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arXiv · 2512.09858

Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing

Ali Khalesi·Mohammad Reza Deylam Salehi
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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.

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Ali Khalesi, Mohammad Reza Deylam Salehi. 2025-12-10. Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing. https://arxiv.org/abs/2512.09858

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