Distributed computing frameworks such as MapReduce have become essential for large-scale data processing by decomposing tasks across multiple nodes. The multi-access distributed computing (MADC) model further advances this paradigm by decoupling mapper and reducer roles: dedicated mapper nodes store data and compute intermediate values, while reducer nodes are connected to multiple mappers and aggregate results to compute final outputs. This separation reduces communication bottlenecks without requiring file replication. In this paper, we introduce privacy constraints into MADC and develop private coded schemes for two specific connectivity models. We construct new families of extended placement delivery arrays and derive corresponding coding schemes that guarantee privacy of each reducer's assigned function.

翻译：MapReduce等分布式计算框架通过将任务分解至多个节点，已成为大规模数据处理的关键技术。多接入分布式计算（MADC）模型通过解耦映射器与归约器角色进一步推进了该范式：专用映射器节点存储数据并计算中间值，而归约器节点则连接至多个映射器，通过聚合结果计算最终输出。这种分离机制在无需文件复制的条件下缓解了通信瓶颈。本文在MADC模型中引入隐私约束，并针对两种特定连接模型开发了私有编码方案。我们构建了新型扩展放置交付阵列族，并推导出相应的编码方案，以确保每个归约器所分配函数的隐私性。