Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing
Ali Khalesi, Mohammad Reza Deylam Salehi
TL;DR
The paper studies typical-case performance of multi-user linearly-decomposable distributed computing (MUDC) in constrained networks like aircraft and satellites. It introduces thresholded graph edit distance (GED) as a structural fidelity metric and develops a Gaussian surrogate for reachability, enabling a computable typical Frobenius risk under spike-and-slab ensembles. It establishes deterministic links between GED and norm-based risks, provides concentration results, and yields a compute-cap knee with a boundary rule to guide design under SLA recall constraints. The work offers a practical design map for aeronautical and satellite deployments, balancing coverage (reachability) and efficiency while connecting structural metrics to energy and compute budgets.
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.