Theoretical Foundations and Applications of Space Complexity in Distributed and Geometric Computation

Abstract

Space Complexity. This paper presents a formal examination of space complexity across distributed consensus, geometric clustering, decision-tree inference, and functional convolution. Drawing on five recent research contributions, the study unifies theoretical models and structural bounds to characterize minimal spatial requirements under diverse computational frameworks. The analysis employs indistin-guishability and valency arguments, coreset-based compression theory, functional-space metrics, and convolutional operations. The results establish several tight lower bounds and structural equivalences, providing methodological insights for the design of algorithms operating under stringent memory constraints.