On the Extension of Private Distributed Matrix Multiplication Schemes to the Grid Partition
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915753487237120 |
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| author | Hofmeister, Christoph Tajeddine, Razane Wachter-Zeh, Antonia Bitar, Rawad |
| author_facet | Hofmeister, Christoph Tajeddine, Razane Wachter-Zeh, Antonia Bitar, Rawad |
| contents | We consider polynomial codes for private distributed matrix multiplication (PDMM/SDMM). Existing codes for PDMM are either specialized for the outer product partitioning (OPP), or inner product partitioning (IPP), or are valid for the more general grid partitioning (GP). We design extension operations that can be applied to a large class of OPP code designs to extend them to the GP case. Applying them to existing codes improves upon the state-of-the-art for certain parameters. Additionally, we show that the GP schemes resulting from extension fulfill additional combinatorial constraints, potentially limiting their performance. We illustrate this point by presenting a new GP scheme that does not adhere to these constraints and outperforms the state-of-the-art for a range of parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Extension of Private Distributed Matrix Multiplication Schemes to the Grid Partition Hofmeister, Christoph Tajeddine, Razane Wachter-Zeh, Antonia Bitar, Rawad Information Theory Distributed, Parallel, and Cluster Computing We consider polynomial codes for private distributed matrix multiplication (PDMM/SDMM). Existing codes for PDMM are either specialized for the outer product partitioning (OPP), or inner product partitioning (IPP), or are valid for the more general grid partitioning (GP). We design extension operations that can be applied to a large class of OPP code designs to extend them to the GP case. Applying them to existing codes improves upon the state-of-the-art for certain parameters. Additionally, we show that the GP schemes resulting from extension fulfill additional combinatorial constraints, potentially limiting their performance. We illustrate this point by presenting a new GP scheme that does not adhere to these constraints and outperforms the state-of-the-art for a range of parameters. |
| title | On the Extension of Private Distributed Matrix Multiplication Schemes to the Grid Partition |
| topic | Information Theory Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2601.17834 |