Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917137355898880 |
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| author | Khalesi, Ali Salehi, Mohammad Reza Deylam |
| author_facet | Khalesi, Ali Salehi, Mohammad Reza Deylam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_09858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing Khalesi, Ali Salehi, Mohammad Reza Deylam Information Theory 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. |
| title | Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing |
| topic | Information Theory |
| url | https://arxiv.org/abs/2512.09858 |