Optimizing Relational Queries over Array-Valued Data in Columnar Systems

TL;DR

This paper presents A3D-RA, an extended relational algebra for array-valued data, with optimization techniques that improve query performance in columnar database systems handling mixed relational and array data.

Contribution

It introduces a formal algebraic framework and optimization strategies for relational queries involving array attributes, enhancing performance in analytical systems.

Findings

Consistent performance improvements across three database engines.

A complete set of equivalence-preserving transformation rules.

Polynomial-time plan enumeration with optimality guarantees.

Abstract

Modern analytical workloads increasingly combine relational data with array-valued attributes. While columnar database systems efficiently process such workloads, their ability to optimize queries that interleave relational operators with array manipulations remains limited. This paper introduces A3D-RA, an extended relational algebra supporting array-valued attributes, together with a comprehensive framework for algebraic reasoning and optimization. We formalize its data model and semantics, develop a complete set of equivalence-preserving transformation rules capturing pairwise interactions between relational and array operators, and propose a plan enumeration strategy with an optimality guarantee that remains polynomial in all non-join operators. We design A3D-RA as a modular, backend-independent optimization layer that can be instantiated over existing analytical database systems. Experimental results across three high-performance engines on a real-world workload show consistent performance gains enabled by the proposed algebraic optimization layer.