The paper presents an improved upper bound (achievability result) on the optimal tradeoff between Normalized Delivery Time (NDT) and computation load for distributed computing MapReduce systems in certain ranges of the parameters. The upper bound is based on interference alignment combined with zero-forcing. The paper further provides a lower bound (converse) on the optimal NDT-computation tradeoff that can be achieved when IVAs are partitioned into sub-IVAs, and these sub-IVAs are then transmitted (in an arbitrary form) by a single node, without cooperation among nodes. For appropriate linear functions (e.g., XORs), such non-cooperative schemes can achieve some of the best NDT-computation tradeoff points so far obtained in the literature. However, as our lower bound shows, any non-cooperative scheme achieves a worse NDT-computation tradeoff than our new proposed scheme for certain parameters, thus proving the necessity of cooperative schemes like zero-forcing to attain the optimal NDT-computation tradeoff.

翻译：本文针对分布式计算MapReduce系统，在特定参数范围内提出了关于归一化传输时间与计算负载之间最优权衡的改进上界（可达性结果）。该上界基于干扰对齐与迫零预编码相结合的技术。本文进一步给出了当中间值数组被划分为子中间值数组，且这些子中间值数组由单个节点（以任意形式）独立传输（节点间无协作）时，可达到的最优NDT-计算权衡下界（逆命题）。对于适当的线性函数（如异或运算），此类非协作方案能够实现文献中迄今获得的部分最佳NDT-计算权衡点。然而，如我们的下界所证明，在特定参数条件下，任何非协作方案实现的NDT-计算权衡均劣于本文提出的新方案，从而证实了采用迫零预编码等协作方案对于获得最优NDT-计算权衡的必要性。