Analytic Performance Model of a Main-Memory Index Structure

TL;DR

This paper develops a numerical cost model for the Elf, a main-memory index structure optimized for multi-dimensional low-selectivity queries, enabling accurate prediction of search performance and guiding parameter tuning.

Contribution

It introduces a novel cost model for the Elf index, predicting its search region size and response time, addressing the need for robust configuration in high-dimensional data.

Findings

Cost model predicts Elf region size with less than 5% error for up to 15 dimensions.

Elf region size correlates strongly with search response time, with 80% accuracy.

Skewed data distributions can be modeled as reductions in attribute cardinality.

Abstract

Efficient evaluation of multi-dimensional range queries in a main-memory database is an important, but difficult task. State-of-the-art techniques rely on optimised sequential scans or tree-based structures. For range queries with small result sets, sequential scans exhibit poor asymptotic performance. Also, as the dimensionality of the data set increases, the performance of tree-based structures degenerates due to the curse of dimensionality. Recent literature proposed the Elf, a main-memory structure that is optimised for the case of such multi-dimensional low-selectivity queries. The Elf outperforms other state-of-the-art methods in manually tuned scenarios. However, choosing an optimal parameter configuration for the Elf is vital, since for poor configurations, the search performance degrades rapidly. Consequently, further knowledge about the behaviour of the Elf in different configurations is required to achieve robust performance. In this thesis, we therefore propose a numerical cost model for the Elf. Like all main-memory index structures, the Elf response time is not dominated by disk accesses, refusing a straightforward analysis. Our model predicts the size and shape of the Elf region that is examined during search. We propose that the response time of a search is linear to the size of this region. Furthermore, we study the impact of skewed data distributions and correlations on the shape of the Elf. We find that they lead to behaviour that is accurately describable through simple reductions in attribute cardinality. Our experimental results indicate that for data sets of up to 15 dimensions, our cost model predicts the size of the examined Elf region with relative errors below 5%. Furthermore, we find that the size of the Elf region examined during search predicts the response time with an accuracy of 80%.