Typical Solutions of Multi-User Linearly-Decomposable Distributed Computing

2025-12-10

AI Summary

This work addresses performance modeling and optimization in multi-user linearly decomposable distributed computing under canonical settings. Problematically, it establishes, for the first time, a deterministic relationship between thresholded graph edit distance (GED) and norm-based reconstruction error for real-valued encoders/decoders and demand matrices, and reveals a fundamental performance inflection point under computational constraints via an explicit-recall Gaussian surrogate model. Methodologically, it integrates second-moment risk analysis of spike-and-slab ensembles, operator-norm control, concentration inequalities, and Gaussian approximation to jointly guarantee concentration of both GED and operator norm. Theoretical contributions include a closed-form solution for Frobenius-risk minimization and the derivation of a computationally constrained optimal scheme deployable in space-air-ground integrated networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Solve multi-user linearly-decomposable distributed computing in typical-case sense
• Model real-valued encoders/decoders and demand matrices for structural fidelity
• Map the computing rules to aeronautical and satellite networks

Innovation

• Closed-form risk analysis for spike-and-slab ensembles
• Thresholded graph edit distance links structure to error
• Compute-capped design with visible performance knee