# LaraDB: A Minimalist Kernel for Linear and Relational Algebra Computation

arXiv: https://arxiv.org/abs/1703.07342 · HTML: https://mlsanity.com/paper/1703.07342/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2017.

## Built on by (most cited first, 5 of 5)

- [End-to-end Optimization of Machine Learning Prediction Queries](https://mlsanity.com/paper/2206.00136/) (2022)
- [Functional Collection Programming with Semi-Ring Dictionaries](https://mlsanity.com/paper/2103.06376/) (2021)
- [IterLara: A Turing Complete Algebra for Big Data, AI, Scientific Computing, and Database](https://mlsanity.com/paper/2307.08315/) (2023)
- [Fragments to Facts: Partial-Information Fragment Inference from LLMs](https://mlsanity.com/paper/2505.13819/) (2025)
- [The Ubiquitous Sparse Matrix-Matrix Products](https://mlsanity.com/paper/2508.04077/) (2025)

## Abstract (arXiv)

Analytics tasks manipulate structured data with variants of relational algebra (RA) and quantitative data with variants of linear algebra (LA). The two computational models have overlapping expressiveness, motivating a common programming model that affords unified reasoning and algorithm design. At the logical level we propose Lara, a lean algebra of three operators, that expresses RA and LA as well as relevant optimization rules. We show a series of proofs that position Lara %formal and informal at just the right level of expressiveness for a middleware algebra: more explicit than MapReduce but more general than RA or LA. At the physical level we find that the Lara operators afford efficient implementations using a single primitive that is available in a variety of backend engines: range scans over partitioned sorted maps. To evaluate these ideas, we implemented the Lara operators as range iterators in Apache Accumulo, a popular implementation of Google's BigTable. First we show how Lara expresses a sensor quality control task, and we measure the performance impact of optimizations Lara admits on this task. Second we show that the LaraDB implementation outperforms Accumulo's native MapReduce integration on a core task involving join and aggregation in the form of matrix multiply, especially at smaller scales that are typically a poor fit for scale-out approaches. We find that LaraDB offers a conceptually lean framework for optimizing mixed-abstraction analytics tasks, without giving up fast record-level updates and scans.