# SlimSell: A Vectorizable Graph Representation for Breadth-First Search

arXiv: https://arxiv.org/abs/2010.09913 · HTML: https://mlsanity.com/paper/2010.09913/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Parallel and Distributed Graph Neural Networks: An In-Depth Concurrency Analysis](https://mlsanity.com/paper/2205.09702/) (2022)
- [Motif Prediction with Graph Neural Networks](https://mlsanity.com/paper/2106.00761/) (2021)
- [Neural Graph Databases](https://mlsanity.com/paper/2209.09732/) (2022)
- [GraphMineSuite: Enabling High-Performance and Programmable Graph Mining Algorithms with Set Algebra](https://mlsanity.com/paper/2103.03653/) (2021)
- [Cached Operator Reordering: A Unified View for Fast GNN Training](https://mlsanity.com/paper/2308.12093/) (2023)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [GraphSeek: Next-Generation Graph Analytics with LLMs](https://mlsanity.com/paper/2602.11052/) (2026)

## Abstract (arXiv)

Vectorization and GPUs will profoundly change graph processing. Traditional graph algorithms tuned for 32- or 64-bit based memory accesses will be inefficient on architectures with 512-bit wide (or larger) instruction units that are already present in the Intel Knights Landing (KNL) manycore CPU. Anticipating this shift, we propose SlimSell: a vectorizable graph representation to accelerate Breadth-First Search (BFS) based on sparse-matrix dense-vector (SpMV) products. SlimSell extends and combines the state-of-the-art SIMD-friendly Sell-C-sigma matrix storage format with tropical, real, boolean, and sel-max semiring operations. The resulting design reduces the necessary storage (by up to 50%) and thus pressure on the memory subsystem. We augment SlimSell with the SlimWork and SlimChunk schemes that reduce the amount of work and improve load balance, further accelerating BFS. We evaluate all the schemes on Intel Haswell multicore CPUs, the state-of-the-art Intel Xeon Phi KNL manycore CPUs, and NVIDIA Tesla GPUs. Our experiments indicate which semiring offers highest speedups for BFS and illustrate that SlimSell accelerates a tuned Graph500 BFS code by up to 33%. This work shows that vectorization can secure high-performance in BFS based on SpMV products; the proposed principles and designs can be extended to other graph algorithms.