Fundamental Limits of Multi-User Distributed Computing of Linearly Separable Functions

2026-01-15

AI Summary

This study addresses the communication-computation trade-off in multi-user distributed computing for linearly separable functions. Under the coordination of a master node, N servers each compute at most M basis subfunctions and transmit linear combinations of their results to at most Δ users, with the goal of minimizing total communication cost. By jointly optimizing task allocation and linear encoding strategies, the work proposes an optimal scheme over the real field and rigorously establishes its optimality via an information-theoretic duality argument. In finite fields, it pioneers a combinatorial counting approach to derive fundamental performance bounds, fully characterizing the problem’s information-theoretic limits. The analysis systematically reveals the theoretical performance boundaries in both real and finite fields and achieves optimal communication cost across a wide range of parameter regimes.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

This work establishes the fundamental limits of the classical problem of multi-user distributed computing of linearly separable functions. In particular, we consider a distributed computing setting involving $L$ users, each requesting a linearly separable function over $K$ basis subfunctions from a master node, who is assisted by $N$ distributed servers. At the core of this problem lies a fundamental tradeoff between communication and computation: each server can compute up to $M$ subfunctions, and each server can communicate linear combinations of their locally computed subfunctions outputs to at most $\Delta$ users. The objective is to design a distributed computing scheme that reduces the communication cost (total amount of data from servers to users), and towards this, for any given $K$, $L$, $M$, and $\Delta$, we propose a distributed computing scheme that jointly designs the task assignment and transmissions, and shows that the scheme achieves optimal performance in the real field under various conditions using a novel converse. We also characterize the performance of the scheme in the finite field using another converse based on counting arguments.

Problem

• distributed computing
• linearly separable functions
• communication-computation tradeoff
• fundamental limits
• multi-user systems

Innovation

• distributed computing
• linearly separable functions
• fundamental limits
• task assignment
• communication-computation tradeoff