# On Optimal Partitioning For Sparse Matrices In Variable Block Row Format

@article{Ahrens2020OnOP, title={On Optimal Partitioning For Sparse Matrices In Variable Block Row Format}, author={Peter Ahrens and Erik G. Boman}, journal={ArXiv}, year={2020}, volume={abs/2005.12414} }

The Variable Block Row (VBR) format is an influential blocked sparse matrix format designed to represent shared sparsity structure between adjacent rows and columns. VBR consists of groups of adjacent rows and columns, storing the resulting blocks that contain nonzeros in a dense format. This reduces the memory footprint and enables optimizations such as register blocking and instruction-level parallelism. Existing approaches use heuristics to determine which rows and columns should be grouped…

## 3 Citations

Load Plus Communication Balancing of Contiguous Sparse Matrix Partitions.

- Computer Science
- 2020

This work considers contiguous partitions, where the rows (or columns) of a sparse matrix with nonzeros are split into $K$ parts without reordering, and proposes exact and approximate contiguous partitioners that minimize the maximum runtime of any processor under a diverse family of cost models.

Load Plus Communication Balancing in Contiguous Partitions for Distributed Sparse Matrices: Linear-Time Algorithms

- Computer ScienceArXiv
- 2020

This work presents exact and approximate contiguous partitioning algorithms that minimize the runtime of the longest-running processor under cost models that combine work factors and hypergraph communication factors.

Contiguous Graph Partitioning For Optimal Total Or Bottleneck Communication

- Computer Science
- 2020

This work proposes the first near-linear time algorithms for several graph partitioning problems in the contiguous regime, and proposes a new bottleneck cost which reflects the sum of communication and computation on each part.

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