Necessity of Cooperative Transmissions for Wireless MapReduce

2026-01-17

AI Summary

This study investigates the fundamental trade-off between computation load and normalized delivery time (NDT) in wireless MapReduce systems, with a focus on whether non-cooperative transmission can achieve the optimal trade-off. By establishing tight upper and lower bounds on the NDT, the work rigorously demonstrates for the first time that, within certain parameter regimes, non-cooperative strategies are insufficient to attain optimality, thereby proving the necessity of inter-node collaboration. To address this, the authors propose a cooperative transmission scheme that integrates interference alignment with zero-forcing beamforming, coupled with a scheduling strategy based on sub-intermediate value (sub-IVA) partitioning. Theoretical analysis shows that the proposed approach significantly outperforms existing non-cooperative methods under specific conditions, highlighting the critical role of cooperation in achieving communication-efficient distributed computing.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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.

Problem

• Wireless MapReduce
• Normalized Delivery Time
• computation load
• cooperative transmission
• NDT-computation tradeoff

Innovation

• cooperative transmission
• interference alignment
• zero-forcing
• Normalized Delivery Time (NDT)
• MapReduce