In this work, we consider the problem of distributed computing of functions of structured sources, focusing on the classical setting of two correlated sources and one user that seeks the outcome of the function while benefiting from low-rate side information provided by a helper node. Focusing on the case where the sources are jointly distributed according to a very general mixture model, we here provide an achievable coding scheme that manages to substantially reduce the communication cost of distributed computing by exploiting the nature of the joint distribution of the sources, the side information, as well as the symmetry enjoyed by the desired functions. Our scheme -- which can readily apply in a variety of real-life scenarios including learning, combinatorics, and graph neural network applications -- is here shown to provide substantial reductions in the communication costs, while simultaneously providing computational savings by reducing the exponential complexity of joint decoding techniques to a complexity that is merely linear.

翻译：本文研究结构化信源函数的分布式计算问题，聚焦于两个相关信源与一个用户（该用户旨在获取函数结果，同时借助辅助节点提供的低速率边信息）的经典场景。针对信源服从一种极具普适性的混合模型的联合分布情况，我们提出了一种可达编码方案，该方案通过挖掘信源联合分布特性、边信息特征以及目标函数所具备的对称性，显著降低了分布式计算的通信开销。该方案可灵活应用于包括学习、组合数学和图神经网络在内的多种现实场景，在显著降低通信成本的同时，通过将联合解码技术的指数级复杂度降为线性复杂度，实现了计算资源的节约。