and workloads. Our work serves as a building block towards an end-to-end learned database system.

• The paper introduces Flood, a novel learned index that optimizes scanning and filtering in analytical databases.
• It employs empirical CDF models to transform skewed data distributions and tailor index density, achieving up to 72× faster range queries.
• Flood demonstrates a pathway toward self-optimizing database systems that reduce manual tuning and adapt dynamically to query workloads.

Overview of "Learning Multi-dimensional Indexes"

The paper explores the design and implementation of a novel multi-dimensional index termed "Flood," focusing on optimizing scanning and filtering operations in modern analytical database engines. Flood is positioned as a learned, in-memory, multi-dimensional index that dynamically adapts its structure based on specific data distributions and query workloads. This approach aims to address the limitations of traditional indexing methods, such as B-Trees and R-Trees, which often fail to provide consistent high performance across varying datasets and query types.

In analytical databases, efficient scanning and filtering are paramount. Current systems often resort to single-dimensional clustered indexes or establish multi-dimensional indexes using tree-based structures or complex sort orders like Z-ordering. However, these methods are limited by significant setup complexity and tuning difficulty, and they tend to perform inconsistently due to varied data and query distributions.

Flood sets itself apart by adopting a learned approach. It constructs an index that simultaneously improves index efficiency and data layout. Key features of Flood include its ability to achieve up to three orders of magnitude faster performance on range queries compared to established multi-dimensional indexes. Its query speed improvements are tied to a sophisticated approach of tailoring index density and structure according to observed query patterns and data characteristics.

Numerical Results and Claims

The paper reports dramatic performance enhancements, claiming Flood can achieve query speedups of up to $72\times$ over Amazon Redshift's Z-encoding and $61\times$ over optimized clustered column index systems on representative datasets such as TPC-H and real sales databases. These results suggest a significant leap in performance, asserting Flood's capability to provide consistent and superior performance across a breadth of practical workloads.

The technical novelty of Flood is in its dual optimization strategy: learning the data distribution and query workload. Firstly, it generates a model of query filters, learning the frequency and selectivity of queried dimensions. Secondly, it employs empirical CDF models to transform a skewed distribution into a more uniform space, thereby enabling efficient data traversal.

Implications and Future Directions

From a practical standpoint, Flood represents an advancement towards self-optimizing database systems—systems capable of dynamically evolving their indexing structures based on workload variations without manual intervention. This adaptability is particularly relevant with the increasing scale and complexity of modern data systems where workload patterns can be unpredictable.

Theoretically, this work suggests new avenues for research into learned data structures—showcasing how database components traditionally implemented with static, pre-defined structures can benefit from model-based learning approaches. Future research could explore extending Flood’s principles to accommodate online transaction processing (OLTP) systems where dynamic updates are frequent, which remains a challenge given Flood's focus on read-optimized environments.

Moreover, integrating Flood into full-fledged database systems could offer insights into the real-world trade-offs between learning overhead and query performance. The pursuit of hybrid structures capable of concurrently supporting analytical and transactional workloads efficiently remains an engaging challenge worthy of exploration.

Conclusion

In summary, the introduction of Flood marks a significant step towards a more intelligent and adaptable approach to indexing in multi-dimensional spaces. Its capacity to autonomously tailor index structures to specific data sets and query loads positions it as a compelling choice for database administrators seeking robust performance across varying scenarios. Flood’s contribution points to a future where the adaptability and precision of AI can enhance the core infrastructures of database systems, allowing them to self-optimize in response to ever-changing conditions.