Piecewise Linear Approximation in Learned Index Structures: Theoretical and Empirical Analysis

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Qin, Jiayong, Zhu, Xianyu, Liu, Qiyu, Zhang, Guangyi, Cai, Zhigang, Liao, Jianwei, Hu, Sha, Peng, Jingshu, Shao, Yingxia, Chen, Lei
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913911838605312
author Qin, Jiayong
Zhu, Xianyu
Liu, Qiyu
Zhang, Guangyi
Cai, Zhigang
Liao, Jianwei
Hu, Sha
Peng, Jingshu
Shao, Yingxia
Chen, Lei
author_facet Qin, Jiayong
Zhu, Xianyu
Liu, Qiyu
Zhang, Guangyi
Cai, Zhigang
Liao, Jianwei
Hu, Sha
Peng, Jingshu
Shao, Yingxia
Chen, Lei
contents A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($ε$-PLA) has emerged as a popular choice due to its simplicity and effectiveness. Despite its central role in many learned indexes, the design and analysis of $ε$-PLA fitting algorithms remain underexplored. In this paper, we revisit $ε$-PLA from both theoretical and empirical perspectives, with a focus on its application in learned index structures. We first establish a fundamentally improved lower bound of $Ω(κ\cdot ε^2)$ on the expected segment coverage for existing $ε$-PLA fitting algorithms, where $κ$ is a data-dependent constant. We then present a comprehensive benchmark of state-of-the-art $ε$-PLA algorithms when used in different learned data structures. Our results highlight key trade-offs among model accuracy, model size, and query performance, providing actionable guidelines for the principled design of future learned data structures.
format Preprint
id arxiv_https___arxiv_org_abs_2506_20139
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Piecewise Linear Approximation in Learned Index Structures: Theoretical and Empirical Analysis
Qin, Jiayong
Zhu, Xianyu
Liu, Qiyu
Zhang, Guangyi
Cai, Zhigang
Liao, Jianwei
Hu, Sha
Peng, Jingshu
Shao, Yingxia
Chen, Lei
Databases
Machine Learning
A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($ε$-PLA) has emerged as a popular choice due to its simplicity and effectiveness. Despite its central role in many learned indexes, the design and analysis of $ε$-PLA fitting algorithms remain underexplored. In this paper, we revisit $ε$-PLA from both theoretical and empirical perspectives, with a focus on its application in learned index structures. We first establish a fundamentally improved lower bound of $Ω(κ\cdot ε^2)$ on the expected segment coverage for existing $ε$-PLA fitting algorithms, where $κ$ is a data-dependent constant. We then present a comprehensive benchmark of state-of-the-art $ε$-PLA algorithms when used in different learned data structures. Our results highlight key trade-offs among model accuracy, model size, and query performance, providing actionable guidelines for the principled design of future learned data structures.
title Piecewise Linear Approximation in Learned Index Structures: Theoretical and Empirical Analysis
topic Databases
Machine Learning
url https://arxiv.org/abs/2506.20139