Necessity of Cooperative Transmissions for Wireless MapReduce

TL;DR

This paper demonstrates that cooperative transmission schemes, such as zero-forcing, are essential for achieving optimal tradeoffs between delivery time and computation load in distributed MapReduce systems, especially for certain parameters.

Contribution

The paper introduces an improved upper bound on the NDT-computation tradeoff using interference alignment and zero-forcing, and proves the necessity of cooperation for optimal performance.

Findings

Non-cooperative schemes cannot achieve the best NDT-computation tradeoff for certain parameters.

Cooperative schemes like zero-forcing outperform non-cooperative schemes in these tradeoffs.

The paper establishes the importance of cooperation in distributed computing for optimal efficiency.

Abstract

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.