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\title{From Comparison Trees to Spatial Classification}

\author{\IEEEauthorblockN{Mohammad~T.~Ismael} \\
\IEEEauthorblockA{Cairo, Egypt \\
mohamed.talaat.ismael@gmail.com}}

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\markboth{Research Draft,~May~2026}{Ismael: Adaptive Range Sorting}

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\begin{abstract}
In this paper we introduce Adaptive Range Sorting (ARS), a hardware-conscious spatial classification framework for high-throughput parallel and streaming data processing.
By projecting the data into a monotonic spatial domain, we enable branch-efficient classification and cache-conscious memory scattering.
We also present the evolutionary development of ARS from recursive spatial trees to the Aero architecture, which utilizes a 1024-entry division-free quantile mapping table to improve robustness under skewed distributions while maintaining competitive performance against state-of-the-art sorters such as IPS4o.
Furthermore, we introduce ARS Exp D, a low-latency streaming architecture based on epoch micro-batching and concurrent spatial consolidation, enabling sustained high-throughput ingestion with bounded memory growth.
Experimental evaluation on modern multi-core hardware demonstrates near-linear throughput scaling, competitive streaming latency, and significant speedups on complex and high-entropy workloads, suggesting that spatial classification is a practical alternative to comparison-driven sorting for modern hardware-conscious data systems.
\end{abstract}

\begin{IEEEkeywords}
Sorting Algorithms, Cache-Conscious Algorithms, Distribution-Adaptive Sorting, Spatial Mapping, Parallel Sorting, Streaming Algorithms, Concurrent Systems.
\end{IEEEkeywords}

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