The work considers the $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multi-variable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions. Our aim is to seek efficient task-allocation and data-communication techniques that reduce computation and communication costs. Towards this, we take a tensor-theoretic approach, in which we represent the requested non-linearly decomposable functions using a properly designed tensor $\bar{\mathcal{F}}$, whose sparse decomposition into a tensor $\bar{\mathcal{E}}$ and matrix $\mathbf{D}$ directly defines the task assignment, connectivity, and communication patterns. We here design an achievable scheme, employing novel fixed-support SVD-based tensor factorization methods and careful multi-dimensional tiling of subtensors, yielding computation and communication protocols whose costs are derived here, and which are shown to perform substantially better than the state of art.

翻译：本文研究具有$K$个用户的$N$服务器分布式计算场景，用户请求的函数是$L$个实数（可能非线性）基子函数的任意多变量多项式求值。我们的目标是寻求能够降低计算与通信成本的高效任务分配与数据通信技术。为此，我们采用张量理论方法：通过精心设计的张量$\bar{\mathcal{F}}$表示所请求的非线性可分解函数，并将其稀疏分解为张量$\bar{\mathcal{E}}$与矩阵$\mathbf{D}$，该分解直接定义了任务分配、连接拓扑与通信模式。本文设计了一种可实现方案，采用基于固定支撑SVD的新型张量分解方法及精细的多维子张量平铺技术，推导了相应的计算与通信协议成本，并证明其性能显著优于现有技术。