# Worst-Case Optimal Join Algorithms: Techniques, Results, and Open Problems

arXiv: https://arxiv.org/abs/1803.09930 · HTML: https://mlsanity.com/paper/1803.09930/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2018.

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning Based Query Vertex Ordering Model for Subgraph Matching](https://mlsanity.com/paper/2201.11251/) (2022)
- [Knowledge Graphs Querying](https://mlsanity.com/paper/2305.14485/) (2023)
- [TCMaster: Confidence-Aware Querying and Workload-Guided Physical Design for Multi-Source Traditional Chinese Medicine Knowledge Graphs](https://mlsanity.com/paper/2609.25712/) (2026)

## Abstract (arXiv)

Worst-case optimal join algorithms are the class of join algorithms whose runtime match the worst-case output size of a given join query. While the first provably worst-case optimal join algorithm was discovered relatively recently, the techniques and results surrounding these algorithms grow out of decades of research from a wide range of areas, intimately connecting graph theory, algorithms, information theory, constraint satisfaction, database theory, and geometric inequalities. These ideas are not just paperware: in addition to academic project implementations, two variations of such algorithms are the work-horse join algorithms of commercial database and data analytics engines. This paper aims to be a brief introduction to the design and analysis of worst-case optimal join algorithms. We discuss the key techniques for proving runtime and output size bounds. We particularly focus on the fascinating connection between join algorithms and information theoretic inequalities, and the idea of how one can turn a proof into an algorithm. Finally, we conclude with a representative list of fundamental open problems in this area.