In this paper, we explore a distributed setting, where a user seeks to compute a linearly-separable Boolean function of degree $M$ from $N$ servers, each with a cache size $M$. Exploiting the fundamental concepts of sensitivity and influences of Boolean functions, we devise a novel approach to capture the interplay between dataset placement across servers and server transmissions and to determine the optimal solution for dataset placement that minimizes the communication cost. In particular, we showcase the achievability of the minimum average joint sensitivity, $\frac{N}{2^{M-1}}$, as a measure for the communication cost.

翻译：本文探讨一种分布式计算场景：用户需要从N个服务器计算一个度为M的线性可分布尔函数，每个服务器的缓存容量为M。通过利用布尔函数敏感度与影响的基本概念，我们提出了一种新方法来刻画服务器间数据集布局与服务器传输的相互作用，并确定最小化通信成本的最优数据集布局方案。特别地，我们证明了以最小平均联合敏感度$\frac{N}{2^{M-1}}$作为通信成本度量指标的可行性。