Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing

TL;DR

This paper analyzes the typical-case solutions for multi-user linearly-decomposable distributed computing problems, providing theoretical insights and practical mappings to aeronautical and satellite networks.

Contribution

It introduces a comprehensive analysis framework for the problem, including closed-form risk expressions and structural fidelity measures, with practical network applications.

Findings

Closed-form second-moment risk under spike-and-slab ensembles

Deterministic links between thresholded GED and norm error

Explicit recall lines via Gaussian surrogate

Abstract

We solve, in the typical-case sense, the multi-sender linearly-decomposable distributed computing problem introduced by tessellated distributed computing. We model real-valued encoders/decoders and demand matrices, and assess structural fidelity via a thresholded graph edit distance between the demand support and the two-hop support of the computed product. Our analysis yields: a closed-form second-moment (Frobenius) risk under spike-and-slab ensembles; deterministic links between thresholded GED and norm error; a Gaussian surrogate with sub-exponential tails that exposes explicit recall lines; concentration of GED and operator-norm control; and a compute-capped design with a visible knee. We map the rules to aeronautical and satellite networks.