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Computer Science > Distributed, Parallel, and Cluster Computing

arXiv:2510.08874 (cs)
[Submitted on 10 Oct 2025]

Title:Slicing Is All You Need: Towards A Universal One-Sided
Algorithm for Distributed Matrix Multiplication

Authors:Benjamin Brock, Renato Golin
View a PDF of the paper titled Slicing Is All You Need: Towards A
Universal One-Sided Algorithm for Distributed Matrix Multiplication,
by Benjamin Brock and Renato Golin
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    Abstract:Many important applications across science, data
    analytics, and AI workloads depend on distributed matrix
    multiplication. Prior work has developed a large array of
    algorithms suitable for different problem sizes and partitionings
    including 1D, 2D, 1.5D, and 2.5D algorithms. A limitation of
    current work is that existing algorithms are limited to a subset
    of partitionings. Multiple algorithm implementations are required
    to support the full space of possible partitionings. If no
    algorithm implementation is available for a particular set of
    partitionings, one or more operands must be redistributed,
    increasing communication costs. This paper presents a universal
    one-sided algorithm for distributed matrix multiplication that
    supports all combinations of partitionings and replication
    factors. Our algorithm uses slicing (index arithmetic) to compute
    the sets of overlapping tiles that must be multiplied together.
    This list of local matrix multiplies can then either be executed
    directly, or reordered and lowered to an optimized IR to maximize
    overlap. We implement our algorithm using a high-level C++-based
    PGAS programming framework that performs direct GPU-to-GPU
    communication using intra-node interconnects. We evaluate
    performance for a wide variety of partitionings and replication
    factors, finding that our work is competitive with PyTorch
    DTensor, a highly optimized distributed tensor library targeting
    AI models.

Subjects: Distributed, Parallel, and Cluster Computing (cs.DC);
          Artificial Intelligence (cs.AI)
Cite as:  arXiv:2510.08874 [cs.DC]
          (or arXiv:2510.08874v1 [cs.DC] for this version)
          https://doi.org/10.48550/arXiv.2510.08874
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Benjamin Brock [view email]
[v1] Fri, 10 Oct 2025 00:11:39 UTC (172 KB)
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