Worst-Case Optimal Radix Triejoin

TL;DR

This paper introduces radix triejoin, a simple and practical worst-case optimal multi-way join algorithm that uses binary encoding and domain reduction to efficiently handle multiple queries without extra indexes.

Contribution

It presents radix triejoin, a new join algorithm that simplifies implementation and improves efficiency by enabling query-independent relation representation through domain reduction.

Findings

Radix triejoin achieves worst-case optimal join performance.

The algorithm handles conjunctive queries with inequalities.

It eliminates the need for additional secondary indexes.

Abstract

Relatively recently, the field of join processing has been swayed by the discovery of a new class of multi-way join algorithms. The new algorithms join multiple relations simultaneously rather than perform a series of pairwise joins. The new join algorithms satisfy stronger worst-case runtime complexity guarantees than any of the existing approaches based on pairwise joins -- they are worst-case optimal in data complexity. These research efforts have resulted in a flurry of papers documenting theoretical and some practical contributions. However, there is still the quest of making the new worst-case optimal join algorithms truly practical in terms of (1) ease of implementation and (2) secondary index efficiency in terms of number of indexes created to answer a query. In this paper, we present a simple worst-case optimal multi-way join algorithm called the radix triejoin. Radix triejoin uses a binary encoding for reducing the domain of a database. Our main technical contribution is that domain reduction allows a bit-interleaving of attribute values that gives rise to a query-independent relation representation, permitting the computation of multiple queries over the same relations worst-case optimally without having to construct additional secondary indexes. We also generalise the core algorithm to conjunctive queries with inequality constraints and provide a new proof technique for the worst-case optimal join result.